GRAND for Fading Channels using Pseudo-soft Information

TL;DR

This paper enhances GRAND decoding for fading channels by using pseudo-soft information derived from noise statistics post-equalization, significantly improving error performance over hard decoding.

Contribution

It introduces a novel pseudo-soft information approach for GRAND decoding in fading channels, eliminating the need for per-bit reliability computation.

Findings

Pseudo-soft GRAND schemes approach state-of-the-art soft decoding performance.

Achieve up to 10dB SNR gain over hard-GRAND at a block-error rate of 10^-3.

Effective with linear equalization methods like ZF and MMSE.

Abstract

Guessing random additive noise decoding (GRAND) is a universal maximum-likelihood decoder that recovers code-words by guessing rank-ordered putative noise sequences and inverting their effect until one or more valid code-words are obtained. This work explores how GRAND can leverage additive-noise statistics and channel-state information in fading channels. Instead of computing per-bit reliability information in detectors and passing this information to the decoder, we propose leveraging the colored noise statistics following channel equalization as pseudo-soft information for sorting noise sequences. We investigate the efficacy of pseudo-soft information extracted from linear zero-forcing and minimum mean square error equalization when fed to a hardware-friendly soft-GRAND (ORBGRAND). We demonstrate that the proposed pseudo-soft GRAND schemes approximate the performance of state-of-the-art decoders of CA-Polar and BCH codes that avail of complete soft information. Compared to hard-GRAND, pseudo-soft ORBGRAND introduces up to 10dB SNR gains for a target 10^-3 block-error rate.