Rate‐compatible systematic polar codes

Abstract

Puncturing and shortening are two common ways to achieve rate-compatible non-systematic polar codes (NSPCs). Systematic polar codes (SPCs) have been shown to outperform NSPCs with the same encoding and decoding complexity. However, rate-compatible SPCs have never been comprehensively studied in previous work. In this paper, two rate-compatible algorithms for SPCs are first proposed: uniform puncturing (UP) algorithm and uniform shortening (US) algorithm, which are referred to as SPC-UP and SPC-US, respectively. In order to effectively estimate the maximum likelihood decoding performance of punctured and shortened polar codes, subsequently, a distance spectrum calculation algorithm based on successive cancellation list (SCL) decoder for rate-compatible polar codes is proposed. Simulation results show that rate-compatible SPCs yield better bit error rate performance than rate-compatible NSPCs while they have the same frame error rate performance under different code rates and decoding algorithms. Eventually, union bounds that are obtained by the distance spectrum to provide the theoretical explanation for the superiority of rate-compatible SPCs are utilised.