The worst additive noise under a covariance constraint

By Suhas N. Diggavi, Thomas M. Cover. IEEE Transactions on Information Theory, 2001

385 citations recorded by the source corpus.

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 R/sub 0/,..., R/sub p/. 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.

Subfields: Computer Networks and Communications, Electrical and Electronic Engineering, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/8a3a18d577829279eb4259de1f904f876daf3790

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Citations in the corpus

An Extremal Inequality Motivated by Multiterminal Information Theoretic Problems (2006, background): “Lemma 2 ([9], [10]): Let Z be a Gaussian vector with zero mean and covariance matrix KZ .”
Gaussian Assumption: The Least Favorable but the Most Useful [Lecture Notes] (2012, background): “ted by the notations Tr{·} and |·|, respectively. Since the vector generalization is quite direct, these results are not mentioned here except the following lemma. Lemma 2 (Worst Additive Noise Lemma [4], [7]): For a random vector w and a Gaussian random vector w G whose covariance matrices are iden”
On the degrees-of-freedom of the MIMO interference channel (2008, background): “(49) Using the results from [15], I(p; t1 +m n 1 +p ) is minimized when s1 is i.”
Information-Theoretic Approach to Strategic Communication as a Hierarchical Game (2015, background): “Proof: The fact that jointly Gaussian X; ; Y triple achieves RDSI S follows from Lemma 4 and the entropy maximization property of jointly Gaussian distributions subject to second order constraints [37].”
A Note on the Secrecy Capacity of the Multi-antenna Wiretap Channel (2007, methodology): “To put in perspective, proving the optimality of Gaussian U = X for the degraded vector Gaussian wiretap channel can be done with relative ease using, for example, the worst additive noise result of Diggavi and Cover [15].”
Channel Estimation and Performance Analysis of One-Bit Massive MIMO Systems (2016, background): “Furthermore, while the quantizer noise qd is non-Gaussian, we can obtain a lower bound on the achievable rate by making the worst-case assumption [41], [42] that in fact it is Gaussian with the same covariance matrix in (41).”
Optimum Co-Design for Spectrum Sharing between Matrix Completion Based MIMO Radars and a MIMO Communication System (2015, methodology): “Here, we consider circularly symmetric complex Gaussian codewords x(l) ∼ CN (0,Rxl), which achieve a lower bound of the channel capacity [50], [51].”