752 research outputs found
Improved constructions of permutation and multi-permutation codes correcting a burst of stable deletions
Permutation codes and multi-permutation codes have been widely considered due
to their various applications, especially in flash memory. In this paper, we
consider permutation codes and multi-permutation codes against a burst of
stable deletions. In particular, we propose a construction of permutation codes
correcting a burst stable deletion of length , with redundancy . Compared to the previous known results, our improvement
relies on a different strategy to retrieve the missing symbol on the first row
of the array representation of a permutation. We also generalize our
constructions for multi-permutations and the variable length burst model.
Furthermore, we propose a linear-time encoder with optimal redundancy for
single stable deletion correcting permutation codes.Comment: Accepted for publication in IEEE Trans. Inf. Theor
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
Efficient File Synchronization: a Distributed Source Coding Approach
The problem of reconstructing a source sequence with the presence of decoder
side-information that is mis-synchronized to the source due to deletions is
studied in a distributed source coding framework. Motivated by practical
applications, the deletion process is assumed to be bursty and is modeled by a
Markov chain. The minimum rate needed to reconstruct the source sequence with
high probability is characterized in terms of an information theoretic
expression, which is interpreted as the amount of information of the deleted
content and the locations of deletions, subtracting "nature's secret", that is,
the uncertainty of the locations given the source and side-information. For
small bursty deletion probability, the asymptotic expansion of the minimum rate
is computed.Comment: 9 pages, 2 figures. A shorter version will appear in IEEE
International Symposium on Information Theory (ISIT), 201
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