6,186 research outputs found
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
Systematic Error-Correcting Codes for Rank Modulation
The rank modulation scheme has been proposed recently for efficiently writing and storing data in nonvolatile memories. Error-correcting codes are very important for rank modulation, and they have attracted interest among researchers. In this work, we explore a new approach, systematic error-correcting codes for rank modulation. In an (n,k) systematic code, we use the permutation induced by the levels of n cells to store data, and the permutation induced by the first k cells (k < n) has a one-to-one mapping to information bits. 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 equipped with the Kendall's τ-distance. We present (k + 2, k) systematic codes for correcting one error, which have optimal sizes unless perfect codes exist. We also study the design of multi-error-correcting codes, and prove that for any 2 ≤ k < n, there always exists an (n, k) systematic code of minimum distance n-k. Furthermore, we prove that for rank modulation, systematic codes achieve the same capacity as general error-correcting codes
Limited-Magnitude Error-Correcting Gray Codes for Rank Modulation
We construct Gray codes over permutations for the rank-modulation scheme,
which are also capable of correcting errors under the infinity-metric. These
errors model limited-magnitude or spike errors, for which only
single-error-detecting Gray codes are currently known. Surprisingly, the
error-correcting codes we construct achieve a better asymptotic rate than that
of presently known constructions not having the Gray property, and exceed the
Gilbert-Varshamov bound. Additionally, we present efficient ranking and
unranking procedures, as well as a decoding procedure that runs in linear time.
Finally, we also apply our methods to solve an outstanding issue with
error-detecting rank-modulation Gray codes (snake-in-the-box codes) under a
different metric, the Kendall -metric, in the group of permutations over
an even number of elements , where we provide asymptotically optimal
codes.Comment: Revised version for journal submission. Additional results include
more tight auxiliary constructions, a decoding shcema, ranking/unranking
procedures, and application to snake-in-the-box codes under the Kendall
tau-metri
Space-time coding techniques with bit-interleaved coded modulations for MIMO block-fading channels
The space-time bit-interleaved coded modulation (ST-BICM) is an efficient
technique to obtain high diversity and coding gain on a block-fading MIMO
channel. Its maximum-likelihood (ML) performance is computed under ideal
interleaving conditions, which enables a global optimization taking into
account channel coding. Thanks to a diversity upperbound derived from the
Singleton bound, an appropriate choice of the time dimension of the space-time
coding is possible, which maximizes diversity while minimizing complexity.
Based on the analysis, an optimized interleaver and a set of linear precoders,
called dispersive nucleo algebraic (DNA) precoders are proposed. The proposed
precoders have good performance with respect to the state of the art and exist
for any number of transmit antennas and any time dimension. With turbo codes,
they exhibit a frame error rate which does not increase with frame length.Comment: Submitted to IEEE Trans. on Information Theory, Submission: January
2006 - First review: June 200
Product Construction of Affine Codes
Binary matrix codes with restricted row and column weights are a desirable
method of coded modulation for power line communication. In this work, we
construct such matrix codes that are obtained as products of affine codes -
cosets of binary linear codes. Additionally, the constructions have the
property that they are systematic. Subsequently, we generalize our construction
to irregular product of affine codes, where the component codes are affine
codes of different rates.Comment: 13 pages, to appear in SIAM Journal on Discrete Mathematic
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