Low-Complexity Fast Fano Decoding for PAC Codes

Polarized-adjusted convolutional (PAC) codes are proposed by Arikan to improve the performance of polar codes by concatenating a polar transform with a convolutional transform. The error-correction performance of PAC codes under sequential decoding can reach the dispersion approximation bound in certain rate cases. However, due to the serial exploration of the codeword, the time and computational complexity caused by sequential decoding, e.g., Fano decoding, are required to be further reduced. In this article, we propose a low-complexity Fano decoding algorithm for PAC codes, called fast Fano decoding, to reduce the decoding complexity. The decoding algorithm considers four types of special nodes, i.e., constitute codes with special bit distribution patterns, to improve the parallelism degree of inner code decoding by immediately returning the messages from these nodes. Moreover, a node-level rewinding scheme including stage-located and partial memory recovery (SL-PM) is proposed to backtrack the intermediate messages efficiently. The results show that for a PAC code with length 128 and half rate, the proposed fast Fano decoding with the SL-PM rewinding scheme achieves more than 90% time and computational complexity reduction without performance degradation compared to the original Fano decoding.