Toward Universal Decoding of Binary Linear Block Codes via Enhanced Polar Transformations

TL;DR

This paper presents $ ext{PD}^+$, a universal decoding algorithm that transforms any binary linear block code into a polar-like code, enabling efficient decoding with improved performance and lower complexity.

Contribution

It introduces a novel universal decoding method that converts diverse BLBCs into polar-like codes, compatible with existing polar decoders, and optimizes transformations using simulated annealing.

Findings

Achieves competitive or superior performance to state-of-the-art algorithms.

Reduces decoding complexity significantly.

Demonstrates versatility across various code types.

Abstract

Binary linear block codes (BLBCs) are essential to modern communication, but their diverse structures often require tailor-made decoders, increasing complexity. This work introduces enhanced polar decoding ($\mathsf{PD}^+$), a universal soft decoding algorithm that transforms any BLBC into a polar-like code compatible with efficient polar code decoders such as successive cancellation list (SCL) decoding. Key innovations in $\mathsf{PD}^+$ include pruning polar kernels, shortening codes, and leveraging a simulated annealing algorithm to optimize transformations. These enable $\mathsf{PD}^+$ to achieve competitive or superior performance to state-of-the-art algorithms like OSD and GRAND across various codes, including extended BCH, extended Golay, and binary quadratic residue codes, with significantly lower complexity. Moreover, $\mathsf{PD}^+$ is designed to be forward-compatible with advancements in polar code decoding techniques and AI-driven search methods, making it a robust and versatile solution for universal BLBC decoding in both present and future systems.