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IEEE TRANSACTIONS ON INFORMATION THEORY, VOL. 58, NO. 1, JANUARY 2012 311 A Generalized Poor-Verd Error Bound for
 

Summary: IEEE TRANSACTIONS ON INFORMATION THEORY, VOL. 58, NO. 1, JANUARY 2012 311
A Generalized Poor-Verdú Error Bound for
Multihypothesis Testing
Po-Ning Chen, Senior Member, IEEE, and Fady Alajaji, Senior Member, IEEE
Abstract--A lower bound on the minimum error probability
for multihypothesis testing is established. The bound, which is
expressed in terms of the cumulative distribution function of the
tilted posterior hypothesis distribution given the observation with
tilting parameter , generalizes an earlier bound due the
Poor and Verdú (1995). A sufficient condition is established under
which the new bound (minus a multiplicative factor) provides the
exact error probability asymptotically in . Examples illustrating
the new bound are also provided.
Index Terms--Channel reliability function, converse channel
coding theorems, hypothesis testing, maximum-a-posteriori esti-
mation, probability of error.
I. INTRODUCTION
I N [3], Poor and Verdú establish a lower bound to the min-
imum error probability of multihypothesis testing. Specif-
ically, given two random variables and with joint distri-

  

Source: Alajaji, Fady - Department of Mathematics and Statistics, Queen's University (Kingston)

 

Collections: Engineering