On the equivalence between Stein and de Bruijn identities

Research output: Contribution to journalArticle

8 Citations (Scopus)

Abstract

This paper focuses on illustrating 1) the equivalence between Stein's identity and De Bruijn's identity, and 2) two extensions of De Bruijn's identity. First, it is shown that Stein's identity is equivalent to De Bruijn's identity under additive noise channels with specific conditions. Second, for arbitrary but fixed input and noise distributions under additive noise channels, the first derivative of the differential entropy is expressed by a function of the posterior mean, and the second derivative of the differential entropy is expressed in terms of a function of Fisher information. Several applications over a number of fields, such as signal processing and information theory, are presented to support the usefulness of the developed results in this paper.

Original languageEnglish
Article number6248705
Pages (from-to)7045-7067
Number of pages23
JournalIEEE Transactions on Information Theory
Volume58
Issue number12
DOIs
Publication statusPublished - 2012

Fingerprint

Additive noise
equivalence
Entropy
Derivatives
Information theory
Signal processing
entropy
information theory

Keywords

  • Bayesian Cramér-Rao lower bound (BCRLB)
  • Costa's EPI
  • Cramér-Rao lower bound (CRLB)
  • De Bruijn's identity
  • entropy power inequality (EPI)
  • Fisher information inequality (FII)
  • Stein's identity

ASJC Scopus subject areas

  • Information Systems
  • Computer Science Applications
  • Library and Information Sciences

Cite this

On the equivalence between Stein and de Bruijn identities. / Park, Sangwoo; Serpedin, Erchin; Qaraqe, Khalid.

In: IEEE Transactions on Information Theory, Vol. 58, No. 12, 6248705, 2012, p. 7045-7067.

Research output: Contribution to journalArticle

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