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Sequence Reconstruction for Grassmann Graphs and Permutations

Yaakobi, Eitan and Schwartz, Moshe and Langberg, Michael and Bruck, Jehoshua (2013) Sequence Reconstruction for Grassmann Graphs and Permutations. California Institute of Technology , Pasadena, CA. (Unpublished)

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The sequence-reconstruction problem was first proposed by Levenshtein in 2001. This problem studies the model where the same word is transmitted over multiple channels. If the transmitted word belongs to some code of minimum distance d and there are at most r errors in every channel, then the minimum number of channels that guarantees a successful decoder (under the assumption that all channel outputs are distinct) has to be greater than the largest intersection of two balls of radius r and with distance at least d between their centers. This paper studies the combinatorial problem of computing the largest intersection of two balls for two cases. In the first part we solve this problem in the Grassmann graph for all values of d and r. In the second part we derive similar results for permutations under Kendall’s t-metric for some special cases of d and r.

Item Type:Report or Paper (Technical Report)
Related URLs:
URLURL TypeDescription
Yaakobi, Eitan0000-0002-9851-5234
Schwartz, Moshe0000-0002-1449-0026
Langberg, Michael0000-0002-7470-0718
Bruck, Jehoshua0000-0001-8474-0812
Additional Information:This work was supported in part by an NSF grant ECCS-0801795 and a BSF grant 2010075.
Group:Parallel and Distributed Systems Group
Funding AgencyGrant Number
Binational Science Foundation (BSF)2010075
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Other Numbering System NameOther Numbering System ID
Record Number:CaltechAUTHORS:20130215-095250632
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:36948
Deposited By: Kristin Buxton
Deposited On:15 Feb 2013 19:29
Last Modified:09 Mar 2020 13:19

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