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  • 1.
    Andersson, Joel
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Strömberg, Jan-Olov
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    On the Theorem of Uniform Recovery of Random Sampling Matrices2014In: IEEE Transactions on Information Theory, ISSN 0018-9448, E-ISSN 1557-9654, Vol. 60, no 3, p. 1700-1710Article in journal (Refereed)
    Abstract [en]

    We consider two theorems from the theory of compressive sensing. Mainly a theorem concerning uniform recovery of random sampling matrices, where the number of samples needed in order to recover an s-sparse signal from linear measurements (with high probability) is known to be m greater than or similar to s(ln s)(3) ln N. We present new and improved constants together with what we consider to be a more explicit proof. A proof that also allows for a slightly larger class of m x N-matrices, by considering what is called effective sparsity. We also present a condition on the so-called restricted isometry constants, delta s, ensuring sparse recovery via l(1)-minimization. We show that delta(2s) < 4/root 41 is sufficient and that this can be improved further to almost allow for a sufficient condition of the type delta(2s) < 2/3.

  • 2.
    Angelakis, Vangelis
    et al.
    Linköping University, Department of Science and Technology. Linköping University, The Institute of Technology.
    Ephremides, Anthony
    Linköping University, Department of Science and Technology, Communications and Transport Systems. Linköping University, The Institute of Technology.
    He, Qing
    Linköping University, Department of Science and Technology, Communications and Transport Systems. Linköping University, The Institute of Technology.
    Yuan, Di
    Linköping University, Department of Science and Technology, Communications and Transport Systems. Linköping University, The Institute of Technology.
    Minimum-Time Link Scheduling for Emptying Wireless Systems: Solution Characterization and Algorithmic Framework2014In: IEEE Transactions on Information Theory, ISSN 0018-9448, E-ISSN 1557-9654, Vol. 60, no 2, p. 1083-1100Article in journal (Refereed)
    Abstract [en]

    We consider a set of transmitter-receiver pairs, or links, that share a wireless medium and address the problem of emptying backlogged queues with given initial size at the transmitters in minimum time. The problem amounts to determining activation subsets of links, and their time durations, to form a minimum-time schedule. Scheduling in wireless networks has been studied under various formulations before. In this paper, we present fundamental insights and solution characterizations that include: 1) showing that the complexity of the problem remains high for any continuous and increasing rate function; 2) formulating and proving sufficient and necessary optimality conditions of two baseline scheduling strategies that correspond to emptying the queues using one-at-a-time or all-at-once strategies; and 3) presenting and proving the tractability of the special case in which the transmission rates are functions only of the cardinality of the link activation sets. These results are independent of physical-layer system specifications and are valid for any form of rate function. We then develop an algorithmic framework for the solution to this problem. The framework encompasses exact as well as sub-optimal, but fast, scheduling algorithms, all under a unified principle design. Through computational experiments, we finally investigate the performance of several specific algorithms from this framework.

  • 3.
    Asraf, Daniel
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Technology, Department of Engineering Sciences, Signals and Systems Group.
    Gustafsson, Mats
    Uppsala University, Disciplinary Domain of Science and Technology, Technology, Department of Engineering Sciences, Signals and Systems Group.
    An analytical series expansion solution to the problem of noncoherent detection2004In: IEEE Transactions on Information Theory, ISSN 0018-9448, E-ISSN 1557-9654, Vol. 50, no 12, p. 3369-3375Article in journal (Refereed)
    Abstract [en]

    The well-known noncoherent detection problem concerns optimal detection of an amplitude-modulated sinusoid, with an unknown phase angle, corrupted by additive Gaussian noise. The classical solution to this problem is the noncoherent detector which is known to be optimal if the envelope belongs to a specific set of functions or satisfies the narrow-band approximation i.e., that the bandwidth of the envelope is narrow in comparison with the (carrier) frequency of the sinusoid. In this work, an analytical series expansion solution to the likelihood ratio for the noncoherent detection problem is derived. This solution offers a generalization of the noncoherent detector in which the conditions imposed on the envelope stated above have been relaxed. Analytical expressions for the joint probability density functions (pdfs) of the in-phase and quadrature components, jointly expressed in polar coordinates, are also derived under the signal-plus-noise and the noise-only hypotheses, respectively. Numerical simulations of the detector performance are presented in the form of receiver operating characteristics (ROC) and minimum probability of error curves. The results from a comparison of the general analytical solution with the classical noncoherent detector show significant differences between the two detectors when the narrow-band approximation does not hold.

  • 4.
    Asraf, Daniel
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Technology, Department of Engineering Sciences, Signals and Systems Group.
    Gustafsson, Mats
    Uppsala University, Disciplinary Domain of Science and Technology, Technology, Department of Engineering Sciences, Signals and Systems Group.
    Detection of Multiple Transient Signals with Unknown Arrival Times2005In: IEEE Transactions on Information Theory, ISSN 0018-9448, E-ISSN 1557-9654, Vol. 51, no 5, p. 1856-1860Article in journal (Refereed)
    Abstract [en]

    The problem of optimal detection of signal transients with unknown arrival times contaminated by additive Gaussian noise is considered. The transients are assumed to be time continuous and belong to a parameterized family with the uncertainty about the parameters described by means of an a priori distribution. Under the assumption of a negligible probability that the independent transient observations overlap in time, a likelihood ratio is derived for the problem of detecting an unknown number of transients from the family, each transient with unknown arrival time. The uncertainty about the arrival times is assumed to be equal for all transients and is also described by means of a distribution. Numerical simulations of the performance of detecting a particular transient signal family are presented in the form of receiver operating characteristics (ROCs) for both the optimal detector and the classical generalized likelihood ratio test (GLRT). The results show that the optimal detector yields noticeable performance improvements over the GLRT. Moreover, the results show that the optimal detector may still outperform the GLRT when the true and modeled uncertainties about arrival times no longer agree.

  • 5.
    Austrin, Per
    et al.
    KTH, School of Electrical Engineering and Computer Science (EECS), Theoretical Computer Science, TCS.
    Kaski, Petteri
    Koivisto, Mikko
    Nederlof, Jesper
    Sharper Upper Bounds for Unbalanced Uniquely Decodable Code Pairs2018In: IEEE Transactions on Information Theory, ISSN 0018-9448, E-ISSN 1557-9654, Vol. 64, no 2, p. 1368-1373Article in journal (Refereed)
    Abstract [en]

    Two sets of 0-1 vectors of fixed length form a uniquely decodeable code pair if their Cartesian product is of the same size as their sumset, where the addition is pointwise over integers. For the size of the sumset of such a pair, van Tilborg has given an upper bound in the general case. Urbanke and Li, and later Ordentlich and Shayevitz, have given better bounds in the unbalanced case, that is, when either of the two sets is sufficiently large. Improvements to the latter bounds are presented.

  • 6.
    Austrin, Per
    et al.
    KTH, School of Computer Science and Communication (CSC), Theoretical Computer Science, TCS.
    Khot, Subhash
    A Simple Deterministic Reduction for the Gap Minimum Distance of Code Problem2014In: IEEE Transactions on Information Theory, ISSN 0018-9448, E-ISSN 1557-9654, Vol. 60, no 10, p. 6636-6645Article in journal (Refereed)
    Abstract [en]

    We present a simple deterministic gap-preserving reduction from SAT to the minimum distance of code problem over F-2. We also show how to extend the reduction to work over any fixed finite field. Previously, a randomized reduction was known due to Dumer, Micciancio, and Sudan, which was recently derandomized by Cheng and Wan. These reductions rely on highly nontrivial coding theoretic constructions, whereas our reduction is elementary. As an additional feature, our reduction gives hardness within a constant factor even for asymptotically good codes, i.e., having constant positive rate and relative distance. Previously, it was not known how to achieve a deterministic reduction for such codes.

