An Efficient Construction and Low Complexity Collaborative Decoding of Reed-Solomon Concatenated with Modified Polar Codes

Polar codes are the first explicit code sequences that provably achieve capacity for discrete memory-less channels. However, their performance with successive cancellation (SC) decoding is unimpressive at practical block-lengths. In this paper, we propose a scheme of concatenating Reed-Solomon (RS) with modified polar codes to improve the performance of SC. Firstly, short repetition block codes are used as outer block codes to modify the construction of polar codes. This step can improve the performance of SC with a lower complexity compared with the other schemes. And secondly, to reduce the probability of the error propagation of SC, the modified polar codes are concatenated with RS codes. We divide the decoding process of the polar codes into several pieces. After one piece is decoded, the RS decoder is used to correct the residual errors from polar codes in this piece. By this collaborative method, the number of the error propagation can be reduced obviously. Simulation shows that the proposed scheme can obtain a good error-rate performance at finite block lengths and have a significantly better error-decay rate with a lower complexity.