Rank Modulation for Translocation Error Correction

Details Rank Modulation for Translocation Error Correction Rank Modulation for Translocation Error Correction

2012-02-05

arxiv.org/abs/1202.0932v1

Computer Science

Information Theory

Scientific paper

We consider rank modulation codes for flash memories that allow for handling arbitrary charge drop errors. Unlike classical rank modulation codes used for correcting errors that manifest themselves as swaps of two adjacently ranked elements, the proposed \emph{translocation rank codes} account for more general forms of errors that arise in storage systems. Translocations represent a natural extension of the notion of adjacent transpositions and as such may be analyzed using related concepts in combinatorics and rank modulation coding. Our results include tight bounds on the capacity of translocation rank codes, construction techniques for asymptotically good codes, as well as simple decoding methods for one class of structured codes. As part of our exposition, we also highlight the close connections between the new code family and permutations with short common subsequences, deletion and insertion error-correcting codes for permutations and permutation arrays.

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