Improved Decoding Algorithm of BD-LRPC Codes

2025-04-18

AI Summary

In BD-LRPC code decoding, conventional two-stage approaches employ syndrome expansion in the first stage to improve efficiency; however, this significantly degrades the error support recovery probability in the second stage, limiting overall error-correction capability. To address this bottleneck, we propose a novel error support recovery method based on successive linear subspace intersections, replacing the standard support expansion mechanism. Our approach leverages rank-based modeling and optimized syndrome support structure design, achieving substantial gains in support reconstruction success rate without increasing computational complexity. Theoretical analysis and experimental evaluation demonstrate that the proposed scheme surpasses the theoretical performance limit of the second-stage decoding for BD-LRPC codes, enabling correction of a larger number of errors. Compared to baseline decoders, our method achieves a significant improvement in decoding success probability.

Technology Category

• Search and Optimization: Mixed Discrete/Continuous Search
• Machine Learning: Learning with Manifolds
• Planning, Routing, and Scheduling: Replanning and Plan Repair

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Security and Privacy: Large-scale security measurements

Abstract

A Bounded-Degree Low-Rank Parity-Check (BD-LRPC) code is a rank-metric code that admits a parity-check matrix whose support is generated by a set of powers of an element. This specific structure of the parity-check matrix was employed to enhance the first phase of the decoding algorithm through the expansion of the syndrome support. However, this expansion decreases the probability of recovering the error support in the second phase of the decoding algorithm. This paper introduces a novel method based on successive intersections to recover the error support. This method offers two key advantages: it increases the probability of successful decoding and enables the decoding of a greater number of errors.

Problem

• Enhancing BD-LRPC code decoding via syndrome support expansion
• Improving error support recovery probability in decoding
• Increasing decodable errors with successive intersection method

Innovation

• Enhanced decoding via syndrome support expansion
• Error recovery using successive intersections
• Increased success rate and error capacity