The worst additive noise under a covariance constraint

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 thes e constraints. The question is, what is the worst additive noise for a comm unication channel given these constraints? Is it the maximum entropy noise? The problem becomes one of extremizing the mutual information over all nois e processes with covariances satisfying the correlation constraints R-0,.., R-p. For high signal powers, the worst additive noise is Gauss-Markov of o rder p as expected. But for low powers, the worst additive noise is Gaussia n with a covariance matrix in a convex set which depends on the signal powe r.