Decoding Algorithms for Majority-Logic Decodable LDPC Codes

R. Lucas, M.P.C. Fossorier, Yu Kou +1 more

Previously, the belief propagation (BP) algorithm has received a lot of attention in the coding community, mostly due to its near-optimum decoding for low-density parity check (LDPC) codes and its connection to turbo decoding. In this paper, we investigate the performance achieved by the BP algorithm for decoding one-step majority logic decodable (OSMLD) codes. The BP algorithm is expressed in terms of likelihood ratios rather than probabilities, as conventionally presented. The proposed algorithm fits better the decoding of OSMLD codes with respect to its numerical stability due to the fact that the weights of their check sums are often much higher than that of the corresponding LDPC codes. Although it has been believed that OSMLD codes are far inferior to LDPC codes, we show that for medium code lengths (say between 200-1000 bits), the BP decoding of OSMLD codes can significantly outperform BP decoding of their equivalent LDPC codes. The reasons for this behavior are elaborated.

Ho-Il Kim

Kenta Kasai, Kohichi Sakaniwa

Yichao Lu, Nanfan Qiu, Zhixiang Chen +1 more

This paper presents a majority-logic based message-passing algorithm for decoding non-binary LDPC codes. Recently, many majority-logic decoding (MLGD) algorithms make huge efforts on reducing the computational complexity for decoding non-binary LDPC codes. Inspired by one step majority-logic decoding and q-ary sum-product algorithm, we devise a novel iterative double-reliability-based (IDRB) MLGD algorithm which carries out an efficient trade-off between decoding computational complexity and error performance. The proposed algorithm achieves a remarkable enhancement on error correct ability and yet requires only integer operations and finite field operations. Simulation results on two NB-LDPC codes show that we succeed in achieving significant coding gain compared with IHRB- and ISRB-MLGD with limited complexity increase.

Juewei Wang, Xiao Ma

In this paper, we propose a two-stage decoding algorithm for spatially-coupled algebraic low-density paritycheck (LDPC) codes with linear computational complexity, which consists of a sliding-window belief propagation (BP) decoding algorithm and a majority logic decoding algorithm. Simulation results are presented, showing that the error rate performance of SC-LDPC codes can be further improved by the majority logic decoding algorithm.

Ligter, Luca