The Kraft sum as a monotone function on the refinement-ordered set of uniquely decipherable codes

Abstract

The set of all uniquely decipherable (UD) codes is partially ordered by re nement, meaning that all strings in the cruder code can be represented as con- catenations of strings taken from the ner code. The Kraft sum is a monotone (increasing) function on this poset. In the re nement order, chains of UD codes having the same Kraft sum are necessarily of the simple descending type.