Generalized Nearest Neighbor Decoding

TL;DR

This paper proposes a generalized nearest neighbor decoding method that improves performance over traditional approaches by incorporating channel state information and codeword scaling, especially in fading and quantized channels.

Contribution

It introduces an optimal generalized nearest neighbor decoding rule based on generalized mutual information for Gaussian channels, extending traditional decoding strategies.

Findings

Improved decoding performance in fading channels with imperfect CSI

Enhanced decoding in channels with quantization effects

Comparison of generalized decoding with existing solutions

Abstract

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 the 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.