Constructions of rank modulation codes

Abstract

Rank modulation is a way of encoding information to correct errors in flash memory devices as well as impulse noise in transmission lines. Modeling rank modulation involves construction of packings of the space of permutations equipped with the Kendall tau distance. We present several general constructions of codes in permutations that cover a broad range of code parameters. In particular, we show that a code that corrects Hamming errors can be used to construct a code for correcting Kendall errors. For instance, from BCH codes we obtain codes correcting t Kendall errors in n memory cells that support the order of n!/ logt n! messages, for any t = 1, 2, ‥‥ We also construct families of codes that correct a number of errors that grows with n at varying rates, from Θ(n) to Θ(n2).