Polarization-Adjusted Convolutional (PAC) Codes: Sequential Decoding vs List Decoding

In the Shannon lecture at 2019 International Symposium on Information Theory (ISIT), Arikan proposed to employ a one-to-one convolutional transform as pre-coding step before polar transform. The resulting codes of this concatenation are called polarization-adjusted (PAC) . scheme, pair mapper and demapper pre- post- processing devices deployed around memoryless channel, which provides polarized information an outer decoder leading improved error correction performance code. paper, list decoding sequential (including Fano stack decoding) first adapted for use decode PAC codes. Then, reduce complexity PAC/polar codes, we propose (i) adaptive heuristic metric, (ii) tree search constraints backtracking avoid exploration unlikely sub-paths, (iii) strategies consistent with pattern occurrence in These contribute reduction average time from 50% 80%, trading 0.05 0.3 dB degradation within FER = $10^{-3}$ range, respectively, relative not applying corresponding strategies. Additionally, important ingredient efficient computation method intermediate LLRs partial sums is provided. This effective avoids storing or restarting process. Eventually, all three algorithms compared terms performance, complexity, resource requirements.