938 research outputs found
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
Constructions of Rank Modulation Codes
Rank modulation is a way of encoding information to correct errors in flash
memory devices as well as impulse noise in transmission lines. Modeling rank
modulation involves construction of packings of the space of permutations
equipped with the Kendall tau distance.
We present several general constructions of codes in permutations that cover
a broad range of code parameters. In particular, we show a number of ways in
which conventional error-correcting codes can be modified to correct errors in
the Kendall space. Codes that we construct afford simple encoding and decoding
algorithms of essentially the same complexity as required to correct errors in
the Hamming metric. For instance, from binary BCH codes we obtain codes
correcting Kendall errors in memory cells that support the order of
messages, for any constant We also construct
families of codes that correct a number of errors that grows with at
varying rates, from to . One of our constructions
gives rise to a family of rank modulation codes for which the trade-off between
the number of messages and the number of correctable Kendall errors approaches
the optimal scaling rate. Finally, we list a number of possibilities for
constructing codes of finite length, and give examples of rank modulation codes
with specific parameters.Comment: Submitted to IEEE Transactions on Information Theor
Estimates on the Size of Symbol Weight Codes
The study of codes for powerlines communication has garnered much interest
over the past decade. Various types of codes such as permutation codes,
frequency permutation arrays, and constant composition codes have been proposed
over the years. In this work we study a type of code called the bounded symbol
weight codes which was first introduced by Versfeld et al. in 2005, and a
related family of codes that we term constant symbol weight codes. We provide
new upper and lower bounds on the size of bounded symbol weight and constant
symbol weight codes. We also give direct and recursive constructions of codes
for certain parameters.Comment: 14 pages, 4 figure
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