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Published May 2014 | Submitted
Journal Article Open

Multipermutation Codes in the Ulam Metric for Nonvolatile Memories

Abstract

We address the problem of multipermutation code design in the Ulam metric for novel storage applications. Multipermutation codes are suitable for flash memory where cell charges may share the same rank. Changes in the charges of cells manifest themselves as errors whose effects on the retrieved signal may be measured via the Ulam distance. As part of our analysis, we study multipermutation codes in the Hamming metric, known as constant composition codes. We then present bounds on the size of multipermutation codes and their capacity, for both the Ulam and the Hamming metrics. Finally, we present constructions and accompanying decoders for multipermutation codes in the Ulam metric.

Additional Information

© 2014 IEEE. Manuscript received May 15, 2013; revised October 1, 2013 and December 10, 2013. This work was supported by NSF grants CCF 0809895, CCF 1218764, and the Emerging Frontiers for Science of Information, CCF 0939370. The authors would like to thank anonymous reviewers for their insightful comments and Eyal En Gad for several useful discussions.

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August 22, 2023
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