  • 7.
    Bassi, German
    et al.
    KTH, School of Electrical Engineering and Computer Science (EECS), Information Science and Engineering. Univ Paris Sud, CNRS, Cent Supelec, Lab Signaux & Syst,L2S,UMR 8506, F-91192 Gif Sur Yvette, France.
    Piantanida, Pablo
    Shamai (Shitz), Shlomo
    The Wiretap Channel With Generalized Feedback: Secure Communication and Key Generation2019In: IEEE Transactions on Information Theory, ISSN 0018-9448, E-ISSN 1557-9654, Vol. 65, no 4, p. 2213-2233Article in journal (Refereed)
    Abstract [en]

    It is a well-known fact that feedback does not increase the capacity of point-to-point memoryless channels, however, its effect in secure communications is not fully understood yet. In this paper, an achievable scheme for the wiretap channel with generalized feedback is presented. This scheme, which uses the feedback signal to generate a shared secret key between the legitimate users, encrypts the message to be sent at the bit level. New capacity results for a class of channels are provided, as well as some new insights into the secret key agreement problem. Moreover, this scheme recovers previously reported rate regions from the literature, and thus it can be seen as a generalization that unifies several results in the field.

  • 8.
    Björnson, Emil
    KTH Royal Institute Technology, Sweden; Supelec, France.
    Kountouris, Marios
    CentraleSupelec, France.
    Debbah, Merouane
    CentraleSupelec, France.
    Massive MIMO Systems with Non-Ideal Hardware: Energy Efficiency, Estimation, and Capacity Limits2014In: IEEE Transactions on Information Theory, ISSN 0018-9448, E-ISSN 1557-9654, Vol. 60, no 11, p. 7112-7139Article in journal (Refereed)
    Abstract [en]

    The use of large-scale antenna arrays can bring substantial improvements in energy and/or spectral efficiency to wireless systems due to the greatly improved spatial resolution and array gain. Recent works in the field of massive multiple-input multiple-output (MIMO) show that the user channels decorrelate when the number of antennas at the base stations (BSs) increases, thus strong signal gains are achievable with little interuser interference. Since these results rely on asymptotics, it is important to investigate whether the conventional system models are reasonable in this asymptotic regime. This paper considers a new system model that incorporates general transceiver hardwareimpairments at both the BSs (equipped with large antenna arrays) and the single-antenna user equipments (UEs). As opposed to the conventional case of ideal hardware, we show that hardwareimpairments create finite ceilings on the channel estimation accuracy and on the downlink/uplink capacity of each UE. Surprisingly, the capacity is mainly limited by the hardware at the UE, while the impact of impairments in the large-scale arrays vanishes asymptotically and interuser interference (in particular, pilot contamination) becomes negligible. Furthermore, we prove that the huge degrees of freedom offered by massive MIMO can be used to reduce the transmit power and/or to tolerate larger hardware impairments, which allows for the use of inexpensive and energy-efficient antenna elements.

  • 9.
    Björnson, Emil
    et al.
    KTH, School of Electrical Engineering (EES), Signal Processing. Linköping University, Sweden.
    Hoydis, Jakob
    Kountouris, Marios
    Debbah, Merouane
    Massive MIMO Systems With Non-Ideal Hardware: Energy Efficiency, Estimation, and Capacity Limits2014In: IEEE Transactions on Information Theory, ISSN 0018-9448, E-ISSN 1557-9654, Vol. 60, no 11, p. 7112-7139Article in journal (Refereed)
    Abstract [en]

    The use of large-scale antenna arrays can bring substantial improvements in energy and/or spectral efficiency to wireless systems due to the greatly improved spatial resolution and array gain. Recent works in the field of massive multiple-input multiple-output (MIMO) show that the user channels decorrelate when the number of antennas at the base stations (BSs) increases, thus strong signal gains are achievable with little interuser interference. Since these results rely on asymptotics, it is important to investigate whether the conventional system models are reasonable in this asymptotic regime. This paper considers a new system model that incorporates general transceiver hardware impairments at both the BSs (equipped with large antenna arrays) and the single-antenna user equipments (UEs). As opposed to the conventional case of ideal hardware, we show that hardware impairments create finite ceilings on the channel estimation accuracy and on the downlink/uplink capacity of each UE. Surprisingly, the capacity is mainly limited by the hardware at the UE, while the impact of impairments in the large-scale arrays vanishes asymptotically and interuser interference (in particular, pilot contamination) becomes negligible. Furthermore, we prove that the huge degrees of freedom offered by massive MIMO can be used to reduce the transmit power and/or to tolerate larger hardware impairments, which allows for the use of inexpensive and energy-efficient antenna elements.

  • 10.
    Blom, Rolf
    Linköping University, Department of Electrical Engineering. Linköping University, The Institute of Technology.
    Bounds on key equivocation for simple substitution ciphers1979In: IEEE Transactions on Information Theory, ISSN 0018-9448, E-ISSN 1557-9654, Vol. 25, no 1, p. 8-18Article in journal (Refereed)
    Abstract [en]

    The equivocation of the key for a simple substitution cipher is upper and lower hounded, when the message source is memoryless. The hounds are shown to be exponentially tight. The results are compared with random ciphering. It is observed that the exponential behavior of the equivocation of the key is not determined by the redundancy in the message source, but by the symbol probabilities which are closest in a certain sense.

  • 11. Bordenave, Charles
    et al.
    McDonald, David
    Proutiere, Alexandre
    KTH, School of Electrical Engineering (EES), Automatic Control.
    Asymptotic Stability Region of Slotted Aloha2012In: IEEE Transactions on Information Theory, ISSN 0018-9448, E-ISSN 1557-9654, Vol. 58, no 9, p. 5841-5855Article in journal (Refereed)
    Abstract [en]

    We analyze the stability of standard, buffered, slotted-Aloha systems. Specifically, we consider a set of users, each equipped with an infinite buffer. Packets arrive into user i's buffer according to some stationary ergodic Markovian process of intensity lambda(i). At the beginning of each slot, if user i has packets in its buffer, it attempts to transmit a packet with fixed probability p(i) over a shared resource/channel. The transmission is successful only when no other user attempts to use the channel. The stability of such systems has been open since their very first analysis in 1979 by Tsybakov and Mikhailov. In this paper, we propose an approximate stability condition that is provably exact when the number of users grows large. We provide theoretical evidence and numerical experiments to explain why the proposed approximate stability condition is extremely accurate even for systems with a restricted number of users (even two or three).

  • 12.
    Brännström, Fredrik
    et al.
    Chalmers University of Technology.
    Rasmussen, Lars Kildehöj
    KTH, School of Electrical Engineering (EES), Communication Theory. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Classification of Unique Mappings for 8PSK Based on Bit-Wise Distance Spectra2009In: IEEE Transactions on Information Theory, ISSN 0018-9448, E-ISSN 1557-9654, Vol. 55, no 3, p. 1131-1145Article in journal (Refereed)
    Abstract [en]

    The performance of bit-interleaved coded modulation (BICM) with (or without) iterative decoding (ID) is significantly influenced by the mapping of bits to the symbol constellation. Our main objective in this paper is to develop a systematic design approach for BICM-ID schemes, ensuring the best possible performance with iterative decoding. Although useful mappings for BICM-ID have been found based on various search strategies, no attempt has been made to systematically enumerate and classify all unique mappers for a given constellation. As the basis for a systematic enumeration and classification, we define the average bit-wise distance spectrum for a mapping from bits to symbols. Different bit-wise distance spectra are derived assuming no prior information or full prior information, respectively. The bit-wise distance spectra determine correspondingbit-wise error probability and bit-wise mutual information. The latter allows us to use theclassification of mappings with unique bit-wise distance spectra to also classifymappings with unique extremal points in the corresponding extrinsic information transfer (EXIT) curves. As an example of our approach, we classify 8PSK mappings into 86 classes of unique mappings according to bit-wise distance spectra. The classificationcan be used to significantly reduce the complexity of the search for suitable mappers for BICM-ID. For 8PSK and a given encoder, only 86 different mappings need to be investigated. As examples of the systematic design approach, the best 8PSK mappingsfor minimizing the convergence threshold are found for concatenation with the rate 1/2 (5, 7)8 and (133,1718 convolutional codes, and the rate 1/2 UMTS turbo code with identical constituent convolutional codes (15/13)8.

