TY - GEN

T1 - Estimation of non-Gaussian random variables in Gaussian noise

T2 - 2008 IEEE International Symposium on Information Theory, ISIT 2008

AU - Guo, Dongning

AU - Shamai, Shlomo

AU - Verdu, Sergio

PY - 2008/9/29

Y1 - 2008/9/29

N2 - This work studies the properties of the minimum mean-square error (MMSE) of estimating an arbitrary random variable contaminated by Gaussian noise based on the observation. The MMSE can be regarded as a function of the signalto-noise ratio (SNR), as well as a functional or transform of the input distribution. This paper shows that the MMSE is analytic in SNR for every random variable. Simple expressions for the derivatives of the MMSE as a function of the SNR are obtained. Since the input-output mutual information can be written as the integral of the MMSE as a function of SNR, the results also lead to higher derivatives of the mutual information. The MMSE and mutual information's convexity in the SNR and concavity in the input distribution are established. It is shown that there can be only one SNR for which the MMSE of a Gaussian random variable and that of a non-Gaussian random variable coincide. Application of the properties of the MMSE to the scalar Gaussian broadcast channel problem is presented.

AB - This work studies the properties of the minimum mean-square error (MMSE) of estimating an arbitrary random variable contaminated by Gaussian noise based on the observation. The MMSE can be regarded as a function of the signalto-noise ratio (SNR), as well as a functional or transform of the input distribution. This paper shows that the MMSE is analytic in SNR for every random variable. Simple expressions for the derivatives of the MMSE as a function of the SNR are obtained. Since the input-output mutual information can be written as the integral of the MMSE as a function of SNR, the results also lead to higher derivatives of the mutual information. The MMSE and mutual information's convexity in the SNR and concavity in the input distribution are established. It is shown that there can be only one SNR for which the MMSE of a Gaussian random variable and that of a non-Gaussian random variable coincide. Application of the properties of the MMSE to the scalar Gaussian broadcast channel problem is presented.

UR - http://www.scopus.com/inward/record.url?scp=52349110120&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=52349110120&partnerID=8YFLogxK

U2 - 10.1109/ISIT.2008.4595154

DO - 10.1109/ISIT.2008.4595154

M3 - Conference contribution

AN - SCOPUS:52349110120

SN - 9781424422579

T3 - IEEE International Symposium on Information Theory - Proceedings

SP - 1083

EP - 1087

BT - Proceedings - 2008 IEEE International Symposium on Information Theory, ISIT 2008

Y2 - 6 July 2008 through 11 July 2008

ER -