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

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.