2015
Salamanca, Luis; Murillo-Fuentes, Juan José; Olmos, Pablo M; Perez-Cruz, Fernando; Verdu, Sergio
Approaching the DT Bound Using Linear Codes in the Short Blocklength Regime Artículo de revista
En: IEEE Communications Letters, vol. 19, no 2, pp. 123–126, 2015, ISSN: 1089-7798.
Resumen | Enlaces | BibTeX | Etiquetas: binary erasure channel, Channel Coding, Complexity theory, finite blocklength regime, LDPC codes, Maximum likelihood decoding, ML decoding, parity check codes, random coding
@article{Salamanca2014bb,
title = {Approaching the DT Bound Using Linear Codes in the Short Blocklength Regime},
author = {Luis Salamanca and Juan Jos\'{e} Murillo-Fuentes and Pablo M Olmos and Fernando Perez-Cruz and Sergio Verdu},
url = {http://ieeexplore.ieee.org/lpdocs/epic03/wrapper.htm?arnumber=6957577},
doi = {10.1109/LCOMM.2014.2371032},
issn = {1089-7798},
year = {2015},
date = {2015-02-01},
journal = {IEEE Communications Letters},
volume = {19},
number = {2},
pages = {123--126},
abstract = {The dependence-testing (DT) bound is one of the strongest achievability bounds for the binary erasure channel (BEC) in the finite block length regime. In this paper, we show that maximum likelihood decoded regular low-density paritycheck (LDPC) codes with at least 5 ones per column almost achieve the DT bound. Specifically, using quasi-regular LDPC codes with block length of 256 bits, we achieve a rate that is less than 1% away from the rate predicted by the DT bound for a word error rate below 103. The results also indicate that the maximum-likelihood solution is computationally feasible for decoding block codes over the BEC with several hundred bits.},
keywords = {binary erasure channel, Channel Coding, Complexity theory, finite blocklength regime, LDPC codes, Maximum likelihood decoding, ML decoding, parity check codes, random coding},
pubstate = {published},
tppubtype = {article}
}
The dependence-testing (DT) bound is one of the strongest achievability bounds for the binary erasure channel (BEC) in the finite block length regime. In this paper, we show that maximum likelihood decoded regular low-density paritycheck (LDPC) codes with at least 5 ones per column almost achieve the DT bound. Specifically, using quasi-regular LDPC codes with block length of 256 bits, we achieve a rate that is less than 1% away from the rate predicted by the DT bound for a word error rate below 103. The results also indicate that the maximum-likelihood solution is computationally feasible for decoding block codes over the BEC with several hundred bits.
2014
Salamanca, Luis; Murillo-Fuentes, Juan José; Olmos, Pablo M; Perez-Cruz, Fernando; Verdu, Sergio
Near DT Bound Achieving Linear Codes in the Short Blocklength Regime Artículo de revista
En: IEEE Communications Letters, vol. PP, no 99, pp. 1–1, 2014, ISSN: 1089-7798.
Resumen | Enlaces | BibTeX | Etiquetas: binary erasure channel, Channel Coding, Complexity theory, finite blocklength regime, LDPC codes, Maximum likelihood decoding, ML decoding, parity check codes, random coding
@article{Salamanca2014bb,
title = {Near DT Bound Achieving Linear Codes in the Short Blocklength Regime},
author = {Luis Salamanca and Juan Jos\'{e} Murillo-Fuentes and Pablo M Olmos and Fernando Perez-Cruz and Sergio Verdu},
url = {http://ieeexplore.ieee.org/lpdocs/epic03/wrapper.htm?arnumber=6957577},
issn = {1089-7798},
year = {2014},
date = {2014-01-01},
journal = {IEEE Communications Letters},
volume = {PP},
number = {99},
pages = {1--1},
abstract = {The dependence-testing (DT) bound is one of the strongest achievability bounds for the binary erasure channel (BEC) in the finite block length regime. In this paper, we show that maximum likelihood decoded regular low-density paritycheck (LDPC) codes with at least 5 ones per column almost achieve the DT bound. Specifically, using quasi-regular LDPC codes with block length of 256 bits, we achieve a rate that is less than 1% away from the rate predicted by the DT bound for a word error rate below 103. The results also indicate that the maximum-likelihood solution is computationally feasible for decoding block codes over the BEC with several hundred bits.},
keywords = {binary erasure channel, Channel Coding, Complexity theory, finite blocklength regime, LDPC codes, Maximum likelihood decoding, ML decoding, parity check codes, random coding},
pubstate = {published},
tppubtype = {article}
}
The dependence-testing (DT) bound is one of the strongest achievability bounds for the binary erasure channel (BEC) in the finite block length regime. In this paper, we show that maximum likelihood decoded regular low-density paritycheck (LDPC) codes with at least 5 ones per column almost achieve the DT bound. Specifically, using quasi-regular LDPC codes with block length of 256 bits, we achieve a rate that is less than 1% away from the rate predicted by the DT bound for a word error rate below 103. The results also indicate that the maximum-likelihood solution is computationally feasible for decoding block codes over the BEC with several hundred bits.
