Rank permutation group codes based on Kendall's correlation statistic

Abstract

A coding scheme based on the properties of rank vectors is presented. The new codes are based on the theory of permutation groups by introducing a new notation for the group operation that simplifies the generation and decoding of desirable rank codes. The use of group theory is made possible by the introduction of the Kendall correlation coefficient as a measure of the distance between code words. This technique provides a method for the choice of rank vector code words superior to those that have been proposed in the past. Much of the terminology used in block coding can also be used to describe rank vector codes, but the actual quantities involved are quite different. The rank vector codes discussed in the paper offer the advantage of low sensitivity of the probability of error to the noise distribution because of the nonparametric character of rank vector detection schemes. Bounds that have been verified by extensive computer simulation have been derived for the probability of error.