434 research outputs found

    A Unified Framework for Linear-Programming Based Communication Receivers

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    It is shown that a large class of communication systems which admit a sum-product algorithm (SPA) based receiver also admit a corresponding linear-programming (LP) based receiver. The two receivers have a relationship defined by the local structure of the underlying graphical model, and are inhibited by the same phenomenon, which we call 'pseudoconfigurations'. This concept is a generalization of the concept of 'pseudocodewords' for linear codes. It is proved that the LP receiver has the 'maximum likelihood certificate' property, and that the receiver output is the lowest cost pseudoconfiguration. Equivalence of graph-cover pseudoconfigurations and linear-programming pseudoconfigurations is also proved. A concept of 'system pseudodistance' is defined which generalizes the existing concept of pseudodistance for binary and nonbinary linear codes. It is demonstrated how the LP design technique may be applied to the problem of joint equalization and decoding of coded transmissions over a frequency selective channel, and a simulation-based analysis of the error events of the resulting LP receiver is also provided. For this particular application, the proposed LP receiver is shown to be competitive with other receivers, and to be capable of outperforming turbo equalization in bit and frame error rate performance.Comment: 13 pages, 6 figures. To appear in the IEEE Transactions on Communication

    Proving Threshold Saturation for Nonbinary SC-LDPC Codes on the Binary Erasure Channel

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    We analyze nonbinary spatially-coupled low-density parity-check (SC-LDPC) codes built on the general linear group for transmission over the binary erasure channel. We prove threshold saturation of the belief propagation decoding to the potential threshold, by generalizing the proof technique based on potential functions recently introduced by Yedla et al.. The existence of the potential function is also discussed for a vector sparse system in the general case, and some existence conditions are developed. We finally give density evolution and simulation results for several nonbinary SC-LDPC code ensembles.Comment: in Proc. 2014 XXXIth URSI General Assembly and Scientific Symposium, URSI GASS, Beijing, China, August 16-23, 2014. Invited pape

    Design and Analysis of Nonbinary LDPC Codes for Arbitrary Discrete-Memoryless Channels

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    We present an analysis, under iterative decoding, of coset LDPC codes over GF(q), designed for use over arbitrary discrete-memoryless channels (particularly nonbinary and asymmetric channels). We use a random-coset analysis to produce an effect that is similar to output-symmetry with binary channels. We show that the random selection of the nonzero elements of the GF(q) parity-check matrix induces a permutation-invariance property on the densities of the decoder messages, which simplifies their analysis and approximation. We generalize several properties, including symmetry and stability from the analysis of binary LDPC codes. We show that under a Gaussian approximation, the entire q-1 dimensional distribution of the vector messages is described by a single scalar parameter (like the distributions of binary LDPC messages). We apply this property to develop EXIT charts for our codes. We use appropriately designed signal constellations to obtain substantial shaping gains. Simulation results indicate that our codes outperform multilevel codes at short block lengths. We also present simulation results for the AWGN channel, including results within 0.56 dB of the unconstrained Shannon limit (i.e. not restricted to any signal constellation) at a spectral efficiency of 6 bits/s/Hz.Comment: To appear, IEEE Transactions on Information Theory, (submitted October 2004, revised and accepted for publication, November 2005). The material in this paper was presented in part at the 41st Allerton Conference on Communications, Control and Computing, October 2003 and at the 2005 IEEE International Symposium on Information Theor

    Nonbinary Spatially-Coupled LDPC Codes on the Binary Erasure Channel

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    We analyze the asymptotic performance of nonbinary spatially-coupled low-density parity-check (SC-LDPC) codes built on the general linear group, when the transmission takes place over the binary erasure channel. We propose an efficient method to derive an upper bound to the maximum a posteriori probability (MAP) threshold for nonbinary LDPC codes, and observe that the MAP performance of regular LDPC codes improves with the alphabet size. We then consider nonbinary SC-LDPC codes. We show that the same threshold saturation effect experienced by binary SC-LDPC codes occurs for the nonbinary codes, hence we conjecture that the BP threshold for large termination length approaches the MAP threshold of the underlying regular ensemble.Comment: Submitted to IEEE International Conference on Communications 201

    Minimum Pseudoweight Analysis of 3-Dimensional Turbo Codes

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    In this work, we consider pseudocodewords of (relaxed) linear programming (LP) decoding of 3-dimensional turbo codes (3D-TCs). We present a relaxed LP decoder for 3D-TCs, adapting the relaxed LP decoder for conventional turbo codes proposed by Feldman in his thesis. We show that the 3D-TC polytope is proper and CC-symmetric, and make a connection to finite graph covers of the 3D-TC factor graph. This connection is used to show that the support set of any pseudocodeword is a stopping set of iterative decoding of 3D-TCs using maximum a posteriori constituent decoders on the binary erasure channel. Furthermore, we compute ensemble-average pseudoweight enumerators of 3D-TCs and perform a finite-length minimum pseudoweight analysis for small cover degrees. Also, an explicit description of the fundamental cone of the 3D-TC polytope is given. Finally, we present an extensive numerical study of small-to-medium block length 3D-TCs, which shows that 1) typically (i.e., in most cases) when the minimum distance dmind_{\rm min} and/or the stopping distance hminh_{\rm min} is high, the minimum pseudoweight (on the additive white Gaussian noise channel) is strictly smaller than both the dmind_{\rm min} and the hminh_{\rm min}, and 2) the minimum pseudoweight grows with the block length, at least for small-to-medium block lengths.Comment: To appear in IEEE Transactions on Communication

    An Iterative Joint Linear-Programming Decoding of LDPC Codes and Finite-State Channels

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    In this paper, we introduce an efficient iterative solver for the joint linear-programming (LP) decoding of low-density parity-check (LDPC) codes and finite-state channels (FSCs). In particular, we extend the approach of iterative approximate LP decoding, proposed by Vontobel and Koetter and explored by Burshtein, to this problem. By taking advantage of the dual-domain structure of the joint decoding LP, we obtain a convergent iterative algorithm for joint LP decoding whose structure is similar to BCJR-based turbo equalization (TE). The result is a joint iterative decoder whose complexity is similar to TE but whose performance is similar to joint LP decoding. The main advantage of this decoder is that it appears to provide the predictability of joint LP decoding and superior performance with the computational complexity of TE.Comment: To appear in Proc. IEEE ICC 2011, Kyoto, Japan, June 5-9, 201

    Spatially Coupled Turbo Codes: Principles and Finite Length Performance

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    In this paper, we give an overview of spatially coupled turbo codes (SC-TCs), the spatial coupling of parallel and serially concatenated convolutional codes, recently introduced by the authors. For presentation purposes, we focus on spatially coupled serially concatenated codes (SC-SCCs). We review the main principles of SC-TCs and discuss their exact density evolution (DE) analysis on the binary erasure channel. We also consider the construction of a family of rate-compatible SC-SCCs with simple 4-state component encoders. For all considered code rates, threshold saturation of the belief propagation (BP) to the maximum a posteriori threshold of the uncoupled ensemble is demonstrated, and it is shown that the BP threshold approaches the Shannon limit as the coupling memory increases. Finally we give some simulation results for finite lengths.Comment: Invited paper, IEEE Int. Symp. Wireless Communications Systems (ISWCS), Aug. 201
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