2013
Olmos, Pablo M; Murillo-Fuentes, Juan Jose; Perez-Cruz, Fernando
Tree-Structure Expectation Propagation for LDPC Decoding Over the BEC Artículo de revista
En: IEEE Transactions on Information Theory, vol. 59, no 6, pp. 3354–3377, 2013, ISSN: 0018-9448.
Resumen | Enlaces | BibTeX | Etiquetas: Algorithm design and analysis, Approximation algorithms, Approximation methods, BEC, belief propagation, Belief-propagation (BP), binary erasure channel, Complexity theory, decode low-density parity-check codes, Decoding, discrete memoryless channels, expectation propagation, finite-length analysis, LDPC codes, LDPC decoding, parity check codes, peeling-type algorithm, Probability density function, random graph evolution, Tanner graph, tree-structure expectation propagation
@article{Olmos2013b,
title = {Tree-Structure Expectation Propagation for LDPC Decoding Over the BEC},
author = {Pablo M Olmos and Juan Jose Murillo-Fuentes and Fernando Perez-Cruz},
url = {http://ieeexplore.ieee.org/lpdocs/epic03/wrapper.htm?arnumber=6451276},
issn = {0018-9448},
year = {2013},
date = {2013-01-01},
journal = {IEEE Transactions on Information Theory},
volume = {59},
number = {6},
pages = {3354--3377},
abstract = {We present the tree-structure expectation propagation (Tree-EP) algorithm to decode low-density parity-check (LDPC) codes over discrete memoryless channels (DMCs). Expectation propagation generalizes belief propagation (BP) in two ways. First, it can be used with any exponential family distribution over the cliques in the graph. Second, it can impose additional constraints on the marginal distributions. We use this second property to impose pairwise marginal constraints over pairs of variables connected to a check node of the LDPC code's Tanner graph. Thanks to these additional constraints, the Tree-EP marginal estimates for each variable in the graph are more accurate than those provided by BP. We also reformulate the Tree-EP algorithm for the binary erasure channel (BEC) as a peeling-type algorithm (TEP) and we show that the algorithm has the same computational complexity as BP and it decodes a higher fraction of errors. We describe the TEP decoding process by a set of differential equations that represents the expected residual graph evolution as a function of the code parameters. The solution of these equations is used to predict the TEP decoder performance in both the asymptotic regime and the finite-length regimes over the BEC. While the asymptotic threshold of the TEP decoder is the same as the BP decoder for regular and optimized codes, we propose a scaling law for finite-length LDPC codes, which accurately approximates the TEP improved performance and facilitates its optimization.},
keywords = {Algorithm design and analysis, Approximation algorithms, Approximation methods, BEC, belief propagation, Belief-propagation (BP), binary erasure channel, Complexity theory, decode low-density parity-check codes, Decoding, discrete memoryless channels, expectation propagation, finite-length analysis, LDPC codes, LDPC decoding, parity check codes, peeling-type algorithm, Probability density function, random graph evolution, Tanner graph, tree-structure expectation propagation},
pubstate = {published},
tppubtype = {article}
}
We present the tree-structure expectation propagation (Tree-EP) algorithm to decode low-density parity-check (LDPC) codes over discrete memoryless channels (DMCs). Expectation propagation generalizes belief propagation (BP) in two ways. First, it can be used with any exponential family distribution over the cliques in the graph. Second, it can impose additional constraints on the marginal distributions. We use this second property to impose pairwise marginal constraints over pairs of variables connected to a check node of the LDPC code's Tanner graph. Thanks to these additional constraints, the Tree-EP marginal estimates for each variable in the graph are more accurate than those provided by BP. We also reformulate the Tree-EP algorithm for the binary erasure channel (BEC) as a peeling-type algorithm (TEP) and we show that the algorithm has the same computational complexity as BP and it decodes a higher fraction of errors. We describe the TEP decoding process by a set of differential equations that represents the expected residual graph evolution as a function of the code parameters. The solution of these equations is used to predict the TEP decoder performance in both the asymptotic regime and the finite-length regimes over the BEC. While the asymptotic threshold of the TEP decoder is the same as the BP decoder for regular and optimized codes, we propose a scaling law for finite-length LDPC codes, which accurately approximates the TEP improved performance and facilitates its optimization.
