13 research outputs found
Coding for Trace Reconstruction over Multiple Channels with Vanishing Deletion Probabilities
Motivated by DNA-based storage applications, we study the problem of
reconstructing a coded sequence from multiple traces. We consider the model
where the traces are outputs of independent deletion channels, where each
channel deletes each bit of the input codeword
independently with probability . We focus on the regime where the deletion
probability when . Our main contribution is
designing a novel code for trace reconstruction that allows reconstructing a
coded sequence efficiently from a constant number of traces. We provide
theoretical results on the performance of our code in addition to simulation
results where we compare the performance of our code to other reconstruction
techniques in terms of the edit distance error.Comment: This is the full version of the short paper accepted at ISIT 202
Optimal k-Deletion Correcting Codes
Levenshtein introduced the problem of constructing k-deletion correcting codes in 1966, proved that the optimal redundancy
of those codes is O(k log N), and proposed an optimal redundancy single-deletion correcting code (using the so-called VT
construction). However, the problem of constructing optimal redundancy k-deletion correcting codes remained open. Our key
contribution is a solution to this longstanding open problem. We present a k-deletion correcting code that has redundancy 8k log n+
o(log n) and encoding/decoding algorithms of complexity O(n^(2k+1)) for constant k
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
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