@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}

}

@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}

}

@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}

}

@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}

}

@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}

}

@article{Bravo-Santos2013,

title = {Polar Codes for Gaussian Degraded Relay Channels},

author = {\'{A}ngel M Bravo-Santos},

url = {http://ieeexplore.ieee.org/articleDetails.jsp?arnumber=6412681},

issn = {1089-7798},

year  = {2013},

date = {2013-01-01},

journal = {IEEE Communications Letters},

volume = {17},

number = {2},

pages = {365--368},

publisher = {IEEE},

abstract = {In this paper we apply polar codes for the Gaussian degraded relay channel. We study the conditions to be satisfied by the codes and provide an efficient method for constructing them. The relay-destination link is special because the noise is the sum of two components: the Gaussian noise and the signals from the source. We study this link and provide the log-likelihood expression to be used by the polar code detector. We perform simulations of the channel and the results show that polar codes of high rate and large codeword length are closer to the theoretical limit than other good codes.},

keywords = {channel capacity, Channel Coding, Decoding, Encoding, Gaussian channels, Gaussian degraded relay channel, Gaussian noise, Gaussian-degraded relay channels, log-likelihood expression, Markov coding, Noise, parity check codes, polar code detector, polar codes, relay-destination link, Relays, Vectors},

pubstate = {published},

tppubtype = {article}

}

@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}

}

@article{Salamanca2012b,

title = {Bayesian Equalization for LDPC Channel Decoding},

author = {Luis Salamanca and Juan Jose Murillo-Fuentes and Fernando Perez-Cruz},

url = {http://ieeexplore.ieee.org/lpdocs/epic03/wrapper.htm?arnumber=6129544},

issn = {1053-587X},

year  = {2012},

date = {2012-01-01},

journal = {IEEE Transactions on Signal Processing},

volume = {60},

number = {5},

pages = {2672--2676},

abstract = {We describe the channel equalization problem, and its prior estimate of the channel state information (CSI), as a joint Bayesian estimation problem to improve each symbol posterior estimates at the input of the channel decoder. Our approach takes into consideration not only the uncertainty due to the noise in the channel, but also the uncertainty in the CSI estimate. However, this solution cannot be computed in linear time, because it depends on all the transmitted symbols. Hence, we also put forward an approximation for each symbol's posterior, using the expectation propagation algorithm, which is optimal from the Kullback-Leibler divergence viewpoint and yields an equalization with a complexity identical to the BCJR algorithm. We also use a graphical model representation of the full posterior, in which the proposed approximation can be readily understood. The proposed posterior estimates are more accurate than those computed using the ML estimate for the CSI. In order to illustrate this point, we measure the error rate at the output of a low-density parity-check decoder, which needs the exact posterior for each symbol to detect the incoming word and it is sensitive to a mismatch in those posterior estimates. For example, for QPSK modulation and a channel with three taps, we can expect gains over 0.5 dB with same computational complexity as the ML receiver.},

keywords = {Approximation methods, Bayes methods, Bayesian equalization, Bayesian estimation problem, Bayesian inference, Bayesian methods, BCJR (Bahl\textendashCocke\textendashJelinek\textendashRaviv) algorithm, BCJR algorithm, Channel Coding, channel decoding, channel equalization, channel equalization problem, Channel estimation, channel state information, CSI, Decoding, equalisers, Equalizers, expectation propagation, expectation propagation algorithm, fading channels, graphical model representation, intersymbol interference, Kullback-Leibler divergence, LDPC, LDPC coding, low-density parity-check decoder, Modulation, parity check codes, symbol posterior estimates, Training},

pubstate = {published},

tppubtype = {article}

}

@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}

}

@article{Olmos2011c,

title = {Tree-Structured Expectation Propagation for Decoding Finite-Length LDPC Codes},

