 
Summary: IEEE TRANSACTIONS ON INFORMATION THEORY, VOL. 58, NO. 1, JANUARY 2012 311
A Generalized PoorVerdú Error Bound for
Multihypothesis Testing
PoNing Chen, Senior Member, IEEE, and Fady Alajaji, Senior Member, IEEE
AbstractA 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 TermsChannel reliability function, converse channel
coding theorems, hypothesis testing, maximumaposteriori 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
