A Path-Survival Analytical Framework for SCL Decoding of Polar Code

2026-06-24

AI Summary

Existing methods struggle to effectively analyze the decoding performance of CRC-aided successive cancellation list (CA-SCL) decoding. This work proposes a theoretical analysis framework based on a path survival model, establishing for the first time an analytical model tailored to CA-SCL decoding that characterizes the evolution of the correct path’s rank throughout the decoding process. The framework overcomes the limitations of conventional approaches such as density evolution, which cannot be directly applied to CA-SCL. Notably, it enables accurate and efficient prediction of decoding performance without relying on Monte Carlo simulations, demonstrating high accuracy and broad applicability across various code lengths, code rates, list sizes, and channel conditions.

Abstract

A theoretical analysis of CRC-aided successive cancellation list (CA-SCL) decoding for polar codes remains an open problem, despite its widespread practical adoption. While low-density parity-check (LDPC) codes benefit from mature analytical tools, such as density evolution (DE), for predicting the performance of belief-propagation (BP) decoding, similar techniques are not directly applicable to CA-SCL decoding. This limitation stems from the complex path-pruning mechanism inherent in CA-SCL decoding. In this paper, we propose an analytical framework based on a novel path-survival model that captures the evolution of the correct path's rank during decoding. The proposed framework enables efficient prediction of CA-SCL decoding performance without requiring exhaustive list-specific Monte Carlo simulations. Extensive numerical evaluations demonstrate its effectiveness across a wide range of code lengths, code rates, list sizes, and channel models.

Problem

• polar codes
• CA-SCL decoding
• path-pruning
• theoretical analysis
• decoding performance

Innovation

• path-survival model
• CA-SCL decoding
• polar codes
• performance prediction
• analytical framework