1,316 research outputs found
Cyclic Low-Density MDS Array Codes
We construct two infinite families of low density MDS array codes which are also cyclic. One of these families includes the first such sub-family with redundancy parameter r > 2. The two constructions have different algebraic formulations, though they both have the same indirect structure. First MDS codes that are not cyclic are constructed and then by applying a certain mapping to their parity check matrices, non-equivalent cyclic codes with the same distance and density properties are obtained. Using the same proof techniques, a third infinite family of quasi-cyclic codes can be constructed
Cyclic lowest density MDS array codes
Three new families of lowest density maximum-distance separable (MDS) array codes are constructed, which are cyclic or quasi-cyclic. In addition to their optimal redundancy (MDS) and optimal update complexity (lowest density), the symmetry offered by the new codes can be utilized for simplified implementation in storage applications. The proof of the code properties has an indirect structure: first MDS codes that are not cyclic are constructed, and then transformed to cyclic codes by a minimum-distance preserving transformation
Error-Correction in Flash Memories via Codes in the Ulam Metric
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 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
- …