On the distribution of the conditional mean estimator in Gaussian noise

Alex Dytso, H. Vincent Poor, Shlomo Shamai

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

Consider the conditional mean estimator of the random variable X from the noisy observation Y = X + N where N is zero mean Gaussian with variance σ2 (i.e., E[X|Y ]). This work characterizes the probability distribution of E[X|Y ]. As part of the proof, several new identities and results are shown. For example, it is shown that the k-th derivative of the conditional expectation is proportional to the (k + 1)-th conditional cumulant. It is also shown that the compositional inverse of the conditional expectation is well-defined and is characterized in terms of a power series by using Lagrange inversion theorem.

Original languageEnglish (US)
Title of host publication2020 IEEE Information Theory Workshop, ITW 2020
PublisherInstitute of Electrical and Electronics Engineers Inc.
ISBN (Electronic)9781728159621
DOIs
StatePublished - Apr 11 2021
Event2020 IEEE Information Theory Workshop, ITW 2020 - Virtual, Riva del Garda, Italy
Duration: Apr 11 2021Apr 15 2021

Publication series

Name2020 IEEE Information Theory Workshop, ITW 2020

Conference

Conference2020 IEEE Information Theory Workshop, ITW 2020
Country/TerritoryItaly
CityVirtual, Riva del Garda
Period4/11/214/15/21

All Science Journal Classification (ASJC) codes

  • Computational Theory and Mathematics
  • Information Systems
  • Signal Processing
  • Software
  • Theoretical Computer Science

Keywords

  • Conditional mean estimator
  • Gaussian Noise

Fingerprint

Dive into the research topics of 'On the distribution of the conditional mean estimator in Gaussian noise'. Together they form a unique fingerprint.

Cite this