High-performance low-complexity error pattern generation for ORBGRAND decoding

TL;DR

This paper introduces a new low-complexity scheduling algorithm for ORBGRAND decoding that improves error correction performance by up to 0.5dB at very low block error rates, leveraging a universal partial order.

Contribution

It proposes a universal partial order for ORBGRAND scheduling and an efficient algorithm to generate logistic weight order, enhancing decoding performance with minimal complexity.

Findings

Improved ORBGRAND schedule yields 0.5dB gain at BLER of 10^{-5}

Low-complexity approximation matches performance without degradation

Universal partial order guides effective error pattern generation

Abstract

Guessing Random Additive Noise Decoding (GRAND) is a recently proposed decoding method searching for the error pattern applied to the transmitted codeword. Ordered reliability bit GRAND (ORBGRAND) uses soft channel information to reorder entries of error patterns, generating them according to a fixed schedule, i.e. their logistic weight. In this paper, we show that every good ORBGRAND scheduling should follow an universal partial order, and we present an algorithm to generate the logistic weight order accordingly. We then propose an improved error pattern schedule that can improve the performance of ORBGRAND of 0.5dB at a block error rate (BLER) of $10^{-5}$, with increasing gains as the BLER decreases. This schedule can be closely approximated with a low-complexity generation algorithm that is shown to incur no BLER degradation.