## 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 Journal Article IEEE Communications Letters, 19 (2), pp. 123–126, 2015, ISSN: 1089-7798. Abstract | Links | BibTeX | Tags: 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 José 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 Journal Article IEEE Communications Letters, PP (99), pp. 1–1, 2014, ISSN: 1089-7798. Abstract | Links | BibTeX | Tags: 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 José 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 |

Salamanca, Luis; Olmos, Pablo M; Murillo-Fuentes, Juan Jose; Perez-Cruz, Fernando Tree Expectation Propagation for ML Decoding of LDPC Codes over the BEC Journal Article IEEE Transactions on Communications, 61 (2), pp. 465–473, 2013, ISSN: 0090-6778. Abstract | Links | BibTeX | Tags: 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. |