A Probabilistic Approach to Some Asymptotics in Noiseless Communication

Renewal theory is a powerful tool in the analysis of source codes. In this paper, we use renewal theory to obtain some asymptotic properties of finite-state noiseless channels. We discuss the relationship between these results and earlier uses of renewal theory to analyze the Lempel- Ziv codes and the Tunstall code. As a new application of our results, we provide a simple derivation of the asymptotic performance of two of the Perl, Garey, and Even prefix condition codes.