Almost-Sure Variable-Length Source Coding Theorems for General Sources

Source coding theorems for general sources are presented. For a source , which is assumed to be a probability measure on all strings of infinite-length sequence with a finite alphabet, the notion of almost-sure sup entropy rate is defined; it is an extension of the Shannon entropy rate. When both an encoder and a decoder know that a sequence is generated by , the following two theorems can be proved: 1) in the almost-sure sense, there is no variable-rate source coding scheme whose coding rate is less than the almost-sure sup entropy rate of . and 2) in the almost-sure sense, there exists a variable-rate source coding scheme whose coding rate achieves the almost-sure sup entropy rate of .