GRAND for Gaussian Intersymbol Interference Channels

Abstract

Channel decoding is challenging in communication channels exhibiting memory effects. In this work, we extend the recently proposed decoding paradigm of guessing random additive noise decoding (GRAND) to channels with memory, focusing on linear Gaussian intersymbol interference (ISI) channels. To characterize error patterns (EPs) under channel memory, we introduce the concept of error bursts and define sequence reliability to quantify the likelihood of an EP. Based on sequence reliability, we develop soft GRAND for ISI channels, termed SGRAND-ISI, which generalizes SGRAND to linear Gaussian ISI channels and is equivalent to maximum-likelihood (ML) decoding. We then develop ordered reliability bit GRAND (ORBGRAND) variants based on SGRAND-ISI that replace exact sequence reliabilities with rank-based approximations to reduce online computation. The proposed framework is first established for binary-input first-order ISI channels and subsequently extended to higher-order channel memory and higher-order modulation. Numerical experiments over first- and second-order ISI channels show that the proposed algorithms achieve multiple-dB gains over GRAND algorithms that ignore channel memory and can operate within $0.1$-$0.2$ dB of the ML benchmark. Compared with the recently proposed ORBGRAND-Approximate Independence algorithm, CDF-ORBGRAND-ISI provides a gain of at least $0.5$ dB at a block error rate (BLER) of $10^{-3}$. We further evaluate the online decoding complexity of the proposed GRAND-ISI algorithms using a module-wise complexity analysis.