Repeat-Free Codes

09/12/2019

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by   Ohad Elishco, et al.

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In this paper we consider the problem of encoding data into repeat-free sequences in which sequences are imposed to contain any k-tuple at most once (for predefined k). First, the capacity and redundancy of the repeat-free constraint are calculated. Then, an efficient algorithm, which uses a single bit of redundancy, is presented to encode length-n sequences for k=2+2log (n). This algorithm is then improved to support any value of k of the form k=alog (n), for 1<a, while its redundancy is o(n). We also calculate the capacity of repeat-free sequences when combined with local constraints which are given by a constrained system, and the capacity of multi-dimensional repeat-free codes.