@article{Stinner2016,

title = {On the Waterfall Performance of Finite-Length SC-LDPC Codes Constructed From Protographs},

author = {Markus Stinner and Pablo M Olmos},

url = {http://ieeexplore.ieee.org/lpdocs/epic03/wrapper.htm?arnumber=7339427},

doi = {10.1109/JSAC.2015.2504279},

issn = {0733-8716},

year  = {2016},

date = {2016-02-01},

journal = {IEEE Journal on Selected Areas in Communications},

volume = {34},

number = {2},

pages = {345--361},

abstract = {An analysis of spatially coupled low-density parity-check (SC-LDPC) codes constructed from protographs is proposed. Given the protograph used to generate the SC-LDPC code ensemble, a set of scaling parameters to characterize the average finite-length performance in the waterfall region is computed. The error performance of structured SC-LDPC code ensembles is shown to follow a scaling law similar to that of unstructured randomly constructed SC-LDPC codes. Under a finite-length perspective, some of the most relevant SC-LDPC protograph structures proposed to date are compared. The analysis reveals significant differences in their finite-length scaling behavior, which is corroborated by simulation. Spatially coupled repeat-accumulate codes present excellent finite-length performance, as they outperform in the waterfall region SC-LDPC codes of the same rate and better asymptotic thresholds.},

keywords = {Analytical models, capacity-achieving codes, Complexity theory, Couplings, Decoding, Encoding, finite-length analysis, Iterative decoding, Low-density parity-check (LDPC) codes, spatially coupled LDPC codes constructed from prot},

pubstate = {published},

tppubtype = {article}

}

@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{Yang2014bb,

title = {Quasi-Static Multiple-Antenna Fading Channels at Finite Blocklength},

author = {Wei Yang and Giuseppe Durisi and Tobias Koch and Yury Polyanskiy},

url = {http://ieeexplore.ieee.org/articleDetails.jsp?arnumber=6802432 http://arxiv.org/abs/1311.2012},

issn = {0018-9448},

year  = {2014},

date = {2014-01-01},

journal = {IEEE Transactions on Information Theory},

volume = {60},

number = {7},

pages = {4232--4265},

publisher = {IEEE},

abstract = {This paper investigates the maximal achievable rate for a given blocklength and error probability over quasi-static multiple-input multiple-output fading channels, with and without channel state information at the transmitter and/or the receiver. The principal finding is that outage capacity, despite being an asymptotic quantity, is a sharp proxy for the finite-blocklength fundamental limits of slow-fading channels. Specifically, the channel dispersion is shown to be zero regardless of whether the fading realizations are available at both transmitter and receiver, at only one of them, or at neither of them. These results follow from analytically tractable converse and achievability bounds. Numerical evaluation of these bounds verifies that zero dispersion may indeed imply fast convergence to the outage capacity as the blocklength increases. In the example of a particular 1 $,times,$ 2 single-input multiple-output Rician fading channel, the blocklength required to achieve 90% of capacity is about an order of magnitude smaller compared with the blocklength required for an AWGN channel with the same capacity. For this specific scenario, the coding/decoding schemes adopted in the LTE-Advanced standard are benchmarked against the finite-blocklength achievability and converse bounds.},

keywords = {channel dispersion, Decoding, error probability, finite blocklength regime, MIMO, MIMO channel, outage probability, quasi-static fading channel, Rayleigh channels, Receivers, Transmitters},

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{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{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}

}