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Snake-in-the-Box Codes for Rank Modulation under Kendall’s $\tau $ -Metric in S_{2n+2}.
- Source :
-
IEEE Transactions on Information Theory . Sep2016, Vol. 62 Issue 9, p4814-4818. 5p. - Publication Year :
- 2016
-
Abstract
- Snake-in-the-box codes under Kendall’s \tau -metric are studied in the rank modulation scheme for flash memories, where codewords are a subset of permutations in S_{n} with minimal Kendall’s \tau -distance two, and two cyclically consecutive codewords are connected via a push-to-the-top operation. Studies so far restrict the push-to-the-top operations only on odd indices, resulting in a snake consisting of permutations with the same parity, and thus, the minimal distance constraint is easily satisfied. Asymptotically optimal snake codes have been constructed this way in S2n+1 . As for S2n+2 , this framework keeps the last element fixed, and thus, a snake in S2n+2 is equivalent to a snake in S2n+1 , which is rather trivial. If one wants to do better, then it is inevitable to have some push-to-the-top operations on even indices, resulting in a combination of odd and even permutations in the snake, which increases the difficulty to guarantee the minimal Kendall’s $\tau $ -distance constraint. Thus, Horovitz and Etzion pose the open problem to prove or disprove that the size of the largest snake in ({1}/{4})|S_{2n+2}| . [ABSTRACT FROM PUBLISHER]
Details
- Language :
- English
- ISSN :
- 00189448
- Volume :
- 62
- Issue :
- 9
- Database :
- Academic Search Index
- Journal :
- IEEE Transactions on Information Theory
- Publication Type :
- Academic Journal
- Accession number :
- 117596678
- Full Text :
- https://doi.org/10.1109/TIT.2016.2587764