Sequence reconstruction for Grassmann graphs and permutations

Eitan Yaakobi, Moshe Schwartz, Michael Langberg, Jehoshua Bruck

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

16 Scopus citations

Abstract

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 τ-metric for some special cases of d and r.

Original languageEnglish
Title of host publication2013 IEEE International Symposium on Information Theory, ISIT 2013
Pages874-878
Number of pages5
DOIs
StatePublished - 19 Dec 2013
Event2013 IEEE International Symposium on Information Theory, ISIT 2013 - Istanbul, Turkey
Duration: 7 Jul 201312 Jul 2013

Publication series

NameIEEE International Symposium on Information Theory - Proceedings
ISSN (Print)2157-8095

Conference

Conference2013 IEEE International Symposium on Information Theory, ISIT 2013
Country/TerritoryTurkey
CityIstanbul
Period7/07/1312/07/13

Fingerprint

Dive into the research topics of 'Sequence reconstruction for Grassmann graphs and permutations'. Together they form a unique fingerprint.

Cite this