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IEEE International Symposium on Personal, Indoor and Mobile Radio Communications (PIMRC)

Modeling BP decoding error events with the LDPC codes of the DVB-S2 standard

Jean-Christophe Sibel, Matthieu Crussière, Jean‐François Hèlard

Published Sep 1, 2014• 1 citation
Publisher

Abstract

In this paper, we focus on the behavior of the Belief Propagation (BP) algorithm when decoding the Low-Density Parity-Check (LDPC) code of rate 3/4 in the DVB-S2 standard. By studying the topological structure of its Tanner graph, we raise properties inherent to the degree distribution that turns out to be strongly correlated with the decoding failures. The irregularity of the degrees seriously damages the performance, visible by an abrupt error floor. We accordingly propose a novel model of the error events based on the degree distribution which helps simulate typical error events and observing the flaws of the DVB-S2 code. This work could be used as a good basis to design future codes with a better decoding behavior, especially in the error floor region.

DOI
10.1109/pimrc.2014.7136294

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In this paper, we focus on the behavior of the Belief Propagation (BP) algorithm when decoding the Low-Density Parity-Check (LDPC) code of rate 3/4 in the DVB-S2 standard. By studying the topological structure of its Tanner graph, we raise properties inherent to the degree distribution that turns out to be strongly correlated with the decoding failures. The irregularity of the degrees seriously damages the performance, visible by an abrupt error floor. We accordingly propose a novel model of the error events based on the degree distribution which helps simulate typical error events and observing the flaws of the DVB-S2 code. This work could be used as a good basis to design future codes with a better decoding behavior, especially in the error floor region.
The DVB-S2 standard has been revealed a reliable standard for data transmission thanks to the LDPC codes. The waterfall of the bit-error rate is very abrupt to reach low values of order 10^(-10) in the error floor. In this paper, we propose a novel investigation on the iterative decoding of these codes by the Belief Propagation algorithm on Gaussian channels. Introducing definitions of persistent and created errors, we analyze them according to the degrees of the Tanner graph nodes and the noise power of the channel. We show that the two-degree bits used to accelerate the encoding process of the DVB-S2 are responsible for most decoding errors. This result could help design DVB-S2 codes in a more appropriate way, for instance avoiding the use of BCH codes to tackle the error floor.
At the heart of modern coding theory lies the fact that low-density parity-check (LDPC) codes can be efficiently decoded by belief propagation (BP). The BP is an inference algorithm which operates on a graphical model of a code, and lends itself to low-complexity and high-speed implementations, making it the algorithm of choice in many applications. It has unprecedentedly good error rate performance, so good that when decoded by the BP, LDPC codes approach theoretical limits of channel capacity. However, this capacity approaching property holds only in the asymptotic limit of code length, while codes of practical lengths suffer abrupt performance degradation in the low noise regime known as the error floor phenomenon. Our study of error floor has led to an interesting and surprising finding that it is possible to design iterative decoders which are much simpler yet better than belief propagation! These decoders do not propagate beliefs but a rather different kind of messages that reflect the local structure of the code graph. This has opened a plethora of exciting theoretical problems and applications. This paper introduces this new paradigm.
We consider communication over binary memoryless symmetric channels using random elements from irregular low density parity check code (LDPC) ensembles, and belief propagation (BP) decoding.Under the assumption that the corresponding Tanner graph includes a non-vanishing fraction of degree 2 variable nodes, we determine the large blocklength behavior of the bit error rate for noise levels below threshold.More precisely, we show that the BP bit error rate is, asymptotically, F/n, where n is the blocklength and F an explicit constant.Surprisingly, this is the same behavior found for maximum likelihood (ML) decoding, implying that the BP and ML error floor are asymptotically equal.
In this paper, we focus on the Generalized Belief Propagation (GBP) algorithm to solve trapping sets in Low-Density Parity-Check (LDPC) codes. Trapping sets are topological structures in Tanner graphs of LDPC codes that are not correctly decoded by Belief Propagation (BP), leading to exhibit an error-floor in the Bit-Error Rate (BER). Stemming from statistical physics of spin glasses, GBP consists in passing messages between clusters of Tanner graph nodes in another graph called the region-graph. Here, we introduce a specific clustering of nodes, based on a novel local loopfree principle, that breaks trapping sets such that the resulting region-graph is locally loopfree. We then construct a hybrid decoder made of BP and GBP that proves to be a powerful decoder as it clearly improves the BER and defeats the error-floor.
Abstract—In this paper, we focus on the Generalized Belief Propagation (GBP) algorithm to solve trapping sets in Low-Density Parity-Check (LDPC) codes. Trapping sets are topo-logical structures in Tanner graphs of LDPC codes that are not correctly decoded by Belief Propagation (BP), leading to exhibit an error-floor in the Bit-Error Rate (BER). Stemming from statistical physics of spin glasses, GBP consists in passing messages between clusters of Tanner graph nodes in another graph called the region-graph. Here, we introduce a specific clustering of nodes, based on a novel local loopfree principle, that breaks trapping sets such that the resulting region-graph is locally loopfree. We then construct a hybrid decoder made of BP and GBP that proves to be a powerful decoder as it clearly improves the BER and defeats the error-floor. Index Terms—LDPC codes, Generalized Belief Propagation, trapping sets, error-floor, local clustering
A novel belief propagation(BP) decoding algorithm for convolutional low-density parity-check codes is proposed.The proposed algorithm raises the efficiency of updating the variable information by applying feedback information at each decoding iteration and employs the weighting factor to reduce the error propagation caused by the cycles in the Tanner graph,thus yielding a faster convergence of the decoding.Simulation results show that an error performance better than that of the existing belief propagation algorithm can be achieved,while the 5/8 decoding delay and the computation complexity are effectively reduced.Compared with the existing BP,the proposed algorithm achieves a gain of 0.16dB at the BER of 10-6 with the same number of iterations.