Optimal Single- and Multiple-Tree Almost Instantaneous Variable-to-Fixed Codes

Abstract

Variable-to-fixed codes are often based on dictionaries that obey the prefix-free property. In particular, the Tunstall algorithm builds such codes. However, the prefix-free property is not necessary to have correct variable-to-fixed codes. Removing the constraint to obey the prefix-free property may offer the opportunity to build more efficient codes. Here, we come back on the almost instantaneous variable-to-fixed codes introduced by Yamamoto and Yokoo. They considered both single trees and multiple trees to perform the parsing of the source data. We show that, in some cases, their techniques build suboptimal codes. We propose potential correctives to their techniques. We also propose a new, completely different technique based on dynamic programming that builds optimal dictionary trees.