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The Gaussian isoperimetric inequality and decoding error probabilities for the Gaussian channel

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2 Author(s)
Tillich, J. ; INRIA, France ; Zemor, G.

The Gaussian isoperimetric inequality states that among all sets in Rn with prescribed Gaussian measure, the half-spaces have minimal Gaussian perimeter. We apply this result to Voronoi regions of codes in Euclidean space and obtain a surprisingly precise description of how the maximum-likelihood decoding error probability varies as a function of the minimum Euclidean distance.

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Information Theory, IEEE Transactions on  (Volume:50 ,  Issue: 2 )