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Lecture notes in electrical engineering

Improved Min-Sum Decoding Algorithm for Moderate Length Low Density Parity Check Codes

Waheed Ullah, Jiangtao, Yang FengFan

Published Nov 28, 2011• 7 citations
Publisher
DOI
10.1007/978-94-007-1839-5_101

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This paper proposes a new technique to improve bit error performance of the min-sum decoding algorithm for low density parity check codes. The proposed technique is based on two way normalization of min-sum LDPC decoding algorithm. The variable message is modified by two normalization factors to achieve the optimum approximation for the magnitude overestimation at the check node processing. This new method does not need exhaustive search for the optimum normalization factor when there is a change in code length and code rate. The performance has been evaluated for medium and short length codes using a small number of iterations. The results show improved performance of the proposed method, which makes it attractive for many practical applications.
This paper is concerned with the implementation issues of the so-called min-sum algorithm (also referred to as max-sum or max-product) for the decoding of low-density parity-check (LDPC) codes. The effects of clipping threshold and the number of quantization bits on the performance of the min-sum algorithm at short and intermediate block lengths are studied. It is shown that min-sum is robust against quantization effects, and in many cases, only four quantization bits suffices to obtain close to ideal performance. We also propose modifications to the min-sum algorithm that improve the performance by a few tenths of a dB with just a small increase in decoding complexity.
Low Density Parity Check (LDPC) code approaches Shannon–limit performance for binary field and long code lengths. However, performance of binary LDPC code is degraded when the code word length is small. An optimized min-sum algorithm for LDPC code is proposed in this paper. In this algorithm unlike other decoding methods, an optimization factor has been introduced in both check node and bit node of the Min-sum algorithm. The optimization factor is obtained before decoding program, and the same factor is multiplied twice in one cycle. So the increased complexity is fairly low. Simulation results show that the proposed Optimized Min-Sum decoding algorithm performs very close to the Sum-Product decoding while preserving the main features of the Min-Sum decoding, that is low complexity and independence with respect to noise variance estimation errors.