GRAND for Gaussian Intersymbol Interference Channels

TL;DR

This work applies the recently proposed decoding paradigm of guessing random additive noise decoding (GRAND) to channels with memory, focusing on linear Gaussian intersymbol interference channels, and obtains the optimal GRAND algorithm as a generalization of soft GRAND (SGRAND) for linear Gaussian ISI channels, termed SGRAND-ISI, which is equivalent to the maximum-likelihood (ML) decoding algorithm.

Abstract

Channel decoding is a challenging task in communication channels exhibiting memory effects. In this work, we apply the recently proposed decoding paradigm of guessing random additive noise decoding (GRAND) to channels with memory, focusing on linear Gaussian intersymbol interference (ISI) channels. For describing error patterns (EPs), we introduce the concept of error burst to account for the memory effect, and define sequence reliability to characterize the likelihood of EP. Based on sequence reliability, we obtain the optimal GRAND algorithm as a generalization of soft GRAND (SGRAND) for linear Gaussian ISI channels, termed SGRAND-ISI, which is equivalent to the maximum-likelihood (ML) decoding algorithm. We then develop order-reliability-bit (ORB) GRAND algorithms based on SGRAND-ISI, to facilitate implementation. In numerical experiments, our proposed algorithms achieve multiple-dB improvements compared to GRAND algorithms which ignore channel memory, and can often attain performance within 0.1--0.2dB of the ML lower bound. We also compare our proposed algorithms with the recently proposed ORBGRAND-Approximate Independence algorithm for handling channel memory, and observe a performance gain of at least 0.5dB at block error rate of $10^{-3}$, meanwhile incurring a substantially lower computational complexity.

Figures (8)

• Figure 1: CDFs of sequence reliability in the first-order ISI channel for CA-Polar(128,114+6) with $(h_0,h_1)=(\sqrt{0.9},\sqrt{0.1})$, where the CRC-6 generator polynomial is $g(x)=x^6+x+1$.
• Figure 2: Performance in the first-order ISI channel with $h_0=\sqrt{0.9}$ and $h_1=\sqrt{0.1}$.
• Figure 3: Average number of queries in first-order ISI channel with $h_0=\sqrt{0.9}, h_1=\sqrt{0.1}$ for CA-Polar(128, 114+6).
• Figure 4: Average number of queries in first-order ISI channel with $h_0=\sqrt{0.9}, h_1=\sqrt{0.1}$ for BCH(127, 113).
• Figure 5: Performance in first-order ISI channel with $h_0=\sqrt{0.6}, h_1=\sqrt{0.4}$ for BCH(127, 113).

Theorems & Definitions (14)

• Definition 1
• Example 1
• Definition 2
• Theorem 1
• Lemma 1
• Lemma 2
• Lemma 3
• Example 2
• Definition 3
• Example 3