Generalized Tunstall codes for sources with memory

Tunstall codes are variable-to-fixed length codes that maximize the expected number of source letters per dictionary string for discrete, memoryless sources. We analyze a generalization of Tunstall coding to sources with memory and demonstrate that as the dictionary size increases, the number of code letters per source symbol comes arbitrarily close to the minimum among all variable-to-fixed length codes of the same size. We also find the asymptotic relationship between the dictionary size and the average length of a dictionary entry.