839 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
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
Using graphs for the analysis and construction of permutation distance-preserving mappings
Abstract: A new way of looking at permutation distance-preserving mappings (DPMs) is presented by making use of a graph representation. The properties necessary to make such a graph distance-preserving, are also investigated. Further, this new knowledge is used to analyze previous constructions, as well as to construct a new general mapping algorithm for a previous multilevel construction
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
Importance of Symbol Equity in Coded Modulation for Power Line Communications
The use of multiple frequency shift keying modulation with permutation codes
addresses the problem of permanent narrowband noise disturbance in a power line
communications system. In this paper, we extend this coded modulation scheme
based on permutation codes to general codes and introduce an additional new
parameter that more precisely captures a code's performance against permanent
narrowband noise. As a result, we define a new class of codes, namely,
equitable symbol weight codes, which are optimal with respect to this measure
Synchronization with permutation codes and Reed-Solomon codes
D.Ing. (Electrical And Electronic Engineering)We address the issue of synchronization, using sync-words (or markers), for encoded data. We focus on data that is encoded using permutation codes or Reed-Solomon codes. For each type of code (permutation code and Reed-Solomon code) we give a synchronization procedure or algorithm such that synchronization is improved compared to when the procedure is not employed. The gure of merit for judging the performance is probability of synchronization (acquisition). The word acquisition is used to indicate that a sync-word is acquired or found in the right place in a frame. A new synchronization procedure for permutation codes is presented. This procedure is about nding sync-words that can be used speci cally with permutation codes, such that acceptable synchronization performance is possible even under channels with frequency selective fading/jamming, such as the power line communication channel. Our new procedure is tested with permutation codes known as distance-preserving mappings (DPMs). DPMs were chosen because they have de ned encoding and decoding procedures. Another new procedure for avoiding symbols in Reed-Solomon codes is presented. We call the procedure symbol avoidance. The symbol avoidance procedure is then used to improve the synchronization performance of Reed-Solomon codes, where known binary sync-words are used for synchronization. We give performance comparison results, in terms of probability of synchronization, where we compare Reed-Solomon with and without symbol avoidance applied
First-order limits, an analytical perspective
In this paper we present a novel approach to graph (and structural) limits
based on model theory and analysis. The role of Stone and Gelfand dualities is
displayed prominently and leads to a general theory, which we believe is
naturally emerging. This approach covers all the particular examples of
structural convergence and it put the whole in new context. As an application,
it leads to new intermediate examples of structural convergence and to a "grand
conjecture" dealing with sparse graphs. We survey the recent developments
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