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We address the problem of multipermutation code design in the Ulam metric fornovel storage applications. Multipermutation codes are suitable for flashmemory where cell charges may share the same rank. Changes in the charges ofcells manifest themselves as errors whose effects on the retrieved signal maybe measured via the Ulam distance. As part of our analysis, we studymultipermutation codes in the Hamming metric, known as constant compositioncodes. We then present bounds on the size of multipermutation codes and theircapacity, for both the Ulam and the Hamming metrics. Finally, we presentconstructions and accompanying decoders for multipermutation codes in the Ulammetric.

Multipermutation Codes in the Ulam Metric for Nonvolatile Memories