Source coding for average rate and average distortion: New variable-length coding theorems

Although variable-length codes are known to be an efficient class of codes in noiseless coding, little is known about these codes for sources subjected to a fidelity constraint. Variable-length source coding theorems with a fidelity criterion are proved and variable-length coding is shown to be applicable to sources without any regularity requirements such as stationarity. Also, unlike fixed-length coding, it is shown that the convergence of average performances to the distortion-rate function does not depend on the sample path properties of the source.