List Viterbi Decoding of PAC Codes

TL;DR

This paper introduces a list Viterbi decoding approach for PAC codes, demonstrating improved error correction performance and analyzing latency-performance trade-offs in decoding strategies.

Contribution

It implements a parallel list Viterbi algorithm for PAC codes and analyzes the impact of different sorting strategies on decoding performance and latency.

Findings

List decoding significantly improves error correction over standard Viterbi decoding.

Local sorting reduces latency but may affect error correction performance.

Global sorting enhances performance at the cost of increased latency.

Abstract

Polarization-adjusted convolutional (PAC) codes are special concatenated codes in which we employ a one-to-one convolutional transform as a pre-coding step before the polar transform. In this scheme, the polar transform (as a mapper) and the successive cancellation process (as a demapper) present a synthetic vector channel to the convolutional transformation. The numerical results show that this concatenation improves the Hamming distance properties of polar codes. In this work, we implement the parallel list Viterbi algorithm (LVA) and show how the error correction performance moves from the poor performance of the Viterbi algorithm (VA) to the superior performance of list decoding by changing the constraint length, list size, and the sorting strategy (local sorting and global sorting) in the LVA. Also, we analyze the latency of the local sorting of the paths in LVA relative to the global sorting in the list decoding and the trade-off between the sorting latency and the error correction performance.