An application of generalized belief propagation: splitting trapping sets in LDPC codes

Sibel, Jean-Christophe; Reynal, Sylvain; Declercq, David

doi:10.1109/isit.2014.6874924

Cited by 5 publications

(5 citation statements)

References 19 publications

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“…Theorem 2. Assume that, for a given region graph, the update function Υ is contractive with parameter 1 − ν 2 as defined in (12). Then, parent-to-child GBP has a unique fixed point m * and the message sequence {m (t) P →R } ∞ t=1 generated by the SGBP algorithm has the following properties:…”

Section: A Convergence Rate Of Sgbp Algorithmmentioning

confidence: 99%

“…Theorem 2. Assume that, for a given region graph, the update function Υ is contractive with parameter 1 − ν 2 as defined in (12). Then, parent-to-child GBP has a unique fixed point m * and the message sequence {m corresponds to those edges of the region graph that perform deterministic update rule (as stated in Algorithm 1 and Remark 3), while m * E∼1 corresponds to the edges that run the stochastic algorithm.…”

Section: A Convergence Rate Of Sgbp Algorithmmentioning

confidence: 99%

“…In their proposed algorithm, local computation is performed by a group of nodes instead of a single node as in BP. According to many empirical observations, GBP outperforms BP in many situations; [9], [10], [11], [12]. However, although GBP algorithm provides accurate results in terms of marginal distribution, it suffers from high order of computation complexity, specially in case of large alphabet size.To overcome the second aforementioned deficiency of BP, lots of research have been conducted to reduce BP complexity for different applications (e.g., refer to [20]).…”

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confidence: 99%

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Low-complexity stochastic Generalized Belief Propagation

Haddadpour

Siavoshani

Noshad

2016

2016 IEEE International Symposium on Information Theory (ISIT)

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The generalized belief propagation (GBP), introduced by Yedidia et al., is an extension of the belief propagation (BP) algorithm, which is widely used in different problems involved in calculating exact or approximate marginals of probability distributions. In many problems, it has been observed that the accuracy of GBP considerably outperforms that of BP. However, because in general the computational complexity of GBP is higher than BP, its application is limited in practice.In this paper, we introduce a stochastic version of GBP called stochastic generalized belief propagation (SGBP) that can be considered as an extension to the stochastic BP (SBP) algorithm introduced by Noorshams et al. They have shown that SBP reduces the complexity per iteration of BP by an order of magnitude in alphabet size. In contrast to SBP, SGBP can reduce the computation complexity if certain topological conditions are met by the region graph associated to a graphical model. However, this reduction can be larger than only one order of magnitude in alphabet size. In this paper, we characterize these conditions and the amount of computation gain that we can obtain by using SGBP. Finally, using similar proof techniques employed by Noorshams et al., for general graphical models satisfy contraction conditions, we prove the asymptotic convergence of SGBP to the unique GBP fixed point, as well as providing non-asymptotic upper bounds on the mean square error and on the high probability error. F. Haddadpour is with Electrical Engineering

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Section: A Convergence Rate Of Sgbp Algorithmmentioning

confidence: 99%

“…Theorem 2. Assume that, for a given region graph, the update function Υ is contractive with parameter 1 − ν 2 as defined in (12). Then, parent-to-child GBP has a unique fixed point m * and the message sequence {m corresponds to those edges of the region graph that perform deterministic update rule (as stated in Algorithm 1 and Remark 3), while m * E∼1 corresponds to the edges that run the stochastic algorithm.…”

Section: A Convergence Rate Of Sgbp Algorithmmentioning

confidence: 99%

mentioning

confidence: 99%

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Low-complexity stochastic Generalized Belief Propagation

Haddadpour

Siavoshani

Noshad

2016

2016 IEEE International Symposium on Information Theory (ISIT)

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“…Namely, they empirically demonstrated that Z R,GBP {b R } can be used to approximate very well the capacity of certain 2D runlengthlimited constraints, whereas Z BP {b i , b a } in general yielded poorer approximations. More empirical results showing that GBP outperforms BP in terms of estimating marginals can be found in [11], [12], [13], [14].…”

Section: Introductionmentioning

confidence: 99%

Generalized belief propagation for estimating the partition function of the 2D Ising model

Chan

Siavoshani

Jaggi

et al. 2015

2015 IEEE International Symposium on Information Theory (ISIT)

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Recent empirical results have demonstrated that generalized belief propagation (GBP) can be used to closely estimate the capacity of certain 2D runlength-limited constraints. We provide a partial analytical validation of these observations by showing that GBP yields a lower bound on the partition function of 2D Ising models with restricted grid size. While previous papers have proved that belief propagation (BP) can be used to obtain a lower bound on the partition function of 2D Ising models, this paper is the first work that analyzes GBP-based partition function approximations of 2D Ising models.

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“…Results are very impressive but the new decoders are hard to adapt on strongly irregular codes. Another decoder, the generalized BP described in [12], is well fitted to treat trapping sets but only for codes of moderate size and degrees. The third strategy proposes decoders with a post-processing task.…”

Section: Introductionmentioning

confidence: 99%

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

Sibel

Crussière

Hélard

2014

2014 IEEE 25th Annual International Symposium on Personal, Indoor, and Mobile Radio Communication (PIMRC)

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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.

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An application of generalized belief propagation: splitting trapping sets in LDPC codes

Cited by 5 publications

References 19 publications

Low-complexity stochastic Generalized Belief Propagation

Low-complexity stochastic Generalized Belief Propagation

Generalized belief propagation for estimating the partition function of the 2D Ising model

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

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