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IEEE International Symposium on Information Theory (ISIT)

A reliability-based computation method for the weight distribution of LDPC codes using the probabilistic algorithm

Masanori Hirotomo, Masami Mohri, Masakatu Morii

Published Jul 1, 2011• 0 citations
Publisher

Abstract

In the analysis of maximum-likelihood decoding performance of low-density parity-check (LDPC) codes, the weight distribution is an important factor. Some methods based on the error impluse method have presented in order to estimate the weight distribution of LDPC codes. However, these methods have no scheme which determine the number of codeword in LDPC codes. In this paper, we propose a reliability-based computation method for the weight distribution of LDPC codes using the probabilistic algorithm. Using the proposed method, we can determine the weight distribution of LDPC codes with small failure probability.

DOI
10.1109/isit.2011.6034146

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In the analysis of maximum-likelihood decoding performance of low-density parity-check (LDPC) codes, the weight distribution is an important factor. Some methods based on the error impluse method have presented in order to estimate the weight distribution of LDPC codes. However, these methods have no scheme which determine the number of codeword in LDPC codes. In this paper, we propose a reliability-based computation method for the weight distribution of LDPC codes using the probabilistic algorithm. Using the proposed method, we can determine the weight distribution of LDPC codes with small failure probability.
In the analysis of maximum-likelihood decoding performance of low-density parity-check (LDPC) codes, the weight distribution is an important factor. We presented a probabilistic method for computing the weight distribution of LDPC codes, and showed results of computing the weight distribution of several LDPC codes. In this paper, we improve our previously presented method and propose a probabilistic computation method with reliability for the weight distribution of LDPC codes. Using the proposed method, we can determine the weight distribution with small failure probability.
Low-density parity-check (LDPC) codes achieve outstanding performance by the sum-product decoder. Its performance approaches the maximum-likelihood (ML) decoding performance at high SNR region. Upper bounds on the error probability of the ML decoded LDPC codes can be computed using the weight distribution. Recently, X.-Y. Hu et al. presented an approximate algorithm for estimating the weight distribution of LDPC codes. However, the weight distribution computed by their method depends on the iterative decoding algorithm, and is not always estimated exactly. In this paper, we propose a probabilistic method for computing the low-part weight distribution of LDPC codes. Using our method, the approximate weight distribution of LDPC codes can be computed with high accuracy
Low-density parity-check (LDPC) codes are linear block codes defined by sparse parity-check matrices. The codes exhibit excellent performance under iterative decoding, and the weight distribution is used to analyze lower error probability of their decoding performance. In this paper, we propose a probabilistic method for computing the weight distribution of LDPC codes. The proposed method efficiently finds low-weight codewords in a given LDPC code by using Stern's algorithm, and stochastically computes the low part of the weight distribution from the frequency of the found codewords. It is based on a relation between the number of codewords with a given weight and the rate of generating the codewords in Stern's algorithm. In the numerical results for LDPC codes of length 504, 1008 and 4896, we could compute the weight distribution by the proposed method with greater accuracy than by conventional methods.
An efficient method for finite-length low-density parity-check (LDPC) code analysis is proposed. This method is based on studying the channel variations when observed during a finite-length codeword. To this end, channel parameters are interpreted as random variables and their distributions are found. Assuming that a decoding failure is the result of an observed channel worse than the code's decoding threshold, the block error probability of finite-length LDPC codes is estimated. Using an extrinsic information transfer chart analysis, bit error probability is obtained from the block error probability. Our results suggest that by considering only the channel variations around its expected behavior and even ignoring the effects of cycles, one can closely predict the performance of LDPC codes of a few thousand bits or longer in the waterfall region.
In this work, reliability based decoding is combined with belief propagation (BP) decoding for low-density parity check (LDPC) codes. At each iteration, the soft output values delivered by the BP algorithm are used as reliability values to perform reduced complexity soft decision decoding of the code considered. This approach allows to bridge the error performance gap between BP decoding which remains suboptimum, and maximum likelihood decoding (MLD) which is too complex to be implemented for the codes considered. A stopping criterion which reduces the average number of iterations at the expense of very little performance degradation is also proposed for this combined decoding approach. Simulations results for several Gallager LDPC codes and different set cyclic (DSC) codes of hundreds of information bits are given and elaborated.