A decision procedure for finite decipherability and synchronizability of multivalued encodings

A multivalued encoding is a variable length coding system in which more than one codeword may correspond to each source symbol. The properties of unique decipherability, decipherability with finite delay, and synchronizability for multivalued encodings are characterized. In particular, the property, of unique decipherability is considered, and a recent conjecture about decipherability with finite delay is proved to be true. The notion of a synchronizable multivalued code is also introduced, and a necessary. and sufficient condition for a multivalued code to be synchronizable is provided. Some auxiliary results are also obtained.