Codes in permutations and error correction for rank modulation
Abstract
Codes Ìý´Ú´Ç°ùÌý rank Ìý modulation Ìýhave been recently proposed as a means of protecting flash memory devices fromÌý errors . We study basicÌý coding Ìýtheoretic problems for suchÌý codes , representing them as subsets of the set ofÌý permutations ÌýofÌý n Ìýelements equipped with the Kendall tau distance. We derive several lower and upper bounds on the size ofÌý codes . These bounds enable us to establish the exact scaling of the size of optimalÌý codes Ìýfor large values of n. We also show the existence ofÌý codes whose size is within a constant factor of the sphere packing bound for any fixed number ofÌý errors .