 
Summary: IEEE TRANSACTIONS ON INFORMATION THEORY, VOL. 48, NO. 1, JANUARY 2002 309
A Note on the PoorVerdú Upper Bound for the Channel
Reliability Function
Fady Alajaji, Senior Member, IEEE,
PoNing Chen, Senior Member, IEEE, and
Ziad Rached, Student Member, IEEE
AbstractIn an earlier work, Poor and Verdú established an upper
bound for the reliability function of arbitrary singleuser discretetime
channels with memory. They also conjectured that their bound is tight for
all coding rates. In this note, we demonstrate via a counterexample in
volving memoryless binary erasure channels (BECs) that the PoorVerdú
upper bound is not tight at low rates. We conclude by examining possible
improvements to this bound.
Index TermsArbitrary channels with memory, binary erasure chan
nels (BECs), channel coding, channel reliability function, information spec
trum, probability of error.
I. INTRODUCTION
Consider an arbitrary input XXX defined by a sequence of finitedimen
sional distributions [9]
XXX 1= Xn = X(n)