author = {Pablo M Olmos and Juan Jose Murillo-Fuentes and Fernando Perez-Cruz},

url = {http://ieeexplore.ieee.org/lpdocs/epic03/wrapper.htm?arnumber=5682215},

issn = {1089-7798},

year  = {2011},

date = {2011-01-01},

journal = {IEEE Communications Letters},

volume = {15},

number = {2},

pages = {235--237},

abstract = {In this paper, we propose Tree-structured Expectation Propagation (TEP) algorithm to decode finite-length Low-Density Parity-Check (LDPC) codes. The TEP decoder is able to continue decoding once the standard Belief Propagation (BP) decoder fails, presenting the same computational complexity as the BP decoder. The BP algorithm is dominated by the presence of stopping sets (SSs) in the code graph. We show that the TEP decoder, without previous knowledge of the graph, naturally avoids some fairly common SSs. This results in a significant improvement in the system performance.},

keywords = {belief propagation decoder, BP algorithm, BP decoder, code graph, communication complexity, computational complexity, Decoding, finite-length analysis, finite-length low-density parity-check code, LDPC code, LDPC decoding, parity check codes, radiowave propagation, stopping set, TEP algorithm, TEP decoder, tree-structured expectation propagation},

pubstate = {published},

tppubtype = {article}

}

@article{Olmos2010a,

title = {Joint Nonlinear Channel Equalization and Soft LDPC Decoding with Gaussian Processes},

author = {Pablo M Olmos and Juan Jose Murillo-Fuentes and Fernando Perez-Cruz},

url = {http://ieeexplore.ieee.org/lpdocs/epic03/wrapper.htm?arnumber=5290078},

issn = {1053-587X},

year  = {2010},

date = {2010-01-01},

journal = {IEEE Transactions on Signal Processing},

volume = {58},

number = {3},

pages = {1183--1192},

abstract = {In this paper, we introduce a new approach for nonlinear equalization based on Gaussian processes for classification (GPC). We propose to measure the performance of this equalizer after a low-density parity-check channel decoder has detected the received sequence. Typically, most channel equalizers concentrate on reducing the bit error rate, instead of providing accurate posterior probability estimates. We show that the accuracy of these estimates is essential for optimal performance of the channel decoder and that the error rate output by the equalizer might be irrelevant to understand the performance of the overall communication receiver. In this sense, GPC is a Bayesian nonlinear classification tool that provides accurate posterior probability estimates with short training sequences. In the experimental section, we compare the proposed GPC-based equalizer with state-of-the-art solutions to illustrate its improved performance.},

keywords = {Bayesian nonlinear classification tool, Bit error rate, Channel Coding, channel equalizers, Channel estimation, Coding, equalisers, equalization, error statistics, Gaussian processes, GPC, joint nonlinear channel equalization, low-density parity-check (LDPC), low-density parity-check channel decoder, Machine learning, nonlinear channel, nonlinear codes, parity check codes, posterior probability estimates, soft LDPC decoding, soft-decoding, support vector machine (SVM)},

pubstate = {published},

tppubtype = {article}

}

@article{Fresia2010,

title = {Joint Source and Channel Coding},

author = {Maria Fresia and Fernando Perez-Cruz and Vincent H Poor and Sergio Verdu},

url = {http://ieeexplore.ieee.org/lpdocs/epic03/wrapper.htm?arnumber=5563107},

issn = {1053-5888},

year  = {2010},

date = {2010-01-01},

journal = {IEEE Signal Processing Magazine},

volume = {27},

number = {6},

pages = {104--113},

abstract = {The objectives of this article are two-fold: First, to present the problem of joint source and channel (JSC) coding from a graphical model perspective and second, to propose a structure that uses a new graphical model for jointly encoding and decoding a redundant source. In the first part of the article, relevant contributions to JSC coding, ranging from the Slepian-Wolf problem to joint decoding of variable length codes with state-of-the-art source codes, are reviewed and summarized. In the second part, a double low-density parity-check (LDPC) code for JSC coding is proposed. The double LDPC code can be decoded as a single bipartite graph using standard belief propagation (BP) and its limiting performance is analyzed by using extrinsic information transfer (EXIT) chart approximations.},

keywords = {belief propagation, Channel Coding, combined source-channel coding, Decoding, Encoding, graphical model, Hidden Markov models, Iterative decoding, joint source channel coding, JSC coding, LDPC code, low density parity check code, Markov processes, parity check codes, Slepian-Wolf problem, variable length codes},

pubstate = {published},

tppubtype = {article}

}