Salamanca, Luis; Olmos, Pablo M; Murillo-Fuentes, Juan Jose; Perez-Cruz, Fernando
Tree Expectation Propagation for ML Decoding of LDPC Codes over the BEC Artículo de revista
En: IEEE Transactions on Communications, vol. 61, no 2, pp. 465–473, 2013, ISSN: 0090-6778.
Resumen | Enlaces | BibTeX | Etiquetas: approximate inference, Approximation algorithms, Approximation methods, BEC, binary codes, binary erasure channel, code graph, Complexity theory, equivalent complexity, Gaussian elimination method, Gaussian processes, generalized tree-structured expectation propagatio, graphical message-passing procedure, graphical models, LDPC codes, Maximum likelihood decoding, maximum likelihood solution, ML decoding, parity check codes, peeling decoder, tree expectation propagation, tree graph, Tree graphs, tree-structured expectation propagation, tree-structured expectation propagation decoder, trees (mathematics)
@article{Salamanca2013b,
title = {Tree Expectation Propagation for ML Decoding of LDPC Codes over the BEC},
author = {Luis Salamanca and Pablo M Olmos and Juan Jose Murillo-Fuentes and Fernando Perez-Cruz},
url = {http://ieeexplore.ieee.org/lpdocs/epic03/wrapper.htm?arnumber=6384612},
issn = {0090-6778},
year = {2013},
date = {2013-01-01},
journal = {IEEE Transactions on Communications},
volume = {61},
number = {2},
pages = {465--473},
abstract = {We propose a decoding algorithm for LDPC codes that achieves the maximum likelihood (ML) solution over the binary erasure channel (BEC). In this channel, the tree-structured expectation propagation (TEP) decoder improves the peeling decoder (PD) by processing check nodes of degree one and two. However, it does not achieve the ML solution, as the tree structure of the TEP allows only for approximate inference. In this paper, we provide the procedure to construct the structure needed for exact inference. This algorithm, denoted as generalized tree-structured expectation propagation (GTEP), modifies the code graph by recursively eliminating any check node and merging this information in the remaining graph. The GTEP decoder upon completion either provides the unique ML solution or a tree graph in which the number of parent nodes indicates the multiplicity of the ML solution. We also explain the algorithm as a Gaussian elimination method, relating the GTEP to other ML solutions. Compared to previous approaches, it presents an equivalent complexity, it exhibits a simpler graphical message-passing procedure and, most interesting, the algorithm can be generalized to other channels.},
keywords = {approximate inference, Approximation algorithms, Approximation methods, BEC, binary codes, binary erasure channel, code graph, Complexity theory, equivalent complexity, Gaussian elimination method, Gaussian processes, generalized tree-structured expectation propagatio, graphical message-passing procedure, graphical models, LDPC codes, Maximum likelihood decoding, maximum likelihood solution, ML decoding, parity check codes, peeling decoder, tree expectation propagation, tree graph, Tree graphs, tree-structured expectation propagation, tree-structured expectation propagation decoder, trees (mathematics)},
pubstate = {published},
tppubtype = {article}
}
We propose a decoding algorithm for LDPC codes that achieves the maximum likelihood (ML) solution over the binary erasure channel (BEC). In this channel, the tree-structured expectation propagation (TEP) decoder improves the peeling decoder (PD) by processing check nodes of degree one and two. However, it does not achieve the ML solution, as the tree structure of the TEP allows only for approximate inference. In this paper, we provide the procedure to construct the structure needed for exact inference. This algorithm, denoted as generalized tree-structured expectation propagation (GTEP), modifies the code graph by recursively eliminating any check node and merging this information in the remaining graph. The GTEP decoder upon completion either provides the unique ML solution or a tree graph in which the number of parent nodes indicates the multiplicity of the ML solution. We also explain the algorithm as a Gaussian elimination method, relating the GTEP to other ML solutions. Compared to previous approaches, it presents an equivalent complexity, it exhibits a simpler graphical message-passing procedure and, most interesting, the algorithm can be generalized to other channels.