It is well known that for Gaussian channels, a nearest neighbor decoding rule, which seeks the minimum Euclidean distance between a codeword and the received channel output vector, is the maximum likelihood solution and hence capacity-achieving. Nearest neighbor decoding remains a convenient and yet mismatched solution for general channels, and the key message of this paper is that the performance of nearest neighbor decoding can be improved by generalizing its decoding metric to incorporate channel state dependent output processing and codeword scaling. Using generalized mutual information, which is a lower bound to the mismatched capacity under independent and identically distributed codebook ensemble, as the performance measure, this paper establishes the optimal generalized nearest neighbor decoding rule, under Gaussian channel input. Several restricted forms of the generalized nearest neighbor decoding rule are also derived and compared with existing solutions. The results are illustrated through several case studies for fading channels with imperfect receiver channel state information and for channels with quantization effects.

中文翻译：

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广义最近邻解码


众所周知，对于高斯信道，最近邻解码规则寻求码字和接收到的信道输出向量之间的最小欧几里德距离，是最大似然解，因此是容量实现。对于一般通道来说，最近邻解码仍然是一种方便但不匹配的解决方案，本文的关键信息是，可以通过概括其解码度量以合并与通道状态相关的输出处理和码字缩放来提高最近邻解码的性能。以独立同分布码本集合下失配容量下界广义互信息为性能指标，建立高斯信道输入下的最优广义最近邻译码规则。还导出了广义最近邻解码规则的几种限制形式，并与现有解决方案进行了比较。通过对具有不完善接收器信道状态信息的衰落信道和具有量化效应的信道的几个案例研究来说明结果。