On the Concatenations of Polar Codes and Non-Binary LDPC Codes

Abstract

An interleaved concatenation scheme of polar codes with non-binary low-density parity check (NBLDPC) codes is proposed in this paper to improve the error-correcting performance of polar codes with finite code length. The information blocks of inner polar codes are split into several information sub-blocks, and several segment successive cancellation list (S-SCL) decoders are carried out in parallel for all inner polar codes. Moreover, for a better error-correcting performance, an improved SCL decoder with a selective extension is proposed for the concatenated polar codes, which will be referred to selective extended segment SCL (SES-SCL) decoder. The SES-SCL decoder uses soft information of some unreliable information sub-blocks for the decoding of subsequent sub-blocks so as to mitigate the error propagation of premature hard decision of S-SCL decoder. Simulation results show that NBLDPC-polar codes can outperform Reed Solomon -polar codes. The NBLDPC-polar codes with the proposed SES-SCL algorithm can also be comparable with pure polar codes with cyclic redundancy check aided successive cancellation list (CA-SCL) decoding with list size $L=4$ in the high SNR, but require lower decoding storage. Therefore, the NBLDPC-polar codes may strike a better balance between memory space and performance compared with the state-of-the-art schemes in the finite length regime.