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The worst additive noise under a covariance constraint

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2 Author(s)
Diggavi, S.N. ; AT&T Shannon Labs., Florham Park, NJ, USA ; Cover, T.M.

The maximum entropy noise under a lag p autocorrelation constraint is known by Burg's theorem to be the pth order Gauss-Markov process satisfying these constraints. The question is, what is the worst additive noise for a communication channel given these constraints? Is it the maximum entropy noise? The problem becomes one of extremizing the mutual information over all noise processes with covariances satisfying the correlation constraints R0,…, Rp. For high signal powers, the worst additive noise is Gauss-Markov of order p as expected. But for low powers, the worst additive noise is Gaussian with a covariance matrix in a convex set which depends on the signal power

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Information Theory, IEEE Transactions on  (Volume:47 ,  Issue: 7 )