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Multistage compute-and-forward with multilevel lattice codes based on product constructions
- in Proc. IEEE ISIT
, 2014
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New Codes on Graphs Constructed by Connecting Spatially Coupled Chains
, 2013
"... A novel code construction based on spatially coupled low-density parity-check (SC-LDPC) codes is presented. The proposed code ensembles are described by protographs, comprised of several protograph-based chains characterizing individual SC-LDPC codes. We demonstrate that code ensembles obtained by c ..."
Abstract
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Cited by 2 (1 self)
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A novel code construction based on spatially coupled low-density parity-check (SC-LDPC) codes is presented. The proposed code ensembles are described by protographs, comprised of several protograph-based chains characterizing individual SC-LDPC codes. We demonstrate that code ensembles obtained by connecting appropriately chosen SC-LDPC code chains at specific points have improved iterative decoding thresholds compared to those of single SC-LDPC coupled chains. In addition, it is shown that the improved decoding properties of the connected ensembles result in reduced decoding complexity required to achieve a specific bit error probability. The constructed ensembles are also asymptotically good, in the sense that the minimum distance grows linearly with the block length. Finally, we show that the improved asymptotic properties of the connected chain ensembles also translate into improved finite length performance.
Threshold Saturation for Spatially-Coupled LDPC and LDGM Codes on BMS Channels
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Approaching the Rate-Distortion Limit with Spatial Coupling, Belief propagation and Decimation
, 2013
"... We investigate an encoding scheme for lossy com-pression of a binary symmetric source based on simple spatially coupled Low-Density Generator-Matrix codes. The degree of the check nodes is regular and the one of code-bits is Poisson distributed with an average depending on the compression rate. The ..."
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We investigate an encoding scheme for lossy com-pression of a binary symmetric source based on simple spatially coupled Low-Density Generator-Matrix codes. The degree of the check nodes is regular and the one of code-bits is Poisson distributed with an average depending on the compression rate. The performance of a low complexity Belief Propagation Guided Decimation algorithm is excellent. The algorithmic rate-distortion curve approaches the optimal curve of the ensemble as the width of the coupling window grows. Moreover, as the check degree grows both curves approach the ultimate Shannon rate-distortion limit. The Belief Propagation Guided Decimation encoder is based on the posterior measure of a binary symmetric test-channel. This measure can be interpreted as a random Gibbs measure at a “temperature ” directly related to the “noise level of the test-channel”. We investigate the links between the algorith-mic performance of the Belief Propagation Guided Decimation encoder and the phase diagram of this Gibbs measure. The phase diagram is investigated thanks to the cavity method of spin glass theory which predicts a number of phase transition thresholds. In particular the dynamical and condensation “phase transition temperatures” (equivalently test-channel noise thresholds) are computed. We observe that: (i) the dynamical temperature of the spatially coupled construction saturates towards the condensation temperature; (ii) for large degrees the condensation temper-ature approaches the temperature (i.e. noise level) related to the information theoretic Shannon test-channel noise parameter of rate-distortion theory. This provides heuristic insight into the excellent performance of the Belief Propagation Guided Decimation algorithm. The paper contains an introduction to the cavity method.
On the Convergence Speed of Spatially Coupled LDPC Ensembles
"... Abstract—Spatially coupled low-density parity-check codes show an outstanding performance under the low-complexity belief propagation (BP) decoding algorithm. They exhibit a peculiar convergence phenomenon above the BP threshold of the underlying non-coupled ensemble, with a wave-like convergence pr ..."
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Abstract—Spatially coupled low-density parity-check codes show an outstanding performance under the low-complexity belief propagation (BP) decoding algorithm. They exhibit a peculiar convergence phenomenon above the BP threshold of the underlying non-coupled ensemble, with a wave-like convergence propagating through the spatial dimension of the graph, allowing to approach the MAP threshold. We focus on this particularly interesting regime in between the BP and MAP thresholds. On the binary erasure channel, it has been proved [1] that the information propagates with a constant speed toward the successful decoding solution. We derive an upper bound on the propagation speed, only depending on the basic parameters of the spatially coupled code ensemble such as degree distribution and the coupling factor w. We illustrate the convergence speed of different code ensembles by simulation results, and show how optimizing degree profiles helps to speed up the convergence. Index Terms—Spatially coupled LDPC ensembles, belief prop-agation, density evolution, convergence speed I.
