Improved Successive Cancellation Decoding of Long Polar Codes Through Perturbing a Posteriori LLRs and Its Theoretical Insights

Abstract

For polar codes, perturbing received information can enhance the successive cancellation (SC) decoding performance. This is an effective approach for realizing low-latency yet high performance for long polar codes, since all the perturbation-enhanced SC (PSC) decoding can be performed in parallel. This paper provides theoretical insights into soft information perturbation. It first reveals that the PSC decoding can be equivalently interpreted as perturbing the a posteriori log-likelihood ratios (LLRs) of information bits. Such a revelation leads to the design of an improved PSC (IPSC) decoding that yields a lower perturbation complexity. By better utilizing the decoding a posteriori LLRs, a set of possibly erroneous estimations can be formed and further perturbed, resulting in the proposed hybrid PSC (HPSC) decoding. During each new SC decoding attempt, it takes turns to flip the first erroneous bit within the SC decoding estimations by introducing a biased perturbation, while the subsequent erroneous estimations are corrected through random perturbations. Our simulation results validate that, for various codeword lengths and rates, the proposed IPSC decoding can achieve a similar performance as the conventional PSC decoding, but yield a significantly reduced perturbation complexity. With the same number of decoding attempts, the proposed HPSC decoding outperforms the thresholded SC-flip (TSCF) decoding and the dynamic SC-flip (DSCF) decoding.