Design of Multilevel Reed–Solomon Codes and Iterative Decoding for Visible Light Communication

Abstract

This paper proposes multilevel Reed–Solomon (MRS) codes and their iterative multistage soft decoding (IMSD) for visible light communication (VLC), realizing both high decoding performance and transmission spectrum efficiency. The proposed IMSD algorithm decodes the MRS codes level-by-level through iterating either hard decisions or extrinsic information of RS coded bits. Each level RS decoding is realized by cascading the adaptive belief propagation (ABP) algorithm that produces the extrinsic information and the Berlekamp–Massey (BM) algorithm that estimates the codeword. The earlier level decoding provides better a priori information for the later ones. A complexity reducing IMSD (CR-IMSD) algorithm is also proposed to facilitate the decoding. This paper further investigates a joint design of color-shift keying (CSK) constellation and the MRS code, optimizing the decoding performance. The CSK constellation is designed by considering both the set partitioning (SP) criterion and the harmonic mean of constellation’s minimum squared Euclidean distance (MSED). The MRS codes are further designed using the capacity and the equal error probability rules. Our simulation results show that the IMSD algorithm achieves significant iterative decoding gains. The performance of the designed MRS code is 0.3 dB away from the capacity limit at the bit error rate (BER) of 10−9.