A probabilistic approach to some asymptotics in source coding

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 the prefix condition code that minimizes the average transmission cost when the source symbols are equiprobable.