Repeat-Free Codes

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 of the repeat-free constraint are calculated. Then, an efficient algorithm, which uses two bits 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.