8 research outputs found
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 . 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 -ary VT codes of length .Comment: This paper will appear in the proceedings of ISIT 201
t-Deletion-s-Insertion-Burst Correcting Codes
Motivated by applications in DNA-based storage and communication systems, we
study deletion and insertion errors simultaneously in a burst. In particular,
we study a type of error named -deletion--insertion-burst (-burst
for short) which is a generalization of the -burst error proposed by
Schoeny {\it et. al}. Such an error deletes consecutive symbols and inserts
an arbitrary sequence of length at the same coordinate. We provide a
sphere-packing upper bound on the size of binary codes that can correct a
-burst error, showing that the redundancy of such codes is at least
. For , an explicit construction of binary -burst
correcting codes with redundancy is given. In
particular, we construct a binary -burst correcting code with redundancy
at most , which is optimal up to a constant.Comment: Part of this work (the (t,1)-burst model) was presented at ISIT2022.
This full version has been submitted to IEEE-IT in August 202
Scalable string reconciliation by recursive content-dependent shingling
We consider the problem of reconciling similar strings in a distributed system. Specifically, we are interested in performing this reconciliation in an efficient manner, minimizing the communication cost. Our problem applies to several types of large-scale distributed networks, file synchronization utilities, and any system that manages the consistency of string encoded ordered data. We present the novel Recursive Content-Dependent Shingling (RCDS) protocol that can handle large strings and has the communication complexity that scales with the edit distance between the reconciling strings. Also, we provide analysis, experimental results, and comparisons to existing synchronization software such as the Rsync utility with an implementation of our protocol.2019-12-03T00:00:00