TY - JOUR
T1 - Second-order asymptotics of mutual information
AU - Prelov, Viacheslav V.
AU - Verdú, Sergio
N1 - Funding Information:
Manuscript received May 10, 2002; revised November 19, 2003. This work was supported in part by DIMACS, by the National Science Foundation under Grant NCR-0074277, and by the Russian Foundation for Basic Research (RFFI) under Grant 03-01-00592. V. V. Prelov is with the Institute for Problems of Information Transmission, Russian Academy of Sciences, Moscow 101447, Russia. S. Verdú is with the Department of Electrical Engineering, Princeton University, Princeton, NJ 08544 USA (e-mail: verdu@princeton.edu). Communicated by ˙. E. Telatar, Associate Editor for Shannon Theory. Digital Object Identifier 10.1109/TIT.2004.831784
PY - 2004/8
Y1 - 2004/8
N2 - A formula for the second-order expansion of the input-output mutual information of multidimensional channels as the signal-to-noise ratio (SNR) 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 study of the second-order asymptotics of mutual information finds application in the analysis of the bandwidth-power tradeoff achieved by various signaling strategies in the wideband regime.
AB - A formula for the second-order expansion of the input-output mutual information of multidimensional channels as the signal-to-noise ratio (SNR) 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 study of the second-order asymptotics of mutual information finds application in the analysis of the bandwidth-power tradeoff achieved by various signaling strategies in the wideband regime.
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U2 - 10.1109/TIT.2004.831784
DO - 10.1109/TIT.2004.831784
M3 - Article
AN - SCOPUS:3943062951
SN - 0018-9448
VL - 50
SP - 1567
EP - 1580
JO - IEEE Transactions on Information Theory
JF - IEEE Transactions on Information Theory
IS - 8
ER -