A Novel SCL Bit-Flipping Decoding Of Polarization-Adjusted Convolutional (PAC) Codes

TL;DR

This paper introduces a novel SCL bit-flipping decoding method for PAC codes, significantly enhancing short-length decoding performance by reducing the required list size for comparable error correction capabilities.

Contribution

It proposes a new bit-flipping decoding algorithm for PAC codes that improves performance with smaller list sizes, reducing decoding complexity.

Findings

PAC-SCLF with list size 32 outperforms traditional PAC-SCL with same list size by 0.3 dB.

PAC-SCLF achieves similar performance with list size 32 as PAC-SCL with list size 128.

Decoding performance improves with the proposed bit-flipping method at short block lengths.

Abstract

Polar codes have attracted the attention of numerous researchers in the past decade due to their excellent performance. However, their performance at short block lengths under standard successive cancellation decoding is far from desirable. An effective method to improve the performance at short lengths is CRC precoding followed by successive-cancellation list decoding. Later, Arikan presented polarization-adjusted convolutional (PAC) codes, which further improve the performance of polar codes. In fact, bit-flipping is another post-processing method that can improve decoding performance. In this paper, we propose a novel SCL Bit-Flipping of PAC Codes. We show that better performance can be achieved using list decoding when the list size is the same for PAC codes (N=128, K=64). The decoding performance of our newly proposed PAC-SCLF with a list size of 32 is 0.3 dB better than that of the traditional PAC-SCL with a list size of 32. We set the maximum number of bit flips to 5. The performance of the list size (L=32) for PAC-SCLF is almost the same as the performance of the list size (L=128) for PAC-SCL.