Vectorized Generalized Nearest Neighbor Decoding for In-block Memory Channel
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 AWGN and phase-noise channels demonstrate consistent GMI gains over conventional scaling-based GNND schemes, suggesting potential performance advantages of Vec-GNNDR in practical communication systems.
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BibTeX
@misc{liu2026vectorized,
title = {{Vectorized Generalized Nearest Neighbor Decoding for In-block Memory Channel}},
author = {Yuhao Liu and Xinwei Li and Shuqin Pang and Hao Wu and Wenyi Zhang},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2605.15950},
eprint = {2605.15950},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2605.15950},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Vectorized Generalized Nearest Neighbor Decoding for In-block Memory Channel
AU - Yuhao Liu
AU - Xinwei Li
AU - Shuqin Pang
AU - Hao Wu
AU - Wenyi Zhang
PY - 2026
DA - 2026/10/14
PB - arXiv
DO - 10.48550/arxiv.2605.15950
UR - https://arxiv.org/abs/2605.15950
AB - 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 AWGN and phase-noise channels demonstrate consistent GMI gains over conventional scaling-based GNND schemes, suggesting potential performance advantages of Vec-GNNDR in practical communication systems.
ER -