Efficient symbol reliability based decoding for QCNB-LDPC codes

Abstract

Abstract —As an extension of binary low-density parity-check(LDPC) codes, non-binary LDPC (NB-LDPC) codes show signif-icantly better performance when the code length is moderateor small. Recently, enhanced iterative hard reliability based(EIHRB) decoding algorithm is proposed to reduce the com-putation complexity. However, the EIHRB algorithm suffers alot from significant performance degradation when the columnweight is small. In this paper, a symbol reliability based (SRB)decoding algorithm, which also performs well when the columnweight is low, is proposed for NB-LDPC decoding to improvethe decoding performance. With the same maximum iterationnumber, around 0.38 dB extra coding gain is achieved. Fur-thermore, the corresponding efficient decoder architecture isproposed. Comparison results have shown that the proposed SRBalgorithm can not only achieve good coding gain, but the costfor hardware implementation is reasonable. I. I NTRODUCTION B INARY low-density parity-check (LDPC) codes, redis-covered by Gallager in 1962 [1], have shown great ca-pabilities in approaching Shannon capacity. Non-binay LDPC(NB-LDPC) codes, which can be treated as an extension oftheir binary counterparts in finite fields with order higherthan 2, were first investigated by Davey and MacKay [2].Having the capabilities of correcting symbol-wise errors, NB-LDPC codes have demonstrated advantages over binary onesin recovering channel impairments [3]. However, the codinggain introduced by NB-LDPC codes comes along with drasticincrease of the decoding complexity.The optimal but most complex decoding algorithm is theFFT-based sum-product algorithm (SPA) proposed in [2]. Tothis end, some alternatives which can achieve better trade-off between decoding complexity and performance, have beenproposed in [4] [5]. Some other algorithms, which are basedon symbol-reliability and majority logic [6] [7] [8], havebeen proposed as well. These algorithms can significantlylower the decoding complexity at the penalty of considerableperformance losses, especially for the codes of small column