752 research outputs found

    Improved constructions of permutation and multi-permutation codes correcting a burst of stable deletions

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    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 ss, with redundancy log⁑n+2log⁑log⁑n+O(1)\log n+ 2\log \log n+O(1). 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

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    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 tt-deletion-ss-insertion-burst ((t,s)(t,s)-burst for short) which is a generalization of the (2,1)(2,1)-burst error proposed by Schoeny {\it et. al}. Such an error deletes tt consecutive symbols and inserts an arbitrary sequence of length ss at the same coordinate. We provide a sphere-packing upper bound on the size of binary codes that can correct a (t,s)(t,s)-burst error, showing that the redundancy of such codes is at least log⁑n+tβˆ’1\log n+t-1. For tβ‰₯2st\geq 2s, an explicit construction of binary (t,s)(t,s)-burst correcting codes with redundancy log⁑n+(tβˆ’sβˆ’1)log⁑log⁑n+O(1)\log n+(t-s-1)\log\log n+O(1) is given. In particular, we construct a binary (3,1)(3,1)-burst correcting code with redundancy at most log⁑n+9\log n+9, 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

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    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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