Variable-Length Code Based on Order Complexity and Its Application in Random Permuted Symbol

Abstract

This paper introduces the concept of order complexity, which represents the minimum number of partial ordering operations to make a string of perfectly ordered symbols. A novel variable-length code expressing such order complexity using binary digits is proposed herein. The proposed code is general, uniquely decipherable, and useful for coding a string of random permuted symbols having unknown statistics or which are preferred to have a uniform distribution.