# On Convexity of Error Rates in Digital Communications

@article{Loyka2013OnCO, title={On Convexity of Error Rates in Digital Communications}, author={Sergey L. Loyka and Victoria Kostina and François Gagnon}, journal={IEEE Transactions on Information Theory}, year={2013}, volume={59}, pages={6501-6516} }

Convexity properties of error rates of a class of decoders, including the maximum-likelihood/min-distance one as a special case, are studied for arbitrary constellations, bit mapping, and coding. Earlier results obtained for the additive white Gaussian noise channel are extended to a wide class of noise densities, including unimodal and spherically invariant noise. Under these broad conditions, symbol and bit error rates are shown to be convex functions of the signal-to-noise ratio (SNR) in the…

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