  • 13.
    Brännström, Fredrik
    et al.
    Chalmers University of Technology.
    Rasmussen, Lars Kildehöj
    University of South Australia.
    Grant, Alex J.
    University of South Australia.
    Convergence analysis and optimal scheduling for multiple concatenated codes2005In: IEEE Transactions on Information Theory, ISSN 0018-9448, E-ISSN 1557-9654, Vol. 51, no 9, p. 3354-3364Article in journal (Refereed)
    Abstract [en]

    An interesting practical consideration for decoding of serial or parallel concatenated codes with more than two components is the determination of the lowest complexity component decoder schedule which results in convergence. This correspondence presents an algorithm that finds such an optimal decoder schedule. A technique is also given for combining and projecting a series of three-dimensional extrinsic information transfer (EXIT) functions onto a single two-dimensional EXIT chart. This is a useful technique for visualizing the convergence threshold for multiple concatenated codes and provides a design tool for concatenated codes with more than two components.

  • 14.
    Brännström, Fredrik
    et al.
    Chalmers University of Technology.
    Rasmussen, Lars Kildehöj
    KTH, School of Electrical Engineering (EES), Communication Theory. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Grant, Alex J.
    University of South Australia.
    Optimal Puncturing Ratios and Energy Allocation for Multiple Parallel Concatenated Codes2009In: IEEE Transactions on Information Theory, ISSN 0018-9448, E-ISSN 1557-9654, Vol. 55, no 5, p. 2062-2077Article in journal (Refereed)
    Abstract [en]

    We propose a systematic design framework for optimal, low-complexity punctured multiple parallel concatenated codes (MPCCs), based on minimizing the convergence threshold using extrinsic information transfer (EXIT) charts. As the convergence threshold is related to the area between the two EXIT curves, the corresponding optimization problem is equivalent to a curve-fitting problem. The EXIT curves are determined by the respective EXIT functions of the constituents, which can be conveniently shaped through the use of random puncturing and unequal energy allocations across parallel coding streams. The design task is therefore to find the optimal combination of constituents, puncturing ratios, and energy allocation for matching the EXIT curves. A search over all rate-one convolutional codes of memory length four or less is performed, identifying 98 classes of codes with unique EXIT functions out of a total of 310 codes. Low-complexity MPCCs with up to four constituents are found, where the convergence thresholds are observed to be within 0.1 dB or less of the fundamental minimum signal-to-noise ratio (SNR) corresponding to the binary phase-shift keying (BPSK) capacity for code rates 1/3 ≤ R < 7/8. Further allowing for unequal energy allocation, the convergence thresholds for lower code rates are similarly improved.

  • 15. Bukh, Boris
    et al.
    Guruswami, Venkatesan
    Håstad, Johan
    KTH, School of Computer Science and Communication (CSC), Theoretical Computer Science, TCS.
    An Improved Bound on the Fraction of Correctable Deletions2017In: IEEE Transactions on Information Theory, ISSN 0018-9448, E-ISSN 1557-9654, Vol. 63, no 1, p. 93-103Article in journal (Refereed)
    Abstract [en]

    We consider codes over fixed alphabets against worst case symbol deletions. For any fixed k >= 2, we construct a family of codes over alphabet of size k with positive rate, which allow efficient recovery from a worst case deletion fraction approaching 1 - (2/(k + root k)). In particular, for binary codes, we are able to recover a fraction of deletions approaching 1/(root 2+1) = root 2-1 approximate to 0.414. Previously, even non-constructively, the largest deletion fraction known to be correctable with positive rate was 1 - Theta (1/root k), and around 0.17 for the binary case. Our result pins down the largest fraction of correctable deletions for k-ary codes as 1 - Theta (1/k), since 1 - 1/k is an upper bound even for the simpler model of erasures where the locations of the missing symbols are known. Closing the gap between (root 2 - 1) and 1/2 for the limit of worst case deletions correctable by binary codes remains a tantalizing open question.

  • 16.
    Cederlöf, Jörgen
    et al.
    Linköping University, Department of Mathematics. Linköping University, The Institute of Technology.
    Larsson, Jan-Åke
    Linköping University, Department of Mathematics, Applied Mathematics. Linköping University, The Institute of Technology.
    Security aspects of the Authentication used in Quantum Cryptography2008In: IEEE Transactions on Information Theory, ISSN 0018-9448, E-ISSN 1557-9654, Vol. 54, no 4, p. 1735-1741Article in journal (Refereed)
    Abstract [en]

    Unconditionally secure message authentication is an important part of Quantum Cryptography (QC). We analyze security effects of using a key obtained from QC for authentication purposes in later rounds of QC. In particular, the eavesdropper gains partial knowledge on the key in QC that may have an effect on the security of the authentication in the later round. Our initial analysis indicates that this partial knowledge has little effect on the authentication part of the system, in agreement with previous results on the issue. However, when taking the full QC protocol into account, the picture is different. By accessing the quantum channel used in QC, the attacker can change the message to be authenticated. This together with partial knowledge of the key does incur a security weakness of the authentication. The underlying reason for this is that the authentication used, which is insensitive to such message changes when the key is unknown, becomes sensitive when used with a partially known key. We suggest a simple solution to this problem, and stress usage of this or an equivalent extra security measure in QC.

  • 17.
    Charalambous, Themistoklis
    et al.
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Charalambous, Charalambos D.
    Rezaei, Farzad
    Optimal Merging Algorithms for Lossless Codes With Generalized Criteria2014In: IEEE Transactions on Information Theory, ISSN 0018-9448, E-ISSN 1557-9654, Vol. 60, no 9, p. 5486-5499Article in journal (Refereed)
    Abstract [en]

    This paper presents lossless prefix codes optimized with respect to a payoff criterion consisting of a convex combination of maximum codeword length and average codeword length. The optimal codeword lengths obtained are based on a new coding algorithm, which transforms the initial source probability vector into a new probability vector according to a merging rule. The coding algorithm is equivalent to a partition of the source alphabet into disjoint sets on which a new transformed probability vector is defined as a function of the initial source probability vector and scalar parameter. The payoff criterion considered encompasses a tradeoff between maximum and average codeword length; it is related to a payoff criterion consisting of a convex combination of average codeword length and average of an exponential function of the codeword length, and to an average codeword length payoff criterion subject to a limited length constraint. A special case of the first related payoff is connected to coding problems involving source probability uncertainty and codeword overflow probability, whereas the second related payoff compliments limited length Huffman coding algorithms.

  • 18.
    Chen, Eric Zhi
    Kristianstad University, School of Engineering.
    An explicit construction of 2-generator quasi-twisted codes2008In: IEEE Transactions on Information Theory, ISSN 0018-9448, E-ISSN 1557-9654, Vol. 54, no 12, p. 5770-5773Article in journal (Refereed)
    Abstract [en]

    Quasi-twisted (QT) codes are a generalization of quasi-cyclic (QC) codes. Based on consta-cyclic simplex codes, a new explicit construction of a family of 2-generator quasi-twisted (QT) two-weight codes is presented. It is also shown that many codes in the family meet the Griesmer bound and therefore are length-optimal. New distance-optimal binary QC [195, 8, 96], [210, 8, 104] and [240, 8, 120] codes, and good ternary QC [208, 6, 135] and [221, 6, 144] codes are also obtained by the construction.

  • 19.
    Chen, Eric Zhi
    Linköping university.
    Further results on difference triangle sets1994In: IEEE Transactions on Information Theory, ISSN 0018-9448, E-ISSN 1557-9654, Vol. 40, no 4, p. 1268-1270Article in journal (Refereed)
    Abstract [en]

    Further results on the upper bounds for difference tri8nglesets (DTS) are derived from disjoint difference sets and additive sequencesof permutations, whit3 greatly improve the known bounds.

