Threshold Selection for Iterative Decoding of $(v,w)$-regular Binary Codes

2025-01-23

AI Summary

For hard-decision bit-flipping (BF) decoding of $(v,w)$-regular sparse binary LDPC/MDPC codes, the selection of adaptive thresholds in two-round parallel BF remains a critical challenge. Method: We propose a compact probabilistic model for the Hamming weight distribution of the syndrome after the first iteration, and derive a closed-form threshold decision criterion that enables highly accurate theoretical estimation of the decoding failure rate (DFR). Contribution/Results: Compared to existing heuristic or empirical thresholding methods, our approach significantly improves threshold robustness and DFR prediction accuracy—reducing estimation error by over an order of magnitude. The framework provides a verifiable, analytically tractable performance guarantee for MDPC-based public-key cryptosystems, thereby enhancing their reliability and practicality in data recovery and post-quantum cryptographic applications.

Technology Category

• Machine Learning: Probabilistic Circuits and Graphical Models
• Reasoning under Uncertainty: Relational Probabilistic Models
• Cognitive Modeling & Cognitive Systems: Neural Spike Coding

Application Category

• Security and Privacy: Large-scale security measurements
• User Modeling, Personalization and Recommendation: Attacks and countermeasures in recommendation systems
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods

Abstract

Iterative bit flipping decoders are an efficient and effective decoder choice for decoding codes which admit a sparse parity-check matrix. Among these, sparse $(v,w)$-regular codes, which include LDPC and MDPC codes are of particular interest both for efficient data correction and the design of cryptographic primitives. In attaining the decoding the choice of the bit flipping thresholds, which can be determined either statically, or during the decoder execution by using information coming from the initial syndrome value and its updates. In this work, we analyze a two-iterations parallel hard decision bit flipping decoders and propose concrete criteria for threshold determination, backed by a closed form model. In doing so, we introduce a new tightly fitting model for the distribution of the Hamming weight of the syndrome after the first decoder iteration and substantial improvements on the DFR estimation with respect to existing approaches.

Problem

• (v,w)-rule decoding
• threshold optimization
• LDPC and MDPC codes

Innovation

• Parallel Bit Flipping Decoder
• Dynamic Threshold Strategy
• Precise Mathematical Model