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IEEE Wireless Communications Letters

A Two-Bit Precision Decoding Algorithm for LDPC Codes Over the Binary Symmetric Channel

Sunghye Cho, Kyeongcheol Yang

Published Jul 26, 2018• 2 citations
Publisher

Abstract

The min-sum algorithm as an approximation of the sum-product algorithm (SPA) for decoding of LDPC codes has much lower computational complexity, but slightly worse performance than the SPA. However, severe performance degradation might occur when it is realized in hardware due to the finite precision effect, especially in two-bit precision. In order to overcome this problem, we propose a two-bit precision decoding algorithm. The proposed algorithm employs one of several decoders adaptively, based on the syndrome weight of the estimated decoder output every iteration. Numerical results show that it has similar performance to the SPA over the binary symmetric channel.

DOI
10.1109/lwc.2018.2859993

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The min-sum algorithm as an approximation of the sum-product algorithm (SPA) for decoding of LDPC codes has much lower computational complexity, but slightly worse performance than the SPA. However, severe performance degradation might occur when it is realized in hardware due to the finite precision effect, especially in two-bit precision. In order to overcome this problem, we propose a two-bit precision decoding algorithm. The proposed algorithm employs one of several decoders adaptively, based on the syndrome weight of the estimated decoder output every iteration. Numerical results show that it has similar performance to the SPA over the binary symmetric channel.
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Low Density Parity Check (LDPC) 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.
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This letter proposes a new algorithm for the check node update in the decoding of low-density parity-check (LDPC) codes. The proposed algorithm is based on a new approximation formula of standard sum-product algorithm (SPA) which can reduce the approximation error of min-sum algorithm (MSA) and has almost the same performance as sum-product algorithm (SPA) under both floating precision operation and fixed-point operation. Besides, the new approximation formula can be implemented in simple structures competitive with MSA.
Low-density parity-check (LDPC) codes are widely used in communication systems. When user messages are encoded by binary LDPC codes and transmitted with higher-order modulations, bits composing the same modulated symbol are generally correlated. Traditional soft-decision decoding algorithms for binary LDPC codes like sum-product algorithm (SPA) and min-sum algorithm (MSA) update messages only based on log-likelihood ratio (LLR) of bits, and correlations introduced by modulation are not utilized. In this paper, symbol-based SPA and MSA (S-SPA and S-MSA) which incorporate symbol-level information in the decoding procedures are proposed to provide an alternative low-cost way to better utilize available information. By narrowing the search space of symbols based on bit-level information, the complexities of the proposed algorithms are independent of modulation order. S-SPA and S-MSA achieve better error-correction performances than SPA and MSA with little additional complexities and S-MSA is friendly to hardware design of LDPC decoder.