A Type Covering Lemma and the Excess Distortion Exponent for Coding Memoryless Laplacian Sources

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 magnitude-error 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 Laplacian-type class, one can employ the classical method of types to solve source coding and source-channel coding problems regarding the MLS