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IEEE TRANSACTIONS ON INFORMATION THEORY, VOL. 48, NO. 1, JANUARY 2002 309 A Note on the PoorVerd Upper Bound for the Channel
 

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,
Po-Ning Chen, Senior Member, IEEE, and
Ziad Rached, Student Member, IEEE
Abstract--In an earlier work, Poor and Verdú established an upper
bound for the reliability function of arbitrary single-user discrete-time
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 Terms--Arbitrary 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 finite-dimen-
sional distributions [9]
XXX 1= Xn = X(n)

  

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

 

Collections: Engineering