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.
Local rank-modulation is a generalization of the rank-modulation scheme, which
has been recently suggested as a way of storing information in flash memory. We
study Gray codes for the local rank-modulation scheme in order to simulate
conventional multi-level flash cells while retaining the benefits of rank
modulation. Unlike the limited scope of previous works, we consider code
constructions for the entire range of parameters including the code length,
sliding window size, and overlap between adjacent windows. We show our
constructed codes have asymptotically-optimal rate. We also provide efficient
encoding, decoding, and next-state algorithms.Comment: 7 pages, 1 figure, shorter version was submitted to ISIT 201

Eyal En Gad

Jehoshua Bruck

Michael Langberg

Moshe Schwartz

Senior Member

English

arXiv

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. Local rank-modu-lation is a generalization of the rank-modulation scheme, which has been recently suggested as a way of storing information in flash memory. We study gray codes for the local rank-modulation scheme in order to simulate conventional multilevel flash cells while retaining the benefits of rank modulation. Unlike the limited scope of previous works, we consider code constructions for the en-tire range of parameters including the code length, sliding-window size, and overlap between adjacent windows. We show that the presented codes have asymptotically optimal rate. We also provide efficient encoding, decoding, and next-state algorithms. Index Terms—Flash memory, gray code, local rank modulation, permutations, rank modulation. I

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Generalized Gray codes for local rank modulation

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. Local rank-modulation is a generalization of the rank-modulation scheme, which has been recently suggested as a way of storing information in flash memory. We study Gray codes for the local rank-modulation scheme in order to simulate conventional multi-level flash cells while retaining the benefits of rank modulation. Unlike the limited scope of previous works, we consider code constructions for the entire range of parameters including the code length, sliding window size, and overlap between adjacent windows. We show our constructed codes have asymptotically-optimal rate. We also provide efficient encoding, decoding, and next-state algorithms

En Gad, Eyal

Langberg, Michael

Schwartz, Moshe

Bruck, Jehoshua

Caltech Authors - Main

Generalized Gray Codes for Local Rank Modulation

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http://paradise.caltech.edu/%7Eeengad/publications/GGCLRM13.pdf

Generalized Gray Codes for Local Rank Modulation

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