DMCA
Convexity of Error Rates in Digital Communications Under Non-Gaussian Noise
BibTeX
@MISC{Loyka_convexityof,
author = {Sergey Loyka and Victoria Kostina and Francois Gagnon},
title = {Convexity of Error Rates in Digital Communications Under Non-Gaussian Noise},
year = {}
}
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Abstract
Abstract—Convexity properties of error rates of a class of decoders, including the ML/min-distance one as a special case, are studied for arbitrary constellations. Earlier results obtained for the AWGN channel are extended to a wide class of (non-Gaussian) noise densities, including unimodal and spherically-invariant noise. Under these broad conditions, symbol error rates are shown to be convex functions of the SNR in the high-SNR regime with an explicitly-determined threshold, which depends only on the constellation dimensionality and minimum distance, thus enabling an application of the powerful tools of convex optimization to such digital communication systems in a rigorous way. It is the decreasing nature of the noise power density around the decision region boundaries that insures the convexity of symbol error rates in the general case. The known high/low SNR bounds of the convexity/concavity regions are tightened and no further improvement is shown to be possible in general. I.
Keyphrases
error rate digital communication non-gaussian noise symbol error rate noise density decision region boundary high-snr regime explicitly-determined threshold convexity concavity region special case general case abstract convexity property rigorous way noise power density arbitrary constellation spherically-invariant noise minimum distance wide class broad condition ml min-distance digital communication system powerful tool decreasing nature convex function convex optimization known high low snr bound constellation dimensionality awgn channel
