10,767 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 ℓ. 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
Systematic Error-Correcting Codes for Rank Modulation
The rank-modulation scheme has been recently proposed for efficiently storing
data in nonvolatile memories. Error-correcting codes are essential for rank
modulation, however, existing results have been limited. In this work we
explore a new approach, \emph{systematic error-correcting codes for rank
modulation}. Systematic codes have the benefits of enabling efficient
information retrieval and potentially supporting more efficient encoding and
decoding procedures. We study systematic codes for rank modulation under
Kendall's -metric as well as under the -metric.
In Kendall's -metric we present -systematic codes for
correcting one error, which have optimal rates, unless systematic perfect codes
exist. We also study the design of multi-error-correcting codes, and provide
two explicit constructions, one resulting in systematic codes
with redundancy at most . We use non-constructive arguments to show the
existence of -systematic codes for general parameters. Furthermore,
we prove that for rank modulation, systematic codes achieve the same capacity
as general error-correcting codes.
Finally, in the -metric we construct two systematic
multi-error-correcting codes, the first for the case of , and the
second for . In the latter case, the codes have the same
asymptotic rate as the best codes currently known in this metric
Systematic Codes for Rank Modulation
The goal of this paper is to construct systematic error-correcting codes for
permutations and multi-permutations in the Kendall's -metric. These codes
are important in new applications such as rank modulation for flash memories.
The construction is based on error-correcting codes for multi-permutations and
a partition of the set of permutations into error-correcting codes. For a given
large enough number of information symbols , and for any integer , we
present a construction for systematic -error-correcting codes,
for permutations from , with less redundancy symbols than the number
of redundancy symbols in the codes of the known constructions. In particular,
for a given and for sufficiently large we can obtain . The same
construction is also applied to obtain related systematic error-correcting
codes for multi-permutations.Comment: to be presented ISIT201
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
one—a distance measure known as Kendall’s τ-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 Kendall’s
τ-metric. Specifically, the one-error-correcting codes we construct
are at least half the ball-packing upper bound
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