Generalized Fast Decoding of Polar Codes

Abstract: Research on polar codes has been constantly gaining attention over the last decade, by academia and industry alike, thanks to their capacity-achieving error-correction performance and low-complexity decoding algorithms. Recently, they have been selected as one of the coding schemes in the $5^{th}$ generation wireless standard (5G). Over the years various polar code decoding algorithms, like SC-list (SCL), have been proposed to improve the mediocre performance of the successive cancellation (SC) decoding algorithm for finite code lengths; however, like SC, they suffer from long decoding latency. Fast decoding of polar codes tries to overcome this problem by identifying particular subcodes in the polar code and decoding them with efficient decoders. In this work, we introduce a generalized approach to fast decoding of polar codes to further reduce SC-based decoding latency. We propose three multi-node polar code subcodes whose identification patterns include most of the existing subcodes, extending them to SCL decoding, and allow to apply fast decoding to larger subsets of bits. Without any error-correction performance degradation, the proposed technique shows up to $23.6\%$ and $29.2\%$ decoding latency gain with respect to fast SC and SCL decoding algorithms, respectively, and up to $63.6\%$ and $49.8\%$ if a performance loss is accepted, whose amount depends on code and decoding algorithm parameters, along with the desired speedup.