Generalisation of Kraft inequality for source coding into permutations

Abstract

We develop a general framework to prove Kraft-type inequalities for prefix-free permutation codes for source coding with various notions of permutation code and prefix. We also show that the McMillan-type converse theorem in most of these cases fails, and give a general form of a counterexample. Our approach is more general and works for other structures besides permutation codes. The classical Kraft inequality for prefix-free codes and results about permutation codes follow as corollaries of our main theorem and main counterexample.