Bounds on the belief propagation threshold of non-binary LDPC codes

Leonid Geller; David Burshtein

doi:10.1109/ITW.2012.6404692

Bounds on the belief propagation threshold of non-binary LDPC codes

Leonid Geller^*, David Burshtein

^*Corresponding author for this work

School of Electrical Engineering

Tel Aviv University

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

1 Scopus citations

Abstract

We consider LDPC code ensembles over non-binary Galois fields, when used for transmission over arbitrary memoryless channels. Belief propagation decoding for these codes has been shown to achieve excellent results. However, computing the decoding threshold using density evolution is usually impractical, since one needs to propagate multi-dimensional probability distributions, and Monte Carlo simulations are required instead. By considering the evolution of the message Bhattacharyya parameter and the message expected value parameter we derive a simple lower bound on the performance of the algorithm. This bound applies for both regular and irregular non-binary LDPC ensembles.

Original language	English
Title of host publication	2012 IEEE Information Theory Workshop, ITW 2012
Pages	357-361
Number of pages	5
DOIs	https://doi.org/10.1109/ITW.2012.6404692
State	Published - 2012
Event	2012 IEEE Information Theory Workshop, ITW 2012 - Lausanne, Switzerland Duration: 3 Sep 2012 → 7 Sep 2012

Publication series

Name	2012 IEEE Information Theory Workshop, ITW 2012

Conference

Conference	2012 IEEE Information Theory Workshop, ITW 2012
Country/Territory	Switzerland
City	Lausanne
Period	3/09/12 → 7/09/12

Keywords

Low-density parity-check (LDPC) codes
belief propagation decoding
non-binary codes

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10.1109/ITW.2012.6404692

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abstract = "We consider LDPC code ensembles over non-binary Galois fields, when used for transmission over arbitrary memoryless channels. Belief propagation decoding for these codes has been shown to achieve excellent results. However, computing the decoding threshold using density evolution is usually impractical, since one needs to propagate multi-dimensional probability distributions, and Monte Carlo simulations are required instead. By considering the evolution of the message Bhattacharyya parameter and the message expected value parameter we derive a simple lower bound on the performance of the algorithm. This bound applies for both regular and irregular non-binary LDPC ensembles.",

keywords = "Low-density parity-check (LDPC) codes, belief propagation decoding, non-binary codes",

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AB - We consider LDPC code ensembles over non-binary Galois fields, when used for transmission over arbitrary memoryless channels. Belief propagation decoding for these codes has been shown to achieve excellent results. However, computing the decoding threshold using density evolution is usually impractical, since one needs to propagate multi-dimensional probability distributions, and Monte Carlo simulations are required instead. By considering the evolution of the message Bhattacharyya parameter and the message expected value parameter we derive a simple lower bound on the performance of the algorithm. This bound applies for both regular and irregular non-binary LDPC ensembles.

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Bounds on the belief propagation threshold of non-binary LDPC codes

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