  • 20.
    Chen, Eric Zhi
    Kristianstad University, School of Engineering.
    New quasi-cyclic codes from simplex codes2007In: IEEE Transactions on Information Theory, ISSN 0018-9448, E-ISSN 1557-9654, Vol. 53, no 3, p. 1193-1196Article in journal (Refereed)
    Abstract [en]

    As a generalization of cyclic codes, quasi-cyclic (QC) codes contain many good linear codes. But quasi-cyclic codes studied so far are mainly limited to one generator (1-generator) QC codes. In this correspondence, 2-generator and 3-generator QC codes are studied, and many good, new QC codes are constructed from simplex codes. Some new binary QC codes or related codes, that improve the bounds on maximum minimum distance for binary linear codes are constructed. They are 5-generator QC [93 17 34] and [254,23, 102] codes, and related [96, 17, 361, [256, 23,104] codes.

  • 21.
    Chen, Eric Zhi
    Linköping university.
    Six new binary quasi-cyclic codes1994In: IEEE Transactions on Information Theory, ISSN 0018-9448, E-ISSN 1557-9654, Vol. 40, no 5, p. 1666-1667Article in journal (Refereed)
    Abstract [en]

    Six new quasi-cyclic codes are presented, which improve thelower bounds on the minimum distance for a binary code. A localexhaustive search is used to find these codes and many other quasi-cycliccodes which attain the lower bounds.

  • 22.
    Cho, Jeong-woo
    et al.
    KTH, School of Information and Communication Technology (ICT), Communication Systems, CoS, Network Systems Laboratory (NS Lab).
    Jiang, Yuming
    NTNU (Norwegian University of Science and Technology).
    Fundamentals of the Backoff Process in 802.11: Dichotomy of the Aggregation2015In: IEEE Transactions on Information Theory, ISSN 0018-9448, E-ISSN 1557-9654, Vol. 61, no 4, p. 1687-1701Article in journal (Refereed)
    Abstract [en]

    This paper discovers fundamental principles of the backoff process that governs the performance of IEEE 802.11. A simplistic principle founded upon regular variation theory is that the backoff time has a truncated Pareto-type tail distribution with an exponent of $ { (log gamma !)/log m}$ ( $boldsymbol {m}$ is the multiplicative factor and $ {gamma }$ is the collision probability). This reveals that the per-node backoff process is heavy-tailed in the strict sense for $ { gamma > 1/m^{2}}$ , and paves the way for the following unifying result. The state-of-the-art theory on the superposition of the heavy-tailed processes is applied to establish a dichotomy exhibited by the aggregate backoff process, putting emphasis on the importance of time-scales on which we view the backoff processes. While the aggregation on normal time-scales leads to a Poisson process, it is approximated by a new limiting process possessing long-range dependence (LRD) on coarse time-scales. This dichotomy turns out to be instrumental in formulating short-term fairness, extending existing formulas to arbitrary population, and to elucidate the absence of LRD in practical situations. A refined wavelet analysis is conducted to strengthen this argument.

  • 23.
    Cho, Jeong-woo
    et al.
    KTH, School of Information and Communication Technology (ICT), Communication Systems, CoS.
    Le Boudec, Jean-Yves
    EPFL (École Polytechnique Fédérale de Lausanne).
    Jiang, Yuming
    NTNU (Norwegian University of Science and Technology).
    On the Asymptotic Validity of the Decoupling Assumption for Analyzing 802.11 MAC Protocol2012In: IEEE Transactions on Information Theory, ISSN 0018-9448, E-ISSN 1557-9654, Vol. 58, no 11, p. 6879-6893Article in journal (Refereed)
    Abstract [en]

    Performance evaluation of the 802.11 MAC protocol is classically based on the decoupling assumption, which hypothesizes that the backoff processes at different nodes are independent. This decoupling assumption results from mean field convergence and is generally true in transient regime in the asymptotic sense (when the number of wireless nodes tends to infinity), but, contrary to widespread belief, may not necessarily hold in stationary regime. The issue is often related with the existence and uniqueness of a solution to a fixed point equation; however, it was also recently shown that this condition is not sufficient; in contrast, a sufficient condition is a global stability property of the associated ordinary differential equation. In this paper, we give a simple condition that establishes the asymptotic validity of the decoupling assumption for the homogeneous case (all nodes have the same parameters). We also discuss the heterogeneous and the differentiated service cases and formulate a new ordinary differential equation. We show that the uniqueness of a solution to the associated fixed point equation is not sufficient; we exhibit one case where the fixed point equation has a unique solution but the decoupling assumption is not valid in the asymptotic sense in stationary regime.

  • 24.
    Chuang, Allen
    et al.
    University of Sydney, Australia.
    Guillen i Fabregas, Albert
    University of Cambridge.
    Rasmussen, Lars Kildehöj
    Institute for Telecommunications Research, University of South Australia.
    Collings, Iain B.
    University of Sydney, Australia.
    Optimal throughput-diversity-delay tradeoff in MIMO ARQ block-fading channels2008In: IEEE Transactions on Information Theory, ISSN 0018-9448, E-ISSN 1557-9654, Vol. 54, no 9, p. 3968-3986Article in journal (Refereed)
    Abstract [en]

    In this paper, we consider an automatic-repeat-request (ARQ) retransmission protocol signaling over a block-fading multiple-input-multiple-output (MIMO) channel. Unlike previous work, we allow for multiple fading blocks within each transmission (ARQ round), and we constrain the transmitter to fixed rate codes constructed over complex signal constellations. In particular, we examine the general case of average input-power-constrained constellations with a fixed signaling alphabet of finite cardinality. This scenario is a suitable model for practical wireless communications systems employing orthogonal frequency division multiplexing (OFDM) techniques over a MIMO ARQ channel. Two cases of fading dynamics are considered, namely, short-term static fading wherechannel fading gains change randomly for each ARQ round, and long-term static fadingwhere channel fading gains remain constant over all ARQ rounds pertaining to a given message. As our main result, we prove that for the block-fading MIMO ARQ channel with a fixed signaling alphabet satisfying a short-term power constraint, the optimal signal-to-noise ratio (SNR) exponent is given by a modified Singleton bound, relating all the system parameters. To demonstrate the practical significance of the theoretical analysis, we present numerical results showing that practical Singleton-bound-achieving maximum distance separable codes achieve the optimal SNR exponent.

  • 25. Cresp, Gregory
    et al.
    Dam, Hai Huyen
    Zepernick, Hans-Jürgen
    Design of Sequence Family Subsets Using a Branch and Bound Technique2009In: IEEE Transactions on Information Theory, ISSN 0018-9448, E-ISSN 1557-9654, Vol. 55, no 8, p. 3847-3857Article in journal (Refereed)
    Abstract [en]

    The number of spreading sequences required for Direct Sequence Code Division Multiple Access (DS-CDMA) systems depends on the number of simultaneous users in the system. Often a sequence family provides more sequences than are required; in many cases the selection of the employed sequences is a computationally intensive task. This selection is a key consideration, as the properties of the sequences assigned affect the error performance in the system. In this paper, a branch and bound algorithm is presented to perform this selection based on two different cost functions. Numerical results are presented to demonstrate the improved performance of this algorithm over previous work.

  • 26.
    Danev, Danyo
    et al.
    Linköping University, The Institute of Technology. Linköping University, Department of Electrical Engineering, Data Transmission.
    Olsson, Jonas
    Linköping University, The Institute of Technology. Linköping University, Department of Electrical Engineering.
    On a sequence of cyclic codes with minimum distance six2000In: IEEE Transactions on Information Theory, ISSN 0018-9448, E-ISSN 1557-9654, Vol. 46, no 2, p. 673-674Article in journal (Refereed)
    Abstract [en]

    A sequence of q-ary cyclic codes is analyzed. For each finite field GF (q), q=4, there is a code with parameters [n, k, d, q] = [q(q-1)+1, q(q-1)-6, 6,q]. All these codes are n-, k-, and d-optimal, with only one exception. The dual codes are considered. Their true minimum distances are calculated in the range 4=q=32.

