Constant-Weight Gray Codes for Local Rank Modulation

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

2010-02-07

arxiv.org/abs/1002.1436v1

Computer Science

Information Theory

Scientific paper

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.

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