Reduced Complexity Belief Propagation Decoders for Polar Codes

Abstract: Polar codes are newly discovered capacity-achieving codes, which have attracted lots of research efforts. Polar codes can be efficiently decoded by the low-complexity successive cancelation (SC) algorithm and the SC list (SCL) decoding algorithm. The belief propagation (BP) decoding algorithm not only is an alternative to the SC and SCL decoders, but also provides soft outputs that are necessary for joint detection and decoding. Both the BP decoder and the soft cancelation (SCAN) decoder were proposed for polar codes to output soft information about the coded bits. In this paper, first a belief propagation decoding algorithm, called reduced complexity soft cancelation (RCSC) decoding algorithm, is proposed. Let $N$ denote the block length. Our RCSC decoding algorithm needs to store only $5N-3$ log-likelihood ratios (LLRs), significantly less than $4N-2+\frac{N\log_2N}{2}$ and $N(\log_2N+1)$ LLRs needed by the BP and SCAN decoders, respectively, when $N\geqslant 64$. Besides, compared to the SCAN decoding algorithm, our RCSC decoding algorithm eliminates unnecessary additions over the real field. Then the simplified SC (SSC) principle is applied to our RCSC decoding algorithm, and the resulting SSC-aided RCSC (S-RCSC) decoding algorithm further reduces the computational complexity. Finally, based on the S-RCSC decoding algorithm, we propose a corresponding memory efficient decoder architecture, which has better error performance than existing architectures. Besides, our decoder architecture consumes less energy on updating LLRs.