 
Summary: A Type Covering Lemma and the Excess Distortion Exponent for Coding
Memoryless Laplacian Sources
Yangfan Zhong, Fady Alajaji and L. Lorne Campbell
Department of Mathematics and Statistics
Queen's University, Kingston, ON K7L 3N6, Canada
Email: {yangfan,fady,campblll}@mast.queensu.ca
Abstract In this work, we introduce the notion of Laplacian
type class and derive a type covering lemma for the memoryless
Laplacian source (MLS) under the magnitudeerror distortion
measure. We then present an application of the type covering
lemma to the lossy coding of the MLS. We establish a simple
analytical lower bound for the excess distortion exponent, namely,
the exponent of the probability of representing the source beyond
a given distortion threshold. It is noted that, by introducing the
Laplaciantype class, one can employ the classical method of
types to solve source coding and sourcechannel coding problems
regarding the MLS.
I. INTRODUCTION
It is well known that the method of types is a very useful
tool in information theory, particularly in Shannon theory,
