1,436 research outputs found
Codes for Asymmetric Limited-Magnitude Errors With Application to Multilevel Flash Memories
Several physical effects that limit the reliability and performance of multilevel flash memories induce errors that have low magnitudes and are dominantly asymmetric. This paper studies block codes for asymmetric limited-magnitude errors over q-ary channels. We propose code constructions and bounds for such channels when the number of errors is bounded by t and the error magnitudes are bounded by â. The constructions utilize known codes for symmetric errors, over small alphabets, to protect large-alphabet symbols from asymmetric limited-magnitude errors. The encoding and decoding of these codes are performed over the small alphabet whose size depends only on the maximum error magnitude and is independent of the alphabet size of the outer code. Moreover, the size of the codes is shown to exceed the sizes of known codes (for related error models), and asymptotic rate-optimality results are proved. Extensions of the construction are proposed to accommodate variations on the error model and to include systematic codes as a benefit to practical implementation
On q-ary codes correcting all unidirectional errors of a limited magnitude
We consider codes over the alphabet Q={0,1,..,q-1}intended for the control of
unidirectional errors of level l. That is, the transmission channel is such
that the received word cannot contain both a component larger than the
transmitted one and a component smaller than the transmitted one. Moreover, the
absolute value of the difference between a transmitted component and its
received version is at most l.
We introduce and study q-ary codes capable of correcting all unidirectional
errors of level l. Lower and upper bounds for the maximal size of those codes
are presented.
We also study codes for this aim that are defined by a single equation on the
codeword coordinates(similar to the Varshamov-Tenengolts codes for correcting
binary asymmetric errors). We finally consider the problem of detecting all
unidirectional errors of level l.Comment: 22 pages,no figures. Accepted for publication of Journal of Armenian
Academy of Sciences, special issue dedicated to Rom Varshamo
Coding over Sets for DNA Storage
In this paper, we study error-correcting codes for the storage of data in
synthetic deoxyribonucleic acid (DNA). We investigate a storage model where
data is represented by an unordered set of sequences, each of length .
Errors within that model are losses of whole sequences and point errors inside
the sequences, such as substitutions, insertions and deletions. We propose code
constructions which can correct these errors with efficient encoders and
decoders. By deriving upper bounds on the cardinalities of these codes using
sphere packing arguments, we show that many of our codes are close to optimal.Comment: 5 page
Correcting Charge-Constrained Errors in the Rank-Modulation Scheme
We investigate error-correcting codes for a the
rank-modulation scheme with an application to flash memory
devices. In this scheme, a set of n cells stores information in the
permutation induced by the different charge levels of the individual
cells. The resulting scheme eliminates the need for discrete
cell levels, overcomes overshoot errors when programming cells (a
serious problem that reduces the writing speed), and mitigates the
problem of asymmetric errors. In this paper, we study the properties
of error-correcting codes for charge-constrained errors in the
rank-modulation scheme. In this error model the number of errors
corresponds to the minimal number of adjacent transpositions required
to change a given stored permutation to another erroneous
oneâa distance measure known as Kendallâs Ï-distance.We show
bounds on the size of such codes, and use metric-embedding techniques
to give constructions which translate a wealth of knowledge
of codes in the Lee metric to codes over permutations in Kendallâs
Ï-metric. Specifically, the one-error-correcting codes we construct
are at least half the ball-packing upper bound
Asymmetric Lee Distance Codes for DNA-Based Storage
We consider a new family of codes, termed asymmetric Lee distance codes, that
arise in the design and implementation of DNA-based storage systems and systems
with parallel string transmission protocols. The codewords are defined over a
quaternary alphabet, although the results carry over to other alphabet sizes;
furthermore, symbol confusability is dictated by their underlying binary
representation. Our contributions are two-fold. First, we demonstrate that the
new distance represents a linear combination of the Lee and Hamming distance
and derive upper bounds on the size of the codes under this metric based on
linear programming techniques. Second, we propose a number of code
constructions which imply lower bounds
Constructions of Pure Asymmetric Quantum Alternant Codes Based on Subclasses of Alternant Codes
In this paper, we construct asymmetric quantum error-correcting codes(AQCs)
based on subclasses of Alternant codes. Firstly, We propose a new subclass of
Alternant codes which can attain the classical Gilbert-Varshamov bound to
construct AQCs. It is shown that when , -parts of the AQCs can attain
the classical Gilbert-Varshamov bound. Then we construct AQCs based on a famous
subclass of Alternant codes called Goppa codes. As an illustrative example, we
get three AQCs from the well
known binary Goppa code. At last, we get asymptotically good
binary expansions of asymmetric quantum GRS codes, which are quantum
generalizations of Retter's classical results. All the AQCs constructed in this
paper are pure
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