GRAND for Rayleigh Fading Channels

TL;DR

This paper introduces Fading-GRAND, an extension of GRAND decoding tailored for Rayleigh fading channels, which adapts to fading conditions and outperforms traditional decoders in terms of error rate and complexity.

Contribution

The paper proposes Fading-GRAND, a novel variant of GRAND that accounts for Rayleigh fading, improving decoding performance and reducing complexity compared to existing methods.

Findings

Fading-GRAND outperforms B-M decoding for BCH codes by 0.5-6.5 dB at FER 10^-7.

Fading-GRAND surpasses GRANDAB by 0.2-8 dB at FER 10^-7.

Fading-GRAND has approximately half to one-fortieth the complexity of GRANDAB.

Abstract

Guessing Random Additive Noise Decoding (GRAND) is a code-agnostic decoding technique for short-length and high-rate channel codes. GRAND tries to guess the channel noise by generating test error patterns (TEPs), and the sequence of the TEPs is the main difference between different GRAND variants. In this work, we extend the application of GRAND to multipath frequency non-selective Rayleigh fading communication channels, and we refer to this GRAND variant as Fading-GRAND. The proposed Fading-GRAND adapts its TEP generation to the fading conditions of the underlying communication channel, outperforming traditional channel code decoders in scenarios with $L$ spatial diversity branches as well as scenarios with no diversity. Numerical simulation results show that the Fading-GRAND outperforms the traditional Berlekamp-Massey (B-M) decoder for decoding BCH code $(127,106)$ and BCH code $(127,113)$ by $\mathbf{0.5\sim6.5}$ dB at a target FER of $10^{-7}$. Similarly, Fading-GRAND outperforms GRANDAB, the hard-input variation of GRAND, by $0.2\sim8$ dB at a target FER of $10^{-7}$ with CRC $(128,104)$ code and RLC $(128,104)$. Furthermore the average complexity of Fading-GRAND, at $\frac{E_b}{N_0}$ corresponding to target FER of $10^{-7}$, is $\frac{1}{2}\times\sim \frac{1}{46}\times$ the complexity of GRANDAB.