DIMACS TR: 2002-16

Second-order Asymptotics of Mutual Information

Authors: Viacheslav Prelov and Sergio Verdú


A formula for the second-order expansion of the input-output mutual information of multidimensional channels as the signal-to-noise ratio goes to zero is obtained. While the additive noise is assumed to be Gaussian, we deal with very general classes of input and channel distributions. As special cases, these channel models include fading channels, channels with random parameters and channels with almost Gaussian noise. When the channel is unknown at the receiver, the second term in the asymptotic expansion depends not only on the covariance matrix of the input signal but also on the fourth mixed moments of its components. The second-order asymptotics of mutual information finds application in the analysis of the bandwidth-power tradeoff achieved by specific (not necessarily optimum) input signaling in the wideband regime.

Keywords: Mutual Information, Channel Capacity, Fading Channels, Nonlinear Channels, Low-power communication.

Paper Available at: ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/2002/2002-16.ps.gz

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