Snake-in-the-Box Codes for Rank Modulation
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چکیده
Motivated by the rank-modulation scheme with applications to flash memory, we consider Gray codes capable of detecting a single error, also known as snake-in-the-box codes. We study two error metrics: Kendall’s τ-metric, which applies to charge-constrained errors, and the `∞-metric, which is useful in the case of limited-magnitude errors. In both cases we construct snake-in-the-box codes with rate asymptotically tending to 1.
منابع مشابه
Snake-in-the-Box Codes for Rank Modulation under Kendall's $τ$-Metric
For a Gray code in the scheme of rank modulation for flash memories, the codewords are permutations and two consecutive codewords are obtained using a push-to-the-top operation. We consider snake-in-the-box codes under Kendall’s τ -metric, which is a Gray code capable of detecting one Kendall’s τ -error. We answer two open problems posed by Horovitz and Etzion. Firstly, we prove the validity of...
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In the rank modulation scheme, Gray codes are very useful in the realization of flash memories. For a Gray code in this scheme, two adjacent codewords are obtained by using one “push-to-the-top” operation. Moreover, snake-in-the-box codes under the l∞-metric are Gray codes, which can be capable of detecting one l∞-error. In this paper, we give two constructions of l∞snakes. On the one hand, ins...
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تاریخ انتشار 2012