  • 27.
    Do, Hieu T.
    et al.
    KTH, School of Electrical Engineering (EES), Communication Theory. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre. Ericsson Research, Sweden.
    Oechtering, Tobias J.
    KTH, School of Electrical Engineering (EES), Communication Theory. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Skoglund, Mikael
    KTH, School of Electrical Engineering (EES), Communication Theory. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Layered Coding for the Interference Channel With a Relay2014In: IEEE Transactions on Information Theory, ISSN 0018-9448, E-ISSN 1557-9654, Vol. 60, no 10, p. 6154-6180Article in journal (Refereed)
    Abstract [en]

    This paper studies and derives new results for the interference channel with a relay (ICR). Three inner bounds for the discrete memoryless ICR are proposed, based on three coding strategies that employ layered code at the relay. The first scheme is inspired by layered noisy network coding, proposed by Lim et al. for the two-way relay channel, the second and the third schemes rely on simpler encoding and decoding processes, dubbed layered quantize-forward. Performance of the proposed schemes is investigated for two classes of channels with Gaussian noise: the interference channel with in-band relay reception/out-of-band relay transmission and the interference with in-band relay reception/in-band relay transmission. For the former class of channels, it is shown that the first proposed scheme achieves the same inner bound as the generalized hash-forward scheme with incremental binning. In addition, the inner bound is within 0.5 bit of the capacity region under certain conditions on the channel parameters. For the latter class of channels, new upper bounds on sum-rate are established by extending known upper bounds for symmetric channels. The first inner bound is shown to be within 0.5 bit of the capacity region if the relay's power exceeds a certain threshold, which depends on channel parameters. Numerical examples show that the proposed schemes can achieve significantly higher sum-rates when compared with other compress-forward schemes. Analysis also reveals a tradeoff between achievable rates, coding delay, and complexity of the proposed schemes. Results in this paper provide a better understanding of coding for the ICR, in particular, they show that layered coding is a beneficial element in multiuser networks with relays.

  • 28.
    Du, Jinfeng
    et al.
    KTH, School of Electrical Engineering (EES), Communication Theory. MIT, Cambridge, USA.
    Medard, Muriel
    Xiao, Ming
    KTH, School of Electrical Engineering (EES), Communication Theory. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Skoglund, Mikael
    KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre. KTH, School of Electrical Engineering (EES), Communication Theory.
    Scalable Capacity Bounding Models for Wireless Networks2016In: IEEE Transactions on Information Theory, ISSN 0018-9448, E-ISSN 1557-9654, Vol. 62, no 1, p. 208-229Article in journal (Refereed)
    Abstract [en]

    The framework of network equivalence theory developed by Koetter et al. introduces a notion of channel emulation to construct noiseless networks as upper (respectively, lower) bounding models, which can be used to calculate the outer (respectively, inner) bounds for the capacity region of the original noisy network. Based on the network equivalence framework, this paper presents scalable upper and lower bounding models for wireless networks with potentially many nodes. A channel decoupling method is proposed to decompose wireless networks into decoupled multiple-access channels and broadcast channels. The upper bounding model, consisting of only point-to-point bit pipes, is constructed by first extending the one-shot upper bounding models developed by Calmon et al. and then integrating them with network equivalence tools. The lower bounding model, consisting of both point-to-point and point-to-points bit pipes, is constructed based on a two-step update of the lower bounding models to incorporate the broadcast nature of wireless transmission. The main advantages of the proposed methods are their simplicity and the fact that they can be extended easily to large networks with a complexity that grows linearly with the number of nodes. It is demonstrated that the resulting upper and lower bounds can approach the capacity in some setups.

  • 29.
    Dubrova, Elena
    KTH, School of Information and Communication Technology (ICT), Electronic Systems.
    A Scalable Method for Constructing Galois NLFSRs With Period 2(n)-1 Using Cross-Join Pairs2013In: IEEE Transactions on Information Theory, ISSN 0018-9448, E-ISSN 1557-9654, Vol. 59, no 1, p. 703-709Article in journal (Refereed)
    Abstract [en]

    A method for constructing n-stage Galois NLFSRs with period 2(n) - 1 from n-stage maximum length LFSRs is presented. Nonlinearity is introduced into state cycles by adding a non-linear Boolean function to the feedback polynomial of the LFSR. Each assignment of variables for which this function evaluates to 1 acts as a crossing point for the LFSR state cycle. The effect of non-linearity is cancelled and state cycles are joined back by adding a copy of the same function to a later stage of the register. The presented method requires no extra time steps and it has a smaller area overhead compared to the previous approaches based on cross-join pairs. It is feasible for large n.

  • 30.
    Dubrova, Elena
    KTH, School of Information and Communication Technology (ICT), Electronic, Computer and Software Systems, ECS.
    A Transformation From the Fibonacci to the Galois NLFSRs2009In: IEEE Transactions on Information Theory, ISSN 0018-9448, E-ISSN 1557-9654, Vol. 55, no 11, p. 5263-5271Article in journal (Refereed)
    Abstract [en]

    Conventional nonlinear feedback shift registers (NLFSRs) use the Fibonacci configuration in which the feedback is applied to the last bit only. In this paper, we show how to transform a Fibonacci NLFSR into an equivalent NLFSR in the Galois configuration, in which the feedback can be applied to every bit. Such a transformation can potentially reduce the depth of the circuits implementing feedback functions, thus decreasing the propagation time and increasing the throughput.

  • 31.
    Dubrova, Elena
    KTH, School of Information and Communication Technology (ICT), Electronic Systems.
    Finding Matching Initial States for Equivalent NLFSRs in the Fibonacci and the Galois Configurations2010In: IEEE Transactions on Information Theory, ISSN 0018-9448, E-ISSN 1557-9654, Vol. 56, no 6, p. 2961-2966Article in journal (Refereed)
    Abstract [en]

    The Fibonacci and the Galois configurations of nonlinear feedback shift registers (NLFSRs) are considered. In the former, the feedback is applied to the input bit of the shift register only. In the latter, the feedback can potentially be applied to every bit. The sufficient conditions for equivalence of NLFSRs in the Fibonacci and the Galois configurations have been formulated previously. The equivalent NLFSRs in different configurations normally have to be initialized to different states to generate the same output sequences. The mapping between the initial states of two equivalent NLFSRs in the Fibonacci and the Galois configurations is derived in this paper.

  • 32.
    Dubrova, Elena
    KTH, School of Information and Communication Technology (ICT), Electronic Systems.
    Synthesis of Binary Machines2011In: IEEE Transactions on Information Theory, ISSN 0018-9448, E-ISSN 1557-9654, Vol. 57, no 10, p. 6890-6893Article in journal (Refereed)
    Abstract [en]

    The problem of constructing a binary machine with the minimum number of stages generating a given binary sequence is addressed. Binary machines are a generalization of nonlinear feedback shift registers (NLFSRs) in which both connections, feedback and feedforward, are allowed and no chain connection between the register stages is required. An algorithm for constructing a shortest binary machine generating a given periodic binary sequence is presented.

  • 33.
    Fan, Yijia
    et al.
    Department of Electrical Engineering, Princeton University.
    Wang, Chao
    Institute for Digital Communications, The University of Edinburgh.
    Poor, H. Vincent
    Department of Electrical Engineering, Princeton University.
    Thompson, John
    Institute for Digital Communications, The University of Edinburgh.
    Cooperative multiplexing: Toward higher spectral efficiency in multiple-antenna relay networks2009In: IEEE Transactions on Information Theory, ISSN 0018-9448, E-ISSN 1557-9654, Vol. 55, no 9, p. 3909-3926Article in journal (Refereed)
    Abstract [en]

    Previous work on cooperative communications has concentrated primarily on the diversity benefits of such techniques. This paper, instead, considers the multiplexing benefits of cooperative communications. First, a new interpretation on the fundamental tradeoff between the transmission rate and outage probability in multiple-antenna relay networks is given. It follows that multiplexing gains can be obtained at any finite signal-to-noise ratio (SNR), in full-duplex multiple-antenna relay networks. Thus, relaying can offer not only stronger link reliability, but also higher spectral efficiency.

