New Constructions of Polar Code Based on Refined Error Probability Analysis

TL;DR

This paper introduces refined error probability analysis for polar codes, leading to new construction algorithms optimized for SC and SCL decoding, resulting in improved performance over existing designs in various channel conditions.

Contribution

It provides a novel BLER expression based on LLRs and develops construction methods optimized for SC and SCL decoding, enhancing polar code performance.

Findings

Up to 0.2 dB performance gain over benchmarks under DSCF decoding.

Superior performance of proposed codes over 5G and Reed-Muller polar codes.

Effective SCL-optimized constructions with gains up to 0.4 dB.

Abstract

This paper presents a refined analysis of the block error rate (BLER) of polar codes over symmetric binary-input discrete memoryless channels under successive cancellation (SC) and successive cancellation list (SCL) decoding. A novel expression for the BLER under SC decoding is derived directly in terms of the decoder's LLRs. Building on this formulation, we propose a polar code construction algorithm optimized for SC decoding and evaluate its performance under SC and dynamic SC flip (DSCF) decoding against established SC-optimized constructions, including Gaussian approximation (GA)-based and Tal-Vardy polar codes. Furthermore, by decomposing the BLER into path loss and path selection components, we derive a novel LLR-based expression for the path loss probability, which enables an SCL-optimized polar code construction method. The proposed constructions are evaluated under SCL decoding with list sizes 2, 4, and 8, and are compared with 5G standard polar codes, GA-based designs, and Reed-Muller polar codes. Simulation results show that the proposed SC-optimized polar codes achieve up to a 0.2 dB performance gain under DSCF decoding over the AWGN channel compared to benchmark constructions, and exhibit superior performance over binary symmetric channels. For SCL-optimized polar codes, the proposed method achieves comparable or improved performance across all considered list sizes, with gains of up to 0.4 dB relative to benchmark designs.