162,906 research outputs found
Construction of Codes for Network Coding
Based on ideas of K\"otter and Kschischang we use constant dimension
subspaces as codewords in a network. We show a connection to the theory of
q-analogues of a combinatorial designs, which has been studied in Braun, Kerber
and Laue as a purely combinatorial object. For the construction of network
codes we successfully modified methods (construction with prescribed
automorphisms) originally developed for the q-analogues of a combinatorial
designs. We then give a special case of that method which allows the
construction of network codes with a very large ambient space and we also show
how to decode such codes with a very small number of operations
Simplified random network codes for multicast networks
Thesis (M. Eng. and S.B.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2005.Includes bibliographical references (p. 43).Network coding is a method of data transmission across a network which involves coding at intermediate nodes. Network coding is particularly attractive for multicast. Building on the work done on random linear network codes, we develop a constrained, simplified code construction suitable for multicast in wireless networks. We analyze bounds on sufficient code size and code success probability via an algebraic framework for network coding. We also present simulation results that compare generalized random network codes with our code construction. Issues unique to the simplified code are explored and a relaxation of the code to improve code performance is discussed.by Anna H. Lee.M.Eng.and S.B
Construction algorithm for network error-correcting codes attaining the Singleton bound
We give a centralized deterministic algorithm for constructing linear network
error-correcting codes that attain the Singleton bound of network
error-correcting codes. The proposed algorithm is based on the algorithm by
Jaggi et al. We give estimates on the time complexity and the required symbol
size of the proposed algorithm. We also estimate the probability of a random
choice of local encoding vectors by all intermediate nodes giving a network
error-correcting codes attaining the Singleton bound. We also clarify the
relationship between the robust network coding and the network error-correcting
codes with known locations of errors.Comment: To appear in IEICE Trans. Fundamentals
(http://ietfec.oxfordjournals.org/), vol. E90-A, no. 9, Sept. 2007. LaTeX2e,
7 pages, using ieice.cls and pstricks.sty. Version 4 adds randomized
construction of network error-correcting codes, comparisons of the proposed
methods to the existing methods, additional explanations in the proo
Algebraic List-decoding of Subspace Codes
Subspace codes were introduced in order to correct errors and erasures for
randomized network coding, in the case where network topology is unknown (the
noncoherent case). Subspace codes are indeed collections of subspaces of a
certain vector space over a finite field. The Koetter-Kschischang construction
of subspace codes are similar to Reed-Solomon codes in that codewords are
obtained by evaluating certain (linearized) polynomials. In this paper, we
consider the problem of list-decoding the Koetter-Kschischang subspