On the labeling problem of permutation group codes under the infinity metric

Itzhak Tamo, Moshe Schwartz

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

Abstract

Codes over permutations under the infinity norm have been recently suggested as a coding scheme for correcting limited-magnitude errors in the rank modulation scheme. Given such a code, we show that a simple relabeling operation, which produces an isomorphic code, may drastically change the minimal distance of the code. Thus, we may choose a code structure for efficient encoding/decoding procedures, and then optimize the code's minimal distance via relabeling. We formally define the relabeling problem, and show that all codes may be relabeled to get a minimal distance at most 2. The decision problem of whether a code may be relabeled to distance 1 is shown to be NP-complete, and calculating the best achievable minimal distance after relabeling is proved hard to approximate. Finally, we consider general bounds on the relabeling problem. We specifically show the optimal relabeling distance of cyclic groups. A specific case of a general probabilistic argument is used to show AGL(p) may be relabeled to a minimal distance of p -O(√pIn)

Original languageEnglish
Title of host publication2011 IEEE International Symposium on Information Theory Proceedings, ISIT 2011
Pages844-848
Number of pages5
DOIs
StatePublished - 26 Oct 2011
Event2011 IEEE International Symposium on Information Theory Proceedings, ISIT 2011 - St. Petersburg, Russian Federation
Duration: 31 Jul 20115 Aug 2011

Publication series

NameIEEE International Symposium on Information Theory - Proceedings
ISSN (Print)2157-8104

Conference

Conference2011 IEEE International Symposium on Information Theory Proceedings, ISIT 2011
Country/TerritoryRussian Federation
CitySt. Petersburg
Period31/07/115/08/11

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Information Systems
  • Modeling and Simulation
  • Applied Mathematics

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