PAC Codes Meet CRC-Polar Codes

TL;DR

This paper introduces polarization-adjusted convolutional (PS-PAC) codes with CRC-Polar codes, improving error performance and weight distribution through precoding and continuous deployment of parity check bits, achieving notable power gains.

Contribution

It proposes a novel PS-PAC coding scheme that enhances polar code performance by applying a shifted rate-profile and convolutional precoding techniques.

Findings

Up to 0.5 dB power gain with short PS-PAC codes.

Improved weight distribution of polar codes.

Enhanced medium-length code performance with 0.12 dB improvement.

Abstract

CRC-Polar codes under SC list decoding are well-regarded for their competitive error performance. This paper examines these codes by focusing on minimum weight codewords, breaking them down into the rows of the polar transform. Inspired by the significant impact of parity check bits and their positions, we apply a shifted rate-profile for polarization-adjusted convolutional (PS-PAC) codes, thereby achieving similar improvements in the weight distribution of polar codes through precoding. The results demonstrate a significant improvement in error performance, achieving up to a 0.5 dB power gain with short PS-PAC codes. Additionally, leveraging convolutional precoding in PAC codes, we adopt a continuous deployment (masking) of parity check bits derived from the remainder of continuous division of the partial message polynomial and the CRC polynomial over frozen positions in the rate-profile. This approach enhances performance for medium-length codes, with an overall improvement of 0.12 dB.