Fine-tuning ORBGRAND with Very Few Channel Soft Values

2025-07-11

AI Summary

To address the performance degradation of ORBGRAND under finite-length codes caused by inaccurate pattern ordering, this paper proposes a low-complexity soft-information refinement method: starting from the predetermined error-pattern sequence generated by ORB, it incorporates only a minimal number of original channel log-likelihood ratios (LLRs) to fine-tune the testing order. The key contribution is a novel metric—“ordering well-orderedness”—grounded in asymptotic integer partition theory, enabling efficient evaluation and optimization of the ranking quality of critical error patterns. This metric requires no iterative computation or parameter training, substantially reducing reliance on soft information. Experimental results demonstrate that the proposed method achieves near-maximum-likelihood (ML) decoding performance with negligible computational overhead—particularly pronounced for medium-to-short code lengths—thereby closing the gap between practical GRAND variants and the ML bound.

Technology Category

• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Machine Learning: Learning Preferences or Rankings
• Search and Optimization: Mixed Discrete/Continuous Search

Application Category

• Security and Privacy: Large-scale security measurements
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs

Abstract

Guessing random additive noise decoding (GRAND) is a universal decoding paradigm that decodes by repeatedly testing error patterns until identifying a codeword, where the ordering of tests is generated by the received channel values. On one hand, while testing error patterns in a descending order of posterior probabilities leads to maximum likelihood decoding, its implementation complexity is prohibitive. On the other hand, testing error patterns with a prescribed set of error patterns permuted by the ranking among magnitudes of log-likelihood ratios (i.e., ordered reliability bits, ORB) enables efficient implementation, but results in performance loss for finite-length codes. Aiming at harnessing the strengths of these two approaches, this work proposes a fine-tuning method to improve ORBGRAND, adjusting the ordering of tests with the aid of very few exact channel soft values. This method is based on a metric for assessing the ``well-orderedness'' of error patterns. The metric is studied via the lens of the asymptotic theory of integer partitioning, which provides highly accurate estimation in numerical experiments. The metric then leads to an effective identification of fine-tuning to conduct, at the cost of a negligible increment of complexity. Numerical experiments demonstrate that the proposed fine-tuning method achieves a substantial performance enhancement compared with ORBGRAND.

Problem

• Improving ORBGRAND decoding with minimal channel soft values
• Reducing performance loss in finite-length codes via fine-tuning
• Enhancing error pattern ordering with low-complexity adjustments

Innovation

• Fine-tuning ORBGRAND with few soft values
• Metric for assessing error pattern order
• Asymptotic theory guides fine-tuning efficiency