Constant-weight gray codes for local rank modulation

Eyal Gad, Michael Langberg, Moshe Schwartz, Jehoshua Bruck

פרסום מחקרי: פרסום בכתב עתמאמרביקורת עמיתים


We consider the local rank-modulation (LRM) scheme in which a sliding window going over a sequence of real-valued variables induces a sequence of permutations. LRM is a generalization of the rank-modulation scheme, which has been recently suggested as a way of storing information in flash memory. We study constant-weight Gray codes for the LRM scheme in order to simulate conventional multilevel flash cells while retaining the benefits of rank modulation. We present a practical construction of codes with asymptotically-optimal rate and weight asymptotically half the length, thus having an asymptotically-optimal charge difference between adjacent cells. Next, we turn to examine the existence of optimal codes by specifically studying codes of weight 2 and 3. In the former case, we upper bound the code efficiency, proving that there are no such asymptotically-optimal cyclic codes. In contrast, for the latter case we construct codes which are asymptotically- optimal. We conclude by providing necessary conditions for the existence of cyclic and cyclic optimal Gray codes.

שפה מקוריתאנגלית
מספר המאמר5959206
עמודים (מ-עד)7431-7442
מספר עמודים12
כתב עתIEEE Transactions on Information Theory
מספר גיליון11
מזהי עצם דיגיטלי (DOIs)
סטטוס פרסוםפורסם - נוב׳ 2011

הערה ביבליוגרפית

Funding Information:
Manuscript received December 29, 2010; revised May 13, 2011; accepted July 07, 2011. Date of current version November 11, 2011. This work was supported in part by the ISF under Grant 134/10 and Grant 480/08, by the Open University of Israel’s research fund under Grant 46114, and by the NSF under Grant NSF-0801795, and under an NSF-NRI award.

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