Performance Analysis for Polar Codes under Successive Cancellation List Decoding with Fixed List Size

TL;DR

This paper analyzes the error events in polar codes under SCL decoding, derives bounds on error probabilities, and proposes a greedy bit-swapping algorithm to optimize code construction for improved decoding performance.

Contribution

It introduces a detailed error event analysis, derives lower bounds on error probabilities, and develops a bit-swapping algorithm to enhance polar code performance under SCL decoding.

Findings

BLER performance close to the lower bound at high SNR

The greedy bit-swapping algorithm improves decoding performance

Performance bounds can guide polar code design

Abstract

In this paper, we first indicate that the block error event of polar codes under successive cancellation list (SCL) decoding is composed of path loss (PL) error event and path selection (PS) error event, where the PL error event is that correct codeword is lost during the SCL decoding and the PS error event is that correct codeword is reserved in the decoded list but not selected as the decoded codeword. Then, we simplify the PL error event by assuming the all-zero codeword is transmitted and derive the probability lower bound via the joint probability density of the log-likelihood ratios of information bits. Meanwhile, the union bound calculated by the minimum weight distribution is used to evaluate the probability of the PS error event. With the performance analysis, we design a greedy bit-swapping (BS) algorithm to construct polar codes by gradually swapping information bit and frozen bit to reduce the performance lower bound of SCL decoding. The simulation results show that the BLER performance of SCL decoding is close to the lower bound in the medium to high signal-to-noise ratio region and we can optimize the lower bound to improve the BLER performance of SCL decoding by the BS algorithm.