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.

翻译：本文将最初为无记忆信道接收机架构提出的广义最近邻译码（GNND）扩展至适用于块内存储（IBM）信道的向量化GNND（Vec-GNND）。利用广义互信息（GMI）作为失配容量操作下界，针对采用高斯码本的通用IBM信道，获得了最优Vec-GNND的解析刻画。该形式化方法进一步为接收机架构的受限变体提供了闭式最优性条件及可达GMI。此外，我们提出了基于GMI的高斯码本协方差与译码度量联合设计观点。由于对于固定协方差度量优化存在闭式解，联合设计可简化为输入协方差优化问题；针对对角协方差族，推导了一阶自洽最优性条件。在块非相干加性高斯白噪声信道与相位噪声信道上的数值评估表明，相较于传统缩放基线方法具有持续性能提升，突显了所提Vec-GNND在实际通信场景中的显著优势与潜在应用价值。