2015
Olmos, Pablo M; Urbanke, Rudiger
A Scaling Law to Predict the Finite-Length Performance of Spatially-Coupled LDPC Codes Artículo de revista
En: IEEE Transactions on Information Theory, vol. 61, no 6, pp. 3164–3184, 2015, ISSN: 0018-9448.
Resumen | Enlaces | BibTeX | Etiquetas: asymptotic analysis, asymptotic properties, binary erasure channel, Channel Coding, Codes on graphs, Couplings, Decoding, Differential equations, error probability, finite length performance, finite length spatially coupled code, finite-length code performance, finite-length performance, Iterative decoding, iterative decoding thresholds, Journal, parity check codes, Probability, SC-LDPC codes, scaling law, Sockets, spatially coupled LDPC codes, spatially-coupled LDPC codes
@article{Olmos2015bb,
title = {A Scaling Law to Predict the Finite-Length Performance of Spatially-Coupled LDPC Codes},
author = {Pablo M Olmos and Rudiger Urbanke},
url = {http://ieeexplore.ieee.org/lpdocs/epic03/wrapper.htm?arnumber=7086074},
doi = {10.1109/TIT.2015.2422816},
issn = {0018-9448},
year = {2015},
date = {2015-06-01},
journal = {IEEE Transactions on Information Theory},
volume = {61},
number = {6},
pages = {3164--3184},
abstract = {Spatially-coupled low-density parity-check (SC-LDPC) codes are known to have excellent asymptotic properties. Much less is known regarding their finite-length performance. We propose a scaling law to predict the error probability of finite-length spatially coupled code ensembles when transmission takes place over the binary erasure channel. We discuss how the parameters of the scaling law are connected to fundamental quantities appearing in the asymptotic analysis of these ensembles and we verify that the predictions of the scaling law fit well to the data derived from simulations over a wide range of parameters. The ultimate goal of this line of research is to develop analytic tools for the design of SC-LDPC codes under practical constraints.},
keywords = {asymptotic analysis, asymptotic properties, binary erasure channel, Channel Coding, Codes on graphs, Couplings, Decoding, Differential equations, error probability, finite length performance, finite length spatially coupled code, finite-length code performance, finite-length performance, Iterative decoding, iterative decoding thresholds, Journal, parity check codes, Probability, SC-LDPC codes, scaling law, Sockets, spatially coupled LDPC codes, spatially-coupled LDPC codes},
pubstate = {published},
tppubtype = {article}
}
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}
}
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}
}
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}
}
Salamanca, Luis; Olmos, Pablo M; Perez-Cruz, Fernando; Murillo-Fuentes, Juan Jose
Tree-Structured Expectation Propagation for LDPC Decoding over BMS Channels Artículo de revista
En: IEEE Transactions on Communications, vol. 61, no 10, pp. 4086–4095, 2013, ISSN: 0090-6778.
Resumen | Enlaces | BibTeX | Etiquetas: Approximation algorithms, Approximation methods, BEC, belief propagation, binary erasure channel, binary memoryless symmetric channels, BMS channels, Channel Coding, Complexity theory, convolutional codes, convolutional low-density parity-check codes, Decoding, decoding block, expectation propagation, finite-length codes, LDPC decoding, message-passing algorithm, parity check codes, Probability density function, sparse linear codes, TEP algorithm, tree-structured expectation propagation, trees (mathematics), Vegetation
@article{Salamanca2013a,
title = {Tree-Structured Expectation Propagation for LDPC Decoding over BMS Channels},
author = {Luis Salamanca and Pablo M Olmos and Fernando Perez-Cruz and Juan Jose Murillo-Fuentes},
url = {http://ieeexplore.ieee.org/lpdocs/epic03/wrapper.htm?arnumber=6587624},
issn = {0090-6778},
year = {2013},
date = {2013-01-01},
journal = {IEEE Transactions on Communications},
volume = {61},
number = {10},
pages = {4086--4095},
abstract = {In this paper, we put forward the tree-structured expectation propagation (TEP) algorithm for decoding block and convolutional low-density parity-check codes over any binary channel. We have already shown that TEP improves belief propagation (BP) over the binary erasure channel (BEC) by imposing marginal constraints over a set of pairs of variables that form a tree or a forest. The TEP decoder is a message-passing algorithm that sequentially builds a tree/forest of erased variables to capture additional information disregarded by the standard BP decoder, which leads to a noticeable reduction of the error rate for finite-length codes. In this paper, we show how the TEP can be extended to any channel, specifically to binary memoryless symmetric (BMS) channels. We particularly focus on how the TEP algorithm can be adapted for any channel model and, more importantly, how to choose the tree/forest to keep the gains observed for block and convolutional LDPC codes over the BEC.},
keywords = {Approximation algorithms, Approximation methods, BEC, belief propagation, binary erasure channel, binary memoryless symmetric channels, BMS channels, Channel Coding, Complexity theory, convolutional codes, convolutional low-density parity-check codes, Decoding, decoding block, expectation propagation, finite-length codes, LDPC decoding, message-passing algorithm, parity check codes, Probability density function, sparse linear codes, TEP algorithm, tree-structured expectation propagation, trees (mathematics), Vegetation},
pubstate = {published},
tppubtype = {article}
}
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}
}
2012
Olmos, Pablo M; Salamanca, Luis; Murillo-Fuentes, Juan Jose; Perez-Cruz, Fernando
On the Design of LDPC-Convolutional Ensembles Using the TEP Decoder Artículo de revista
En: IEEE Communications Letters, vol. 16, no 5, pp. 726–729, 2012, ISSN: 1089-7798.
Resumen | Enlaces | BibTeX | Etiquetas: belief propagation decoding, binary erasure channel, channel capacity, Complexity theory, convolutional codes, convolutional LDPC codes, Decoding, design, Error analysis, finite-length analysis, Iterative decoding, LDPC-convolutional ensemble design, LDPCC code decoding, low-density parity-check convolutional code, parity check codes, tree-expectation propagation decoder, tree-structured expectation propagation, window-sliding scheme
@article{Olmos2012b,
title = {On the Design of LDPC-Convolutional Ensembles Using the TEP Decoder},
author = {Pablo M Olmos and Luis Salamanca and Juan Jose Murillo-Fuentes and Fernando Perez-Cruz},
url = {http://ieeexplore.ieee.org/lpdocs/epic03/wrapper.htm?arnumber=6168872},
issn = {1089-7798},
year = {2012},
date = {2012-01-01},
journal = {IEEE Communications Letters},
volume = {16},
number = {5},
pages = {726--729},
abstract = {Low-density parity-check convolutional (LDPCC) codes asymptotically achieve channel capacity under belief propagation (BP) decoding. In this paper, we decode LDPCC codes using the Tree-Expectation Propagation (TEP) decoder, recently proposed as an alternative decoding method to the BP algorithm for the binary erasure channel (BEC). We show that, for LDPCC codes, the TEP decoder improves the BP solution with a comparable complexity or, alternatively, it allows using shorter codes to achieve similar error rates. We also propose a window-sliding scheme for the TEP decoder to reduce the decoding latency.},
keywords = {belief propagation decoding, binary erasure channel, channel capacity, Complexity theory, convolutional codes, convolutional LDPC codes, Decoding, design, Error analysis, finite-length analysis, Iterative decoding, LDPC-convolutional ensemble design, LDPCC code decoding, low-density parity-check convolutional code, parity check codes, tree-expectation propagation decoder, tree-structured expectation propagation, window-sliding scheme},
pubstate = {published},
tppubtype = {article}
}