Vectorized Generalized Nearest Neighbor Decoding for In-block Memory Channel

TL;DR

This paper introduces a vectorized generalized nearest neighbor decoding method for in-block memory channels, providing analytical optimality conditions and demonstrating performance improvements over traditional methods.

Contribution

It extends GNND to in-block memory channels, offering a closed-form optimality analysis and a joint design framework for decoding metrics and Gaussian codebook covariance.

Findings

Achieves performance gains over baseline methods in simulations.

Provides closed-form optimality conditions for the proposed decoding scheme.

Demonstrates the method's effectiveness on noncoherent AWGN and phase noise channels.

Abstract

This work extends the generalized nearest neighbor decoding (GNND), originally developed as a receiver architecture for memoryless channels, to a vectorized GNND (Vec-GNND) suitable for in-block memory (IBM) channels. Leveraging the generalized mutual information (GMI) as an operational lower bound on the mismatch capacity, an analytical characterization of the optimal Vec-GNND is obtained for general IBM channels with Gaussian codebooks. The formalism further provides closed-form optimality conditions and achievable GMIs for restricted variants of the receiver architecture. Furthermore, we formulate a GMI-based joint design viewpoint for Gaussian codebook covariance and decoding metrics. Since the metric optimization admits a closed-form solution for each fixed covariance, the joint design is reduced to an input-covariance optimization problem; for the diagonal covariance family, we derive first-order self-consistent optimality conditions. Numerical evaluations on block noncoherent additive white Gaussian noise channels and phase noise channels demonstrate consistent performance gains over conventional scaling-based baselines, highlighting the substantial advantages and potential relevance of the proposed Vec-GNND in realistic communication scenarios.