Erasure-correction-enhanced iterative decoding for LDPC-RS product codes

Low-density parity-check (LDPC) codes are widely used due to their significant error-correction capability and linear decoding complexity. However, it is not sufficient for LDPC codes to satisfy the ultra low bit error rate (BER) requirement of next-generation ultra-high-speed communications due to the error floor phenomenon. According to the residual error characteristics of LDPC codes, we consider using the high rate Reed-Solomon (RS) codes as the outer codes to construct LDPC-RS product codes to eliminate the error floor and propose the hybrid error-erasure-correction decoding algorithm for the outer code to exploit erasure-correction capability effectively. Furthermore, the overall performance of product codes is improved using iteration between outer and inner codes. Simulation results validate that BER of the product code with the proposed hybrid algorithm is lower than that of the product code with no erasure correction. Compared with other product codes using LDPC codes, the proposed LDPC-RS product code with the same code rate has much better performance and smaller rate loss attributed to the maximum distance separable (MDS) property and significant erasure-correction capability of RS codes.