44 research outputs found
Compressed Encoding for Rank Modulation
Rank modulation has been recently proposed as
a scheme for storing information in flash memories. While
rank modulation has advantages in improving write speed and
endurance, the current encoding approach is based on the "push
to the top" operation that is not efficient in the general case. We
propose a new encoding procedure where a cell level is raised to
be higher than the minimal necessary subset -instead of all - of
the other cell levels. This new procedure leads to a significantly
more compressed (lower charge levels) encoding. We derive an
upper bound for a family of codes that utilize the proposed
encoding procedure, and consider code constructions that achieve
that bound for several special cases
Computing the Ball Size of Frequency Permutations under Chebyshev Distance
Let be the set of all permutations over the multiset
where
. A frequency permutation array (FPA) of minimum distance is a
subset of in which every two elements have distance at least .
FPAs have many applications related to error correcting codes. In coding
theory, the Gilbert-Varshamov bound and the sphere-packing bound are derived
from the size of balls of certain radii. We propose two efficient algorithms
that compute the ball size of frequency permutations under Chebyshev distance.
Both methods extend previous known results. The first one runs in time and space. The second one runs in time and
space. For small constants and ,
both are efficient in time and use constant storage space.Comment: Submitted to ISIT 201
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
Generalized Gray Codes for Local Rank Modulation
We consider the local rank-modulation scheme in which a sliding window going
over a sequence of real-valued variables induces a sequence of permutations.
Local rank-modulation is a generalization of the rank-modulation scheme, which
has been recently suggested as a way of storing information in flash memory. We
study Gray codes for the local rank-modulation scheme in order to simulate
conventional multi-level flash cells while retaining the benefits of rank
modulation. Unlike the limited scope of previous works, we consider code
constructions for the entire range of parameters including the code length,
sliding window size, and overlap between adjacent windows. We show our
constructed codes have asymptotically-optimal rate. We also provide efficient
encoding, decoding, and next-state algorithms.Comment: 7 pages, 1 figure, shorter version was submitted to ISIT 201
On Optimal Anticodes over Permutations with the Infinity Norm
Motivated by the set-antiset method for codes over permutations under the
infinity norm, we study anticodes under this metric. For half of the parameter
range we classify all the optimal anticodes, which is equivalent to finding the
maximum permanent of certain -matrices. For the rest of the cases we
show constraints on the structure of optimal anticodes
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