Reverse PAC Codes: Look-ahead List Decoding

TL;DR

This paper introduces reverse PAC codes with look-ahead list decoding, significantly reducing error coefficients and improving block error rates at high code rates compared to traditional PAC and polar codes.

Contribution

It proposes a novel reverse precoding method and a look-ahead list decoding algorithm that outperform existing PAC codes in minimizing minimum-weight codewords.

Findings

Notable reduction in error coefficients compared to PAC and polar codes

Significant improvement in block error rate at high code rates

Decoding complexity remains comparable to standard list decoding

Abstract

Convolutional precoding in polarization-adjusted convolutional (PAC) codes is a recently introduced variant of polar codes. It has demonstrated an effective reduction in the number of minimum weight codewords (a.k.a error coefficient) of polar codes. This reduction has the potential to significantly improve the error correction performance. From a codeword formation perspective, this reduction has limitations. Capitalizing on the understanding of the decomposition of minimum-weight codewords, this paper studies reverse precoding that can effectively reduce minimum-weight codewords more than in PAC codes. We propose a look-ahead list decoding for the reverse PAC codes, which has the same order of complexity as list decoding in PAC codes. Through numerical analysis, we demonstrate a notable reduction in error coefficients compared to PAC codes and polar codes, resulting in a remarkable improvement in the block error rate, in particular at high code rates.