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International Journal of Applied Research on Information Technology and Computing

Optimising LDPC Codes Using Modified Log SPA Algorithm

Abdessadek Aaroud, Mohammed Mensouri

Published Jan 1, 2014• 0 citations
Publisher

Abstract

We present in this paper a new method for improving the decoding of the LDPC (low-density parity check) codes by optimising the log-SPA (sum-product algorithm). Currently, the LDPC codes give very good results with iterative decoding algorithm, log-SPA, based on the propagation confidence BP (belief propagation). To improve the existing log-SPA, we propose a decoding algorithm (log-SPA modified), which minimises the error decoding of words that could not be previously decoded. This algorithm is based on the dependency between the weight of the syndrome and the weight of the error sequence generated during iterations of decoding. Simulations illustrate the performance of our approach compared with classical LDPC code based on log-SPA.

DOI
10.5958/0975-8089.2014.00001.3

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We present in this paper a new method for improving the decoding of the LDPC (low-density parity check) codes by optimising the log-SPA (sum-product algorithm). Currently, the LDPC codes give very good results with iterative decoding algorithm, log-SPA, based on the propagation confidence BP (belief propagation). To improve the existing log-SPA, we propose a decoding algorithm (log-SPA modified), which minimises the error decoding of words that could not be previously decoded. This algorithm is based on the dependency between the weight of the syndrome and the weight of the error sequence generated during iterations of decoding. Simulations illustrate the performance of our approach compared with classical LDPC code based on log-SPA.
This paper analyzes the correlation between the error weights and the syndrome weights during the sum product algorithm (SPA) decoding process of low density parity check codes (LDPC) in order to improve the error performance and the decoding speed. In this paper, we propose a modified SPA decoding algorithm to improve the decoding performance of the non-decoded codewords and investigate if this new algorithm takes indeed the best decoding decision for each codeword. The effect of the averaged decoding over the error weights and syndrome weights are analyzed as well as their correlation. The correlation coefficients between them are computed and a weight enumerator polynomial is used to jointly represent the error and syndrome weight distribution for each codeword.
Low-Density Parity check (LDPC) codes offer high-performance error correction near the Shannon limit which employs large code lengths and some iterations in the decoding process. The conventional decoding algorithm of LDPC is the Log Likelihood Ratio based Belief Propagation (LLR BP) which is also known as the `Sum-Product algorithm' which gives the best decoding performance and requires the most computational complexity and implementations with increased hardware complexity. Another simpler variant of this algorithm is used which is known as `min-sum algorithm' which reduces computational complexity as well as hardware complexity but with reduced accuracy. This paper analyzes the reason min-sum algorithm is more prone to errors when compared to the sum-product algorithm, and puts forward two improved algorithms which improve the performance of the min-sum algorithm with comparable algorithmic complexity.
Many classes of high-performance Low-density parity check codes are based on parity check matrices composed of permutation sub matrices. The emulation-simulation framework further allows the algorithm and implementation to be iteratively redefined to improve the error floor performance of message passing decoder. Log-Like hood-Ratio (LLR) based Belief-Propagation (BP) algorithm is presented for Low Density Parity Check codes. Numerically accurate representation of check node update computation used in LLR-BP decoding is described. The implementation of Sum-Product algorithm (SPA) within Low Density Parity Check Code (LDPC) decoder is described in this paper and the correction term is used to improve the decoding performance of min-sum algorithm (MSA). Quantization and log-tanh function approximation in sum-product decoder strongly affect which absorbing set dominates in error floor region. For LDPC decoder, bit error rate (BER) decreases with increase in the signal to noise ratio.
Effect of channel mismatch on decoding performance of low density parity check (LDPC) codes over binary symmetric channel (BSC) under sum-product algorithm (SPA) is analyzed in this paper. Density evolution is employed in theoretical analysis to get optimal initial value for SPA. Based on the results, a modified SPA algorithm is proposed. When decoding using this modified SPA algorithm, no channel information is needed at the decoder side. This will be of significant value for time-varying channels. Theoretical claims from density evolution are confirmed by extensive simulations. Our simulations show that by fixing the initial value for all channel conditions, decoding performance can be improved. One channel state estimation algorithm is proposed in this paper based on the error detection ability of LDPC codes. Maximum number of iterations taken when decoding a LDPC code can be dynamically adjusted according to the estimated channel state. Further performance improvements can be achieved by using the dynamic iteration number adjusting scheme together with the modified sum-product algorithm
Among the decoding algorithms for low-density parity-check(LDPC) code,sum-product algorithm(SPA) has the optimal performance but high complexity,while min-sum algorithm has simple implementation complexity but worse performance.Considering this performance-complexity contradiction,some modified min-sum algorithms are proposed.In this paper,researches are done based on one of the modified min-sum algorithms that is close to SPA in performance but the way modifying fraction works is simplified.Simplified algorithm remains similar in performance to sum-product algorithm but has a remarkably reduced implementation complexity.