 
Summary: On the Computation of the Joint SourceChannel
Error Exponent for Memoryless Systems 1
Yangfan Zhong, Fady Alajaji, and L. Lorne Campbell
Dept. of Mathematics and Statistics
Queen's University, Kingston, Ontario, K7L 3N6, Canada
{yangfan, fady, campblll}@mast.queensu.ca
Abstract  We study the analytical computation of
Csisz’ar's [2] randomcoding lower bound and sphere
packing upper bound for the lossless joint source
channel (JSC) error exponent, EJ (Q, W ), for a dis
crete memoryless source (DMS) Q and a discrete
memoryless channel (DMC) W . We provide equiva
lent expressions for these bounds, which can be read
ily calculated for arbitrary (Q, W ) pairs. We also es
tablish explicit conditions under which the bounds co
incide, thereby exactly determining EJ (Q, W ).
I. Csisz’ ar's Upper and Lower Bounds
Definition 1 A JSC code with blocklength n for a DMS with
finite alphabet S and distribution Q, and a DMC with finite
input alphabet X , finite output alphabet Y and transition
