Block Markov Superposition Transmission of Repetition and Single-Parity-Check Codes

This letter presents a method to construct a family of codes with rate K/N(K = 1,2,...,N - 1) for any given integer N > 1. This family of codes, referred to as RSPC codes for short, consist of the repetition (R) code, the single-parity-check (SPC) code and the codes obtained by time-sharing between the R code and the SPC code. The RSPC codes have extremely simple encoding and soft-input soft-output (SISO) decoding algorithms, hence can be integrated into the recently proposed block Markov superposition transmission (BMST) system. The BMST introduces memory across short codes by spatially coupling the generator matrices of the short codes. A distinguished feature of the BMST system is the simple relation between the asymptotic coding gain and the spatially coupling depth (encoding memory). Furthermore, the BMST-RSPC codes can share a pair of easily reconfigurable encoder and decoder. Simulation results show that the BMST-RSPC codes perform well (within one dB away from the corresponding Shannon limits) in a wide range of code rates.