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Constant-Weight Gray Codes for Local Rank...
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Constant-Weight Gray Codes for Local Rank Modulation

Abstract

We consider the local rank-modulation scheme in which a sliding window going over a sequence of real-valued variables induces a sequence of permutations. The local rank-modulation, as a generalization of the rank-modulation scheme, has been recently suggested as a way of storing information in flash memory. We study constant-weight Gray codes for the local rank-modulation scheme in order to simulate conventional multi-level flash cells while retaining the benefits of rank modulation. We provide necessary conditions for the existence of cyclic and cyclic optimal Gray codes. We then specifically study codes of weight 2 and upper bound their efficiency, thus proving that there are no such asymptotically-optimal cyclic codes. In contrast, we study codes of weight 3 and efficiently construct codes which are asymptotically-optimal.

Authors

Schwartz M

Pagination

pp. 869-873

Publisher

Institute of Electrical and Electronics Engineers (IEEE)

Publication Date

June 1, 2010

DOI

10.1109/isit.2010.5513592

Name of conference

2010 IEEE International Symposium on Information Theory
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