Bit Reliability-Based Decoders for Non-Binary LDPC Codes

Abstract

Message-passing decoders typically perform well for nonbinary low-density parity-check (NB-LDPC) codes with large computational complexity. As another type of simplified decoders, symbol-reliability-based decoders further reduce the computational complexity. However, the previously proposed algorithms suffer severe error performance degradation for NB-LDPC codes with low column weights. In this paper, a weighted bit-reliability based (wBRB) decoder for NB-LDPC codes is developed and implemented with efficient layered partial-parallel structure. It not only balances the tradeoff between complexity and error performance, but also reduces the memory usage significantly. Furthermore, to enhance the performance of the wBRB decoder, a full bit-reliability-based (FBRB) decoder is proposed. The FBRB decoder is derived based on the binary matrix representation of the nonzero entries in the parity-check matrix. Since more bit-reliability values are passed through the edges of the Tanner graph, the FBRB decoder can achieve better error performance and faster convergence rate than the wBRB decoder. Both of the decoders are implemented on a Xilinx Virtex-5 XC5VLX155T FPGA device for a (403,226) code over GF(2 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">5</sup> ). The results shows that they achieve 118.98 and 95.73 Mbps throughput with 15 iterations, respectively.