Codes in Permutations and Error Correction for Rank Modulation

Details Codes in Permutations and Error Correction for Rank Modulation Codes in Permutations and Error Correction for Rank Modulation

2009-08-27

arxiv.org/abs/0908.4094v3

IEEE Transactions on Information Theory, Vol. 56, Issue 7, July 2010, pp. 3158 - 3165

Computer Science

Information Theory

Some typos corrected from the published journal version

Scientific paper

10.1109/TIT.2010.2048455

Codes for rank modulation have been recently proposed as a means of protecting flash memory devices from errors. We study basic coding theoretic problems for such codes, representing them as subsets of the set of permutations of $n$ elements equipped with the Kendall tau distance. We derive several lower and upper bounds on the size of codes. These bounds enable us to establish the exact scaling of the size of optimal codes for large values of $n$. We also show the existence of codes whose size is within a constant factor of the sphere packing bound for any fixed number of errors.

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