The interplay between estimation theory and information theory

Sergio Verdu

doi:10.1109/SPAWC.2005.1505855

The interplay between estimation theory and information theory

Sergio Verdu

Research output: Contribution to conference › Paper › peer-review

1 Scopus citations

Abstract

For signals observed in Gaussian noise, there are several interesting intersections between information theory and linear and nonlinear minimum mean-square error (MMSE) estimation. We unveil a new relationship between the input-output mutual information and the MMSE achievable by the optimal estimator of the input. This relationship holds for arbitrarily distributed scalar and vector signals, as well as for discrete-time and continuous-time noncausal MMSE estimation (smoothing). We will also focus on two applications of these information theoretic results: the mercury/waterfilling formula for power allocation with arbitrary input constellations; and a universal continuous-time nonlinear filtering formula that couples the signal-to-noise ratios achievable by smoothing and filtering.

Original language	English (US)
Pages	xxiv
DOIs	https://doi.org/10.1109/SPAWC.2005.1505855
State	Published - 2005
Event	2005 IEEE 6th Workshop on Signal Processing Advances in Wireless Communications, SPAWC 2005 - New York, NY, United States Duration: Jun 5 2005 → Jun 8 2005

Other

Other	2005 IEEE 6th Workshop on Signal Processing Advances in Wireless Communications, SPAWC 2005
Country/Territory	United States
City	New York, NY
Period	6/5/05 → 6/8/05

All Science Journal Classification (ASJC) codes

Signal Processing
General Engineering

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10.1109/SPAWC.2005.1505855

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abstract = "For signals observed in Gaussian noise, there are several interesting intersections between information theory and linear and nonlinear minimum mean-square error (MMSE) estimation. We unveil a new relationship between the input-output mutual information and the MMSE achievable by the optimal estimator of the input. This relationship holds for arbitrarily distributed scalar and vector signals, as well as for discrete-time and continuous-time noncausal MMSE estimation (smoothing). We will also focus on two applications of these information theoretic results: the mercury/waterfilling formula for power allocation with arbitrary input constellations; and a universal continuous-time nonlinear filtering formula that couples the signal-to-noise ratios achievable by smoothing and filtering.",

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year = "2005",

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note = "2005 IEEE 6th Workshop on Signal Processing Advances in Wireless Communications, SPAWC 2005 ; Conference date: 05-06-2005 Through 08-06-2005",

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AB - For signals observed in Gaussian noise, there are several interesting intersections between information theory and linear and nonlinear minimum mean-square error (MMSE) estimation. We unveil a new relationship between the input-output mutual information and the MMSE achievable by the optimal estimator of the input. This relationship holds for arbitrarily distributed scalar and vector signals, as well as for discrete-time and continuous-time noncausal MMSE estimation (smoothing). We will also focus on two applications of these information theoretic results: the mercury/waterfilling formula for power allocation with arbitrary input constellations; and a universal continuous-time nonlinear filtering formula that couples the signal-to-noise ratios achievable by smoothing and filtering.

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T2 - 2005 IEEE 6th Workshop on Signal Processing Advances in Wireless Communications, SPAWC 2005

Y2 - 5 June 2005 through 8 June 2005

ER -

The interplay between estimation theory and information theory

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