Variable-length source coding with a cost depending only on the code word length

Abstract

Variable-length noiseless coding of sequences of length n produced by a discrete memoryless source is considered, where the cost of coding a sequence is assumed to be a function only of the code word length. A class of decision rules is defined for deciding which of two sources can be coded with smaller expected cost as n → ∞. It is shown that for a large family of cost functions, there exists a best decision rule.