Reconstructing strings from random traces
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
Reconstruction of permutations distorted by reversal errors
Discrete Applied Mathematics
Trace reconstruction with constant deletion probability and related results
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Improved string reconstruction over insertion-deletion channels
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Reconstruction of a graph from 2-vicinities of its vertices
Discrete Applied Mathematics
A Survey of Results for Deletion Channels and Related Synchronization Channels
SWAT '08 Proceedings of the 11th Scandinavian workshop on Algorithm Theory
Error graphs and the reconstruction of elements in groups
Journal of Combinatorial Theory Series A
A subsequence-histogram method for generic vocabulary recognition over deletion channels
ISIT'09 Proceedings of the 2009 IEEE international conference on Symposium on Information Theory - Volume 4
Efficient reconstruction of RC-equivalent strings
IWOCA'10 Proceedings of the 21st international conference on Combinatorial algorithms
A linear algorithm for string reconstruction in the reverse complement equivalence model
Journal of Discrete Algorithms
Hi-index | 754.84 |
We introduce and solve some new problems of efficient reconstruction of an unknown sequence from its versions distorted by errors of a certain type. These erroneous versions are considered as outputs of repeated transmissions over a channel, either a combinatorial channel defined by the maximum number of permissible errors of a given type, or a discrete memoryless channel. We are interested in the smallest N such that N erroneous versions always suffice to reconstruct a sequence of length n, either exactly or with a preset accuracy and/or with a given probability. We are also interested in simple reconstruction algorithms. Complete solutions for combinatorial channels with some types of errors of interest in coding theory, namely, substitutions, transpositions, deletions, and insertions of symbols are given. For these cases, simple reconstruction algorithms based on majority and threshold principles and their nontrivial combination are found. In general, for combinatorial channels the considered problem is reduced to a new problem of reconstructing a vertex of an arbitrary graph with the help of the minimum number of vertices in its metrical ball of a given radius. A certain sufficient condition for solution of this problem is presented. For a discrete memoryless channel, the asymptotic behavior of the minimum number of repeated transmissions which are sufficient to reconstruct any sequence of length n within Hamming distance d with error probability ε is found when d/n and ε tend to 0 as n→∞. A similar result for the continuous channel with discrete time and additive Gaussian noise is also obtained