Fast-SSC-Flip Decoding of Polar Codes

Polar codes are widely considered as one of the most exciting recent discoveries in channel coding. For short to moderate block lengths, their error-correction performance under list decoding can outperform that of other modern error-correcting codes. However, high-speed list-based decoders with moderate complexity are challenging to implement. Successive-cancellation (SC)-flip decoding was shown to be capable of a competitive error-correction performance compared to that of list decoding with a small list size, at a fraction of the complexity, but suffers from a variable execution time and a higher worst-case latency. In this work, we show how to modify the state-of-the-art high-speed SC decoding algorithm to incorporate the SC-flip ideas. The algorithmic improvements are presented as well as average execution-time results tailored to a hardware implementation. The results show that the proposed fast-SSC-flip algorithm has a decoding speed close to an order of magnitude better than the previous works while retaining a comparable error-correction performance.Comment: 5 pages, 3 figures, appeared at IEEE Wireless Commun. and Netw. Conf. (WCNC) 201

Improved Successive Cancellation Flip Decoding of Polar Codes Based on Error Distribution

Polar codes are a class of linear block codes that provably achieves channel capacity, and have been selected as a coding scheme for $5^{\rm th}$ generation wireless communication standards. Successive-cancellation (SC) decoding of polar codes has mediocre error-correction performance on short to moderate codeword lengths: the SC-Flip decoding algorithm is one of the solutions that have been proposed to overcome this issue. On the other hand, SC-Flip has a higher implementation complexity compared to SC due to the required log-likelihood ratio (LLR) selection and sorting process. Moreover, it requires a high number of iterations to reach good error-correction performance. In this work, we propose two techniques to improve the SC-Flip decoding algorithm for low-rate codes, based on the observation of channel-induced error distributions. The first one is a fixed index selection (FIS) scheme to avoid the substantial implementation cost of LLR selection and sorting with no cost on error-correction performance. The second is an enhanced index selection (EIS) criterion to improve the error-correction performance of SC-Flip decoding. A reduction of $24.6\%$ in the implementation cost of logic elements is estimated with the FIS approach, while simulation results show that EIS leads to an improvement on error-correction performance improvement up to $0.42$ dB at a target FER of $10^{-4}$.Comment: This version of the manuscript corrects an error in the previous ArXiv version, as well as the published version in IEEE Xplore under the same title, which has the DOI:10.1109/WCNCW.2018.8368991. The corrections include all the simulations of SC-Flip-based and SC-Oracle decoders, along with associated comments in-tex