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Ulam Ball Size Analysis for Permutation and Multipermutation Codes Correcting Translocation Errors | IEEE Journals & Magazine | IEEE Xplore

Ulam Ball Size Analysis for Permutation and Multipermutation Codes Correcting Translocation Errors


Abstract:

Permutation and multipermutation codes in the Ulam metric have been suggested for use in non-volatile memory storage systems such as flash memory devices. In this paper w...Show More

Abstract:

Permutation and multipermutation codes in the Ulam metric have been suggested for use in non-volatile memory storage systems such as flash memory devices. In this paper we introduce a new method to calculate permutation ball sizes in the Ulam metric using Young Tableaux and prove the non-existence of non-trivial perfect permutation codes in the Ulam metric. We then extend the study to multipermutations, providing upper and lower bounds on multipermutation Ulam ball sizes and resulting upper and lower bounds on the maximal size of multipermutation codes in the Ulam metric.
Published in: IEEE Transactions on Information Theory ( Volume: 65, Issue: 12, December 2019)
Page(s): 7806 - 7828
Date of Publication: 02 September 2019

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