Vectorized Generalized Nearest Neighbor Decoding for In-block Memory Channel

2026-05-15

AI Summary

This work addresses the performance limitations of conventional decoding methods in communication channels exhibiting intra-block memory. To overcome this challenge, the paper proposes a vectorized generalized nearest neighbor (GNN) decoding architecture and, for the first time, adapts it to such channels. Leveraging generalized mutual information, the authors develop a joint optimization framework that simultaneously designs codebook covariance and decoding metrics, deriving closed-form optimality conditions to enable coherent design of Gaussian codebooks and metrics. Evaluated on block noncoherent additive white Gaussian noise and phase noise channels, the proposed approach consistently outperforms conventional scaled baseline schemes, yielding notable and stable performance gains.

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.

Problem

• in-block memory channel
• generalized nearest neighbor decoding
• vectorized decoding
• mismatch capacity
• Gaussian codebook

Innovation

• Vectorized GNND
• In-block memory channel
• Generalized mutual information
• Joint covariance-metric optimization
• Mismatched decoding