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

2025-01-13

AI Summary

Binary linear block codes (BLBCs) lack efficient, universal soft-decision decoders. Method: This paper proposes Enhanced Polar Decoding (PD⁺), the first framework enabling adaptable structural transformation of arbitrary BLBCs into polar code decoders (e.g., SCL). It introduces a joint transformation framework integrating polar kernel pruning, length shortening, and simulated annealing optimization to achieve code-domain mapping and structural adaptation—preserving forward compatibility while supporting AI-driven search expansion. Contribution/Results: Experiments on extended BCH, extended Golay, and binary quadratic residue codes show PD⁺ matches or surpasses OSD and GRAND in error-correction performance, with significantly lower average computational complexity. PD⁺ establishes the first unified, polar-domain decoding paradigm for BLBCs that is general-purpose, computationally efficient, and theoretically interpretable.

Technology Category

• Search and Optimization: Learning to Search
• Machine Learning: Optimization
• Natural Language Processing: Learning & Optimization for NLP

Application Category

• Security and Privacy: Privacy-enhancing technologies
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Search and Retrieval-Augmented AI: Vertical and domain-specific search

Abstract

Binary linear block codes (BLBCs) are essential to modern communication, but their diverse structures often require multiple 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.

Problem

• Binary Linear Block Codes
• Decoding Process
• Complexity Reduction

Innovation

• Polar Code Decoding
• Simulated Annealing Algorithm
• Binary Linear Block Codes Conversion