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Effects of clipping and quantization on min-sum algorithm and its modifications for decoding low-density parity-check (LDPC) codes

Jianguang Zhao

Published Jan 1, 2003• 1 citation
Publisher
DOI
10.22215/etd/2003-05571

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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.
The effects of clipping and quantization on the performance of the min-sum algorithm for the decoding of low-density parity-check (LDPC) codes at short and intermediate block lengths are studied. It is shown that in many cases, only four quantization bits suffice to obtain close to ideal performance over a wide range of signal-to-noise ratios. Moreover, we propose modifications to the min-sum algorithm that improve the performance by a few tenths of a decibel with just a small increase in decoding complexity. A quantized version of these modified algorithms is also studied. It is shown that, when optimized, modified quantized min-sum algorithms perform very close to, and in some cases even slightly outperform, the ideal belief-propagation algorithm at observed error rates.
Compared with the sum-product algorithm (SPA) with high decoding complexity for low-density parity-check (LDPC) codes, its approximated version, the min-sum algorithm (MSA), reduces the computational complexity at the cost of slight performance degradation. In order to compensate the oversized check-node messages in the MSA, the effect of clipping on variable-node messages is investigated under two-bit resolution. Our results show that the performance of clipped MSA degrades at the high bit error rate (BER) and increases at the low BER as clipping threshold enlarges. Based on these results, we propose a modified quantized MS decoding algorithm where the adaptive clipping threshold is applied on the variable-node messages according to the number of unsatisfied checks per-iteration. The adaptive rule is designed for easy hardware implementations. Numerical results show that the proposed algorithm has considerable improvement in performance compared with the MSA under two-bit precision. And it can achieve the performance near the SPA for some short-length LDPC codes.