Low-Complexity Successive-Cancellation List Decoding of $2\times2$ Kernel Non-Binary Polar Codes

Abstract

Non-binary successive cancellation list (NB-SCL) decoding expands each surviving path into $q$ candidate branches at every information symbol, which causes high path expansion, sorting, and pruning complexity. To address this issue, this paper proposes low-complexity list decoding algorithms for $2\times2$ kernel non-binary polar codes (NBPCs). First, we design a split-reduced non-binary successive cancellation list (SR-NBSCL) decoder that skips path splitting when the current symbol is sufficiently reliable. We then exploit the final Rate-1 node structure and switch the last group of information symbols to simplified non-binary successive cancellation (NB-SC) decoding, resulting in the enhanced split-reduced non-binary successive cancellation list (ESR-NBSCL) decoder. To further reduce branch expansion at unreliable symbols, we introduce an accumulated reliability-deviation (ARD) metric and propose an adaptive branch-pruning non-binary successive cancellation list (ABP-NBSCL) decoder, which prunes unreliable candidate branches before sorting and then reduces the dominant sorting complexity. Simulation results show that the proposed decoders achieve frame-error-rate (FER) performance close to that of conventional NB-SCL decoding with much lower complexity. In particular, the ABP-NBSCL decoder reduces the path splitting number (PSN) by more than $80\%$ at several tested signal-to-noise ratios (SNRs), with a negligible performance loss.