10,415 research outputs found
Construction of quasi-cyclic self-dual codes
There is a one-to-one correspondence between -quasi-cyclic codes over a
finite field and linear codes over a ring . Using this correspondence, we prove that every
-quasi-cyclic self-dual code of length over a finite field
can be obtained by the {\it building-up} construction, provided
that char or , is a prime , and
is a primitive element of . We determine possible weight
enumerators of a binary -quasi-cyclic self-dual code of length
(with a prime) in terms of divisibility by . We improve the result of
[3] by constructing new binary cubic (i.e., -quasi-cyclic codes of length
) optimal self-dual codes of lengths (Type I), 54 and
66. We also find quasi-cyclic optimal self-dual codes of lengths 40, 50, and
60. When , we obtain a new 8-quasi-cyclic self-dual code
over and a new 6-quasi-cyclic self-dual code over
. When , we find a new 4-quasi-cyclic self-dual
code over and a new 6-quasi-cyclic self-dual code
over .Comment: 25 pages, 2 tables; Finite Fields and Their Applications, 201
Efficient Algorithms for the Data Exchange Problem
In this paper we study the data exchange problem where a set of users is
interested in gaining access to a common file, but where each has only partial
knowledge about it as side-information. Assuming that the file is broken into
packets, the side-information considered is in the form of linear combinations
of the file packets. Given that the collective information of all the users is
sufficient to allow recovery of the entire file, the goal is for each user to
gain access to the file while minimizing some communication cost. We assume
that users can communicate over a noiseless broadcast channel, and that the
communication cost is a sum of each user's cost function over the number of
bits it transmits. For instance, the communication cost could simply be the
total number of bits that needs to be transmitted. In the most general case
studied in this paper, each user can have any arbitrary convex cost function.
We provide deterministic, polynomial-time algorithms (in the number of users
and packets) which find an optimal communication scheme that minimizes the
communication cost. To further lower the complexity, we also propose a simple
randomized algorithm inspired by our deterministic algorithm which is based on
a random linear network coding scheme.Comment: submitted to Transactions on Information Theor
A Numerical Approach for Designing Unitary Space Time Codes with Large Diversity
A numerical approach to design unitary constellation for any dimension and
any transmission rate under non-coherent Rayleigh flat fading channel.Comment: 32 pages, 6 figure
Computing sum of sources over an arbitrary multiple access channel
The problem of computing sum of sources over a multiple access channel (MAC)
is considered. Building on the technique of linear computation coding (LCC)
proposed by Nazer and Gastpar [2007], we employ the ensemble of nested coset
codes to derive a new set of sufficient conditions for computing the sum of
sources over an \textit{arbitrary} MAC. The optimality of nested coset codes
[Padakandla, Pradhan 2011] enables this technique outperform LCC even for
linear MAC with a structural match. Examples of nonadditive MAC for which the
technique proposed herein outperforms separation and systematic based
computation are also presented. Finally, this technique is enhanced by
incorporating separation based strategy, leading to a new set of sufficient
conditions for computing the sum over a MAC.Comment: Contains proof of the main theorem and a few minor corrections.
Contents of this article have been accepted for presentation at ISIT201
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