Iterative Multistage Soft Decoding of Multilevel Reed-Solomon Codes

This paper proposes an iterative multistage soft decoding (IMSD) for multilevel Reed-Solomon (MRS) codes, achieving both high decoding performance and transmission spectrum efficiency. The proposed IMSD algorithm performs soft-in soft-out (SISO) decoding of each level RS code in a multistage mechanism. The RS decoding is realized by cascading the adaptive belief propagation (ABP) algorithm that produces the extrinsic probabilities for the coded bits and the Berlekamp-Massey (BM) algorithm that estimates the message. The earlier decoding outputs help a later one by providing better a priori information for its decoding. Armed with the IMSD algorithm, the MRS codes are designed by analyzing the equivalent channel capacity of each coded level, leading to the heterogeneous structure for MRS codes. Our simulation results demonstrate the performance advantages of the IMSD algorithm as well as the designed MRS codes.