On the Equivalence Between Stein and De Bruijn Identities Academic Article

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. 1963-2012 IEEE.

authors

• Qaraqe, Khalid
• Serpedin, Erchin

published proceedings

• IEEE TRANSACTIONS ON INFORMATION THEORY

author list (cited authors)

• Park, S., Serpedin, E., & Qaraqe, K.

citation count

• 13

complete list of authors

• Park, Sangwoo||Serpedin, Erchin||Qaraqe, Khalid

publication date

• December 2012

publisher

• Institute of Electrical and Electronics Engineers (IEEE)  Publisher

published in

• IEEE TRANSACTIONS ON INFORMATION THEORY  Journal

keywords

• Bayesian Cramer-rao Lower Bound (bcrlb)
• Costa's Epi
• Cramer-Rao Lower Bound (CRLB)
• De Bruijn's Identity
• Entropy Power Inequality (epi)
• Fisher Information Inequality (fii)
• Stein's Identity

Digital Object Identifier (DOI)

• 10.1109/TIT.2012.2210275

start page

• 7045

end page

• 7067

volume

• 58

issue

• 12

URL

• http://dx.doi.org/10.1109/tit.2012.2210275