Reducing ORBGRAND Latency via Partial Gaussian Elimination

TL;DR

This paper introduces an elimination-aided ORBGRAND decoding scheme that significantly reduces latency and complexity by integrating partial Gaussian elimination, making it suitable for real-time ultra-reliable low-latency communications.

Contribution

It proposes a novel elimination-aided ORBGRAND method that uses partial Gaussian elimination to filter error patterns, reducing latency without sacrificing error correction performance.

Findings

Filters out more than 50% of error patterns

Reduces average and worst-case latency

Maintains block error rate performance

Abstract

Guessing Random Additive Noise Decoding (GRAND) is a universal framework for decoding all block codes by testing candidate error patterns (EPs). Ordered Reliability Bits GRAND (ORBGRAND) facilitates parallel implementation of GRAND by exploiting log-likelihood ratio (LLR) rankings but still suffers from high tail latency under unfavorable channel conditions, limiting its use in real-time systems. We propose an elimination-aided ORBGRAND scheme that reduces decoding latency by integrating the Rank of the Most Reliable Erroneous (RMRE) bit with a partial Gaussian-elimination (GE) filtering mechanism. The scheme groups and jointly verifies EPs that share the same RMRE, and once a valid EP is identified, the ORBGRAND search is resumed. By leveraging prior GE steps to filter out unnecessary guesses, this approach significantly reduces the number of EPs to be tested, thereby lowering both average and worst-case latency while maintaining error-correction performance. Simulation results show that compared to the original ORBGRAND, the elimination-aided ORBGRAND filters out more than 50\% of EPs and correspondingly reduce overall computational complexity, all with no loss in block error rate. This demonstrates that this approach is suitable for ultra-reliable low-latency communication scenarios.