    Specifically, the decode-and-forward protocol is applied and networks that have one source, one destination, and multiple relays are considered. A receive power gain at the relays, which captures the network large-scale fading characteristics, is also considered. It is shown that this power gain can significantly affect the system diversity-multiplexing tradeoff for any finite SNR value. Several relaying protocols are proposed and are shown to offer nearly the same outage probability as if the transmit antennas at the source and the relay(s) were colocated, given certain SNR and receive power gains at the relays. Thus, a higher multiplexing gain than that of the direct link can be obtained if the destination has more antennas than the source.

    Much of the analysis in the paper is valid for arbitrary channel fading statistics. These results point to a view of relay networks as a means for providing higher spectral efficiency, rather than only link reliability.

  • 34. Friedland, S.
    et al.
    Lundow, P. H.
    Markström, Klas
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    The 1-vertex transfer matrix and accurate estimation of channel capacity2010In: IEEE Transactions on Information Theory, ISSN 0018-9448, E-ISSN 1557-9654, Vol. 57, no 8, p. 3692-3699Article in journal (Refereed)
    Abstract [en]

    The notion of a 1-vertex transfer matrix for multidimensional codes is introduced. It is shown that the capacity of such codes, or the topological entropy, can be expressed as the limit of the logarithm of spectral radii of 1-vertex transfer matrices. Storage and computations using the 1-vertex transfer matrix are much smaller than storage and computations needed for the standard transfer matrix. The method is applied to estimate the first 15 digits of the entropy of the 2-D (0, 1) run length limited channel. A large-scale computation of eigenvalues for the (0, 1) run length limited channel in 2-D and 3-D have been carried out. This was done in order to be able to compare the computational cost of the new method with the standard transfer matrix and have rigorous bounds to compare the estimates with. This in turn leads to improvements on the best previous lower and upper bounds for these channels.

  • 35.
    Friedland, Shmuel
    et al.
    Department of Mathematics, Statistics and Computer Science, University of Illinois at Chicago.
    Lundow, Per Håkan
    KTH, School of Engineering Sciences (SCI), Theoretical Physics, Condensed Matter Theory.
    Markström, Klas
    Department of Mathematics and Mathematical Statistics, Umeå University.
    The 1-Vertex Transfer Matrix and Accurate Estimation of Channel Capacity2010In: IEEE Transactions on Information Theory, ISSN 0018-9448, E-ISSN 1557-9654, Vol. 56, no 8, p. 3692-3699Article in journal (Refereed)
    Abstract [en]

    The notion of a 1-vertex transfer matrix for multidimensional codes is introduced. It is shown that the capacity of such codes, or the topological entropy, can be expressed as the limit of the logarithm of spectral radii of 1-vertex transfer matrices. Storage and computations using the 1-vertex transfer matrix are much smaller than storage and computations needed for the standard transfer matrix. The method is applied to estimate the first 15 digits of the entropy of the 2-D (0, 1) run length limited channel. A large-scale computation of eigenvalues for the (0, 1) run length limited channel in 2-D and 3-D have been carried out. This was done in order to be able to compare the computational cost of the new method with the standard transfer matrix and have rigorous bounds to compare the estimates with. This in turn leads to improvements on the best previous lower and upper bounds for these channels.

  • 36.
    Gattami, Ather
    RISE - Research Institutes of Sweden, ICT, SICS.
    Feedback Capacity of Gaussian Channels Revisited2018In: IEEE Transactions on Information Theory, ISSN 0018-9448, E-ISSN 1557-9654, Vol. 65, no 3, p. 1948-1960, article id 8552675Article in journal (Refereed)
    Abstract [en]

    In this paper, we revisit the problem of finding the average capacity of the Gaussian feedback channel. First, we consider the problem of finding the average capacity of the analog Gaussian noise channel where the noise has an arbitrary spectral density. We introduce a new approach to the problem where we solve the problem over a finite number of transmissions and then consider the limit of an infinite number of transmissions. Further, we consider the important special case of stationary Gaussian noise with finite memory. We show that the channel capacity at stationarity can be found by solving a semi-definite program, and hence computationally tractable. We also give new proofs and results of the non stationary solution which bridges the gap between results in the literature for the stationary and non stationary feedback channel capacities. It&#x2019;s shown that a linear communication feedback strategy is optimal. Similar to the solution of the stationary problem, it&#x2019;s shown that the optimal linear strategy is to transmit a linear combination of the information symbols to be communicated and the innovations for the estimation error of the state of the noise process.

  • 37.
    Ghourchian, Hamid
    et al.
    KTH, School of Electrical Engineering and Computer Science (EECS), Information Science and Engineering. Sharif Univ Technol, Elect Engn Dept, Tehran 11155, Iran.
    Amini, Arash
    Sharif Univ Technol, Elect Engn Dept, Tehran 11155, Iran.;Sharif Univ Technol, Adv Commun Res Inst, Tehran 11155, Iran..
    Gohari, Amin
    Sharif Univ Technol, Elect Engn Dept, Tehran 11155, Iran.;Sharif Univ Technol, Adv Commun Res Inst, Tehran 11155, Iran..
    How Compressible Are Innovation Processes?2018In: IEEE Transactions on Information Theory, ISSN 0018-9448, E-ISSN 1557-9654, Vol. 64, no 7, p. 4843-4871Article in journal (Refereed)
    Abstract [en]

    The sparsity and compressibility of finitedimensional signals are of great interest in fields, such as compressed sensing. The notion of compressibility is also extended to infinite sequences of independent identically distributed or ergodic random variables based on the observed error in their nonlinear k-term approximation. In this paper, we use the entropy measure to study the compressibility of continuous-domain innovation processes (alternatively known as white noise). Specifically, we define such a measure as the entropy limit of the doubly quantized (time and amplitude) process. This provides a tool to compare the compressibility of various innovation processes. It also allows us to identify an analogue of the concept of "entropy dimension" which was originally defined by Renyi for random variables. Particular attention is given to stable and impulsive Poisson innovation processes. Here, our results recognize Poisson innovations as the more compressible ones with an entropy measure far below that of stable innovations. While this result departs from the previous knowledge regarding the compressibility of impulsive Poisson laws compared with continuous fat-tailed distributions, our entropy measure ranks alpha-stable innovations according to their tail.

  • 38.
    Ghourchian, Hamid
    et al.
    KTH, School of Electrical Engineering and Computer Science (EECS), Information Science and Engineering. Sharif Univ Technol, Dept Elect Engn, Tehran 11155, Iran..
    Aminian, Gholamali
    Sharif Univ Technol, Dept Elect Engn, Tehran 11155, Iran.;Sharif Univ Technol, Adv Commun Res Inst, Tehran 11155, Iran..
    Gohari, Amin
    Sharif Univ Technol, Dept Elect Engn, Tehran 11155, Iran.;Sharif Univ Technol, Adv Commun Res Inst, Tehran 11155, Iran..
    Mirmohseni, Mahtab
    Sharif Univ Technol, Dept Elect Engn, Tehran 11155, Iran.;Sharif Univ Technol, Adv Commun Res Inst, Tehran 11155, Iran..
    Nasiri-Kenari, Masoumeh
    Sharif Univ Technol, Dept Elect Engn, Tehran 11155, Iran.;Sharif Univ Technol, Adv Commun Res Inst, Tehran 11155, Iran..
    On the Capacity of a Class of Signal-Dependent Noise Channels2018In: IEEE Transactions on Information Theory, ISSN 0018-9448, E-ISSN 1557-9654, Vol. 64, no 12, p. 7828-7846Article in journal (Refereed)
    Abstract [en]

    In some applications, the variance of additive measurement noise depends on the signal that we aim to measure. For instance, additive signal-dependent Gaussian noise (ASDGN) channel models are used in molecular and optical communication. Herein, we provide lower and upper bounds on the capacity of additive signal-dependent noise (ASDN) channels. The first lower bound is based on an extension of majorization inequalities, and the second lower bound utilizes the properties of the differential entropy. The lower bounds are valid for arbitrary ASDN channels. The upper bound is based on a previous idea of the authors ("symmetric relative entropy") and is applied to the ASDGN channels. These bounds indicate that in the ASDN channels (unlike the classical additive white Gaussian noise channels), the capacity does not necessarily become larger by reducing the noise variance function. We also provide sufficient conditions under which the capacity becomes infinite. This is complemented by some conditions implying that the capacity is finite, and a unique capacity achieving measure exists (in the sense of the output measure).

  • 39.
    Giese, Jochen
    et al.
    KTH, School of Electrical Engineering (EES), Communication Theory. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Skoglund, Mikael
    KTH, School of Electrical Engineering (EES), Communication Theory. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Single- and multiple-antenna constellations for communication over unknown frequency-selective fading channels2007In: IEEE Transactions on Information Theory, ISSN 0018-9448, E-ISSN 1557-9654, Vol. 53, no 4, p. 1584-1594Article in journal (Refereed)
    Abstract [en]

    Data transmission through frequency-selective block fading channels is considered in the case where neither the transmitter nor the receiver has any knowledge of the channel coefficients. Standard code design approaches for this scenario take channel uncertainty at the receiver into account by splitting the available channel coherence time into a part dedicated to training symbols utilized for channel estimation and a second part using an error-control coding scheme that is designed without channel uncertainty in mind. In contrast, in this correspondence joint codes are designed that are optimized for communication over the unknown channel and operate over the full coherence time. Using an approximation of the union bound on codeword error probability as design criterion, codes based on general complex-valued symbols are obtained with a gradient search optimization technique. Numerical examples for both single antenna as well as multiple-antenna systems illustrate that significant improvement over training-based schemes can be obtained.

  • 40.
    Giese, Jochen
    et al.
    KTH, School of Electrical Engineering (EES), Communication Theory. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Skoglund, Mikael
    KTH, School of Electrical Engineering (EES), Communication Theory. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Space-time constellation design for partial CSI at the receiver2007In: IEEE Transactions on Information Theory, ISSN 0018-9448, E-ISSN 1557-9654, Vol. 53, no 8, p. 2715-2731Article in journal (Refereed)
    Abstract [en]

    The design of signal constellations for a communication system using multiple transmitter antennas over a Rayleigh-fading channel is considered under the assumption that no channel state information (CSI) is available at the transmitter and the receiver has acquired a CSI estimate with known error covariance. This setup encompasses the Well-studied scenarios of perfect and no channel knowledge at the receiver and allows a smooth transition between these two cases. The data detection performance as a function of the CSI error covariance is analyzed and used to investigate the design of training blocks if such blocks are transmitted to provide CSI to the receiver. Moreover, two approaches to design constellations adapted to the error covariance of the receiver CSI are presented. Whereas the first approach is based on a generic gradient search method, the second approach uses an appropriate combination of constellations designed for perfect and no CSI at the receiver. Simulations confirm the benefits of the presented designs.

  • 41.
    Girnyk, Maksym A.
    et al.
    KTH, School of Electrical Engineering (EES), Communication Theory.
    Vehkaperä, Mikko
    KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Rasmussen, Lars Kildehoj
    Asymptotic Performance Analysis of a K-Hop Amplify-and-Forward Relay MIMO Channel2016In: IEEE Transactions on Information Theory, ISSN 0018-9448, E-ISSN 1557-9654, Vol. 62, no 6, p. 3532-3546Article in journal (Refereed)
    Abstract [en]

    This paper studies the asymptotic performance of multi-hop amplify-and-forward relay multiple-antenna communication channels. Each multi-antenna relay terminal in the considered network amplifies the received signal, sent by a source, and retransmits it upstream toward a destination. Achievable ergodic rates of the relay channel with both jointly optimal detection and decoding and practical separate-decoding receiver architectures for arbitrary signaling schemes, along with average bit error rates for various types of detectors are derived in the regime where the number of antennas at each terminal grows large without a bound. To overcome the difficulty of averaging over channel realizations, we apply a large-system analysis based on the replica method from statistical physics. The validity of the large-system analysis is further verified through Monte Carlo simulations of realistic finite-sized systems.

  • 42.
    Guo, Dongning
    et al.
    Princeton University.
    Verdu, Sergio
    Princeton University.
    Rasmussen, Lars Kildehöj
    University of South Australia.
    Asymptotic normality of linear multiuser receiver outputs2002In: IEEE Transactions on Information Theory, ISSN 0018-9448, E-ISSN 1557-9654, Vol. 48, no 12, p. 3080-3095Article in journal (Refereed)
  • 43. Guruswami, V.
    et al.
    Håstad, Johan
    KTH, Superseded Departments, Numerical Analysis and Computer Science, NADA.
    Sudan, M.
    Zuckerman, D.
    Combinatorial bounds for list decoding2002In: IEEE Transactions on Information Theory, ISSN 0018-9448, E-ISSN 1557-9654, Vol. 48, no 5, p. 1021-1034Article in journal (Refereed)
    Abstract [en]

    Informally, an error-correcting code has nice list-decodability properties if every Hamming ball of large radius has a small number of codewords in it. Here, we report linear codes with nontrivial list-decodability: i.e., codes of large rate that are nicely list-decodable, and codes of large distance that are not nicely list-decodable. Specifically, on the positive side, we show that there exist codes of rate R and block length n that have at most c codewords in every Hamming ball of radius H-1 (1-R-1/c) (.) n. This answers the main open question from the work of Elias. This result also has consequences for the construction of concatenated codes of good rate that are list decodable from a large fraction of errors, improving previous results of Guruswami and Sudan in this vein. Specifically, for every epsilon > 0, we present a polynomial time constructible asymptotically good family of binary codes of rate Omega(epsilon(4)) that can be list-decoded in polynomial time from up to a fraction (1/2 - epsilon) of errors, using lists of size O(epsilon(-2)). On the negative side, we show that for every delta and c, there exists tau < delta, c(1) > 0, and an infinite family of linear codes {C-i}(i) such that if n(i) denotes the block length of C-i, then C-i has minimum distance at least delta (.) n(i) and contains more than c(1) (.) n(i)(c) codewords in some Hamming ball of radius tau (.) n(i). While this result is still far from known bounds on the list-decodability of linear codes, it is the first to bound the radius for list-decodability by a polynomial-sized list away from the minimum distance of the code.

  • 44. Guruswami, Venkatesan
    et al.
    Håstad, Johan
    KTH, School of Computer Science and Communication (CSC), Theoretical Computer Science, TCS.
    Kopparty, Swastik
    On the List-Decodability of Random Linear Codes2011In: IEEE Transactions on Information Theory, ISSN 0018-9448, E-ISSN 1557-9654, Vol. 57, no 2, p. 718-725Article in journal (Refereed)
    Abstract [en]

    The list-decodability of random linear codes is shown to be as good as that of general random codes. Specifically, for every fixed finite field, Gamma(q), p is an element of (0, 1 - 1/q) and epsilon > 0, it is proved that with high probability a random linear code C in F-q(n) of rate (1 - H-q(p) - epsilon) can be list decoded from a fraction p of errors with lists of size at most O(1/epsilon). This also answers a basic open question concerning the existence of highly list-decodable linear codes, showing that a list-size of O(1/epsilon) suffices to have rate within epsilon of the information-theoretically optimal rate of 1 - H-q(p). The best previously known list-size bound was q(O(1/epsilon)) (except in the q = 2 case where a list-size bound of O(1/epsilon) was known). The main technical ingredient in the proof is a strong upper bound on the probability that l random vectors chosen from a Hamming ball centered at the origin have too many (more than Omega(l)) vectors from their linear span also belong to the ball.

  • 45.
    Gómez-Cuba, Felipe
    et al.
    University of Vigo, Spain.
    Du, Jinfeng
    KTH, School of Electrical Engineering (EES), Communication Theory. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre. Research Lab of Electronics, MIT.
    Médard, Muriel
    MIT.
    Erkip, Elza
    NYU Polytechnic School of Engineering, USA.
    Unified Capacity Limit of Non-Coherent Wideband Fading Channels2015In: IEEE Transactions on Information Theory, ISSN 0018-9448, E-ISSN 1557-9654Article in journal (Refereed)
    Abstract [en]

    Peaky and non-peaky signaling schemes have long been considered species apart in non-coherent wideband fading channels, as the first approaches asymptotically the linear-in-power capacity of a wideband AWGN channel with the same SNR, whereas the second reaches a nearly power-limited peak rate at some finite critical bandwidth and then falls to zero as bandwidth grows to infinity. In this paper it is shown that this distinction is in fact an artifact of the limited attention paid in the past to the product between the bandwidth and the fraction of time it is in use. This fundamental quantity, that is termed bandwidth occupancy, measures average bandwidth usage over time. As it turns out, a peaky signal that transmits in an infinite bandwidth but only for an infinitesimal fraction of the time may only have a small bandwidth occupancy, and so does a non-peaky scheme that limits itself to the critical bandwidth even though more spectrum is available, so as to not degrade rate. The two types of signaling in the literature are harmonized to show that, for any type of signals, there is a fundamental limit---a critical bandwidth occupancy. All signaling schemes with the same bandwidth occupancy approach the linear-in-power capacity of wideband AWGN channels with the same asymptotic behavior as the bandwidth occupancy approaches its critical value. For a bandwidth occupancy above the critical value, rate decreases to zero as the occupancy goes to infinity. This unified analysis not only recovers previous results on capacity bounds for (non-)peaky signaling schemes, but also reveals the fundamental tradeoff between accuracy and convergence when characterizing the maximal achievable rate.

  • 46.
    He, Qing
    et al.
    Linköping University, Department of Science and Technology, Communications and Transport Systems. Linköping University, Faculty of Science & Engineering.
    Yuan, Di
    Linköping University, Department of Science and Technology, Communications and Transport Systems. Linköping University, Faculty of Science & Engineering.
    Ephremides, Anthony
    Univ Maryland, MD 20742 USA.
    Optimal Link Scheduling for Age Minimization in Wireless Systems2018In: IEEE Transactions on Information Theory, ISSN 0018-9448, E-ISSN 1557-9654, Vol. 64, no 7, p. 5381-5394Article in journal (Refereed)
    Abstract [en]

    Information age is a recently introduced metric to represent the freshness of information in communication systems. We investigate age minimization in a wireless network and propose a novel approach of optimizing the scheduling strategy to deliver all messages as fresh as possible. Specifically, we consider a set of links that share a common channel. The transmitter at each link contains a given number of packets with time stamps from an information source that generated them. We address the link transmission scheduling problem with the objective of minimizing the overall age. This minimum age scheduling problem (MASP) is different from minimizing the time or the delay for delivering the packets in question. We model the MASP mathematically and prove it is NP-hard in general. We also identify tractable cases as well as optimality conditions. An integer linear programming formulation is provided for performance benchmarking. Moreover, a steepest age descent algorithm with better scalability is developed. Numerical study shows that, by employing the optimal schedule, the overall age is significantly reduced in comparison to other scheduling strategies.

  • 47.
    Jaldén, Joakim
    et al.
    KTH, School of Electrical Engineering (EES), Signal Processing. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Elia, Petros
    DMT Optimality of LR-Aided Linear Decoders for a General Class of Channels, Lattice Designs, and System Models2010In: IEEE Transactions on Information Theory, ISSN 0018-9448, E-ISSN 1557-9654, Vol. 56, no 10, p. 4765-4780Article in journal (Refereed)
    Abstract [en]

    This paper identifies the first general, explicit, and nonrandom MIMO encoder-decoder structures that guarantee optimality with respect to the diversity-multiplexing tradeoff (DMT), without employing a computationally expensive maximum-likelihood (ML) receiver. Specifically, the work establishes the DMT optimality of a class of regularized lattice decoders, and more importantly the DMT optimality of their lattice-reduction (LR)-aided linear counterparts. The results hold for all channel statistics, for all channel dimensions, and most interestingly, irrespective of the particular lattice-code applied. As a special case, it is established that the LLL-based LR-aided linear implementation of the MMSE-GDFE lattice decoder facilitates DMT optimal decoding of any lattice code at a worst-case complexity that grows at most linearly in the data rate. This represents a fundamental reduction in the decoding complexity when compared to ML decoding whose complexity is generally exponential in the rate. The results' generality lends them applicable to a plethora of pertinent communication scenarios such as quasi-static MIMO, MIMO-OFDM, ISI, cooperative-relaying, and MIMO-ARQ channels, in all of which the DMT optimality of the LR-aided linear decoder is guaranteed. The adopted approach yields insight, and motivates further study, into joint transceiver designs with an improved SNR gap to ML decoding.

  • 48.
    Jaldén, Joakim
    et al.
    KTH, School of Electrical Engineering (EES), Signal Processing. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Elia, Petros
    Sphere Decoding Complexity Exponent for Decoding Full-Rate Codes Over the Quasi-Static MIMO Channel2012In: IEEE Transactions on Information Theory, ISSN 0018-9448, E-ISSN 1557-9654, Vol. 58, no 9, p. 5785-5803Article in journal (Refereed)
    Abstract [en]

    In the setting of quasi-static multiple-input multiple-output channels, we consider the high signal-to-noise ratio (SNR) asymptotic complexity required by the sphere decoding (SD) algorithm for decoding a large class of full-rate linear space-time codes. With SD complexity having random fluctuations induced by the random channel, noise, and codeword realizations, the introduced SD complexity exponent manages to concisely describe the computational reserves required by the SD algorithm to achieve arbitrarily close to optimal decoding performance. Bounds and exact expressions for the SD complexity exponent are obtained for the decoding of large families of codes with arbitrary performance characteristics. For the particular example of decoding the recently introduced threaded cyclic-division-algebra-based codes-the only currently known explicit designs that are uniformly optimal with respect to the diversity multiplexing tradeoff-the SD complexity exponent is shown to take a particularly concise form as a non-monotonic function of the multiplexing gain. To date, the SD complexity exponent also describes the minimum known complexity of any decoder that can provably achieve a gap to maximum likelihood performance that vanishes in the high SNR limit.

  • 49.
    Jaldén, Joakim
    et al.
    KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Ottersten, Björn
    KTH, School of Electrical Engineering (EES), Signal Processing. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    On the maximal diversity order of spatial multiplexing with transmit antenna selection2007In: IEEE Transactions on Information Theory, ISSN 0018-9448, E-ISSN 1557-9654, Vol. 53, no 11, p. 4273-4276Article in journal (Refereed)
    Abstract [en]

    Zhang et al. recently derived upper and lower bounds on the achievable diversity of an N-R X N-T, i.i.d. Rayleigh fading multiple antenna system using transmit antenna selection, spatial multiplexing and a linear receiver structure. For the case of L = 2 transmitting (out of N-T available) antennas the bounds are tight and therefore specify the maximal diversity order. For the general case with L

  • 50.
    Jaldén, Joakim
    et al.
    KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Ottersten, Björn
    KTH, School of Electrical Engineering (EES), Signal Processing. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    The diversity order of the semidefinite relaxation detector2008In: IEEE Transactions on Information Theory, ISSN 0018-9448, E-ISSN 1557-9654, Vol. 54, no 4, p. 1406-1422Article in journal (Refereed)
    Abstract [en]

    In this paper, we consider the detection of binary (antipodal) signals transmitted in a spatially multiplexed fashion over a fading multiple-input-multiple-output (MIMO) channel and where the detection is done by means of semidefinite relaxation (SDR). The SDR detector is an attractive alternative to maximum-likelihood (NIL) detection since the complexity is polynomial rather than exponential. Assuming that the channel matrix is drawn with independent identically distributed (i.i.d.) real-valued Gaussian entries, we study the receiver diversity and prove that the SDR detector achieves the maximum possible diversity. Thus, the error probability of the receiver tends to zero at the same rate as the optimal NIL receiver in the high signal-to-noise ratio (SNR) limit. This significantly strengthens previous performance guarantees available for the semidefinite relaxation detector. Additionally, it proves that full diversity detection is also possible in certain scenarios when using a noncombinatorial receiver structure.

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