Abstract
We construct error-correcting codes over permutations under the infinity-metric, which are also Gray codes in the context of rank modulation, i.e., are generated as simple circuits in the rotator graph. These errors model limited-magnitude or spike errors, for which only single-error-detecting Gray codes are currently known. Surprisingly, the error-correcting codes we construct achieve a better asymptotic rate than that of presently known constructions not having the Gray property, and exceed the Gilbert-Varshamov bound. Additionally, we present efficient ranking and unranking procedures, as well as a decoding procedure that runs in linear time. Finally, we also apply our methods to solve an outstanding issue with error-detecting rank-modulation Gray codes (also known in this context as snake-in-the-box codes) under a different metric, the Kendall τ-metric, in the group of permutations over an even number of elements $S-{2n}$ , where we provide asymptotically optimal codes.
Original language | English |
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Article number | 7959111 |
Pages (from-to) | 5774-5792 |
Number of pages | 19 |
Journal | IEEE Transactions on Information Theory |
Volume | 63 |
Issue number | 9 |
DOIs | |
State | Published - 1 Sep 2017 |
Keywords
- Gray codes
- error-correcting codes
- permutations
- rank modulation
- spread-d circuit codes
ASJC Scopus subject areas
- Information Systems
- Computer Science Applications
- Library and Information Sciences