Efficient Systematic Encoding of Non-binary VT Codes

Varshamov-Tenengolts (VT) codes are a class of codes which can correct a single deletion or insertion with a linear-time decoder. This paper addresses the problem of efficient encoding of non-binary VT codes, defined over an alphabet of size $q >2$. We propose a simple linear-time encoding method to systematically map binary message sequences onto VT codewords. The method provides a new lower bound on the size of $q$-ary VT codes of length $n$.Comment: This paper will appear in the proceedings of ISIT 201

File Updates Under Random/Arbitrary Insertions And Deletions

A client/encoder edits a file, as modeled by an insertion-deletion (InDel) process. An old copy of the file is stored remotely at a data-centre/decoder, and is also available to the client. We consider the problem of throughput- and computationally-efficient communication from the client to the data-centre, to enable the server to update its copy to the newly edited file. We study two models for the source files/edit patterns: the random pre-edit sequence left-to-right random InDel (RPES-LtRRID) process, and the arbitrary pre-edit sequence arbitrary InDel (APES-AID) process. In both models, we consider the regime in which the number of insertions/deletions is a small (but constant) fraction of the original file. For both models we prove information-theoretic lower bounds on the best possible compression rates that enable file updates. Conversely, our compression algorithms use dynamic programming (DP) and entropy coding, and achieve rates that are approximately optimal.Comment: The paper is an extended version of our paper to be appeared at ITW 201