A binary analog to the entropy-power inequality
Shamai, S.
Wyner, A.D.
AT&T Bell Lab., Murray Hill, NJ;
This paper appears in: Information Theory, IEEE Transactions on
Publication Date: Nov 1990
Volume: 36,
Issue: 6
On page(s): 1428-1430
ISSN: 0018-9448
References Cited: 7
CODEN: IETTAW
INSPEC Accession Number: 3825318
Digital Object Identifier: 10.1109/18.59938
Current Version Published: 2002-08-06
Abstract
Let {Xn}, {Yn} be
independent stationary binary random sequences with entropy H(
X), H(Y), respectively. Let
h(ζ)=-ζlogζ-(1-ζ)log(1-ζ),
0⩽ζ⩽1/2, be the binary entropy function and let
σ(X)=h-1 (H(X)),
σ(Y)=h-1 (H(Y)).
Let zn=Xn⊕Yn
, where ⊕ denotes modulo-2 addition. The following analog of
the entropy-power inequality provides a lower bound on H(Z
), the entropy of {Zn}:
σ(Z)⩾σ(X)*σ(Y), where
σ(Z)=h-1 (H(Z)),
and α*β=α(1-β)+β(1-α). When {Yn} are independent identically distributed, this reduces to
Mrs. Gerber's Lemma from A.D. Wyner and J. Ziv (1973)
Index
Terms
Available to subscribers and IEEE members.
References
Available to subscribers and IEEE members.
Citing Documents
Available to subscribers and IEEE members.
Cart
