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We investigate the list decodability of symbol-pair codes in this paper. First, we show that the list decodability of every symbol-pair code does not exceed the Gilbert–Varshamov bound. On the other hand, we are able to prove that with high probability, a random symbol-pair code can be list decoded up to the Gilbert–Varshamov bound. Our second result of this paper is to derive the Johnson-type bound, i.e., a lower bound on list decoding radius in terms of minimum distance. Finally, we present a list decoding algorithm of Reed–Solomon codes beyond the Johnson-type bound in the pair metric. 1 A symbol-pair code is referred to a code in the pair metric. [ABSTRACT FROM AUTHOR]

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 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 derivation of the asymptotic capacity of translocation rank codes, construction techniques for asymptotically good codes, as well as simple decoding methods for one class of constructed 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 codes in the Hamming distance. [ABSTRACT FROM PUBLISHER]

A new coding framework is established for channels whose outputs are overlapping pairs of symbols. Such channels are motivated by storage applications in which the spatial resolution of the reader may be insufficient to isolate adjacent symbols. Reading symbols as pairs changes the coding-theoretic error model from the standard bounded number of symbol errors to a bounded number of pair errors. Starting from the most basic coding-theoretic questions, the paper studies codes that protect against pair-errors. It provides answers on pair-error correctability conditions, code construction and decoding, and lower and upper bounds on code sizes. Asymptotic analysis of pair-error correction shows that there exist pair-error codes with rates that are strictly higher than the best known codes in the Hamming metric. [ABSTRACT FROM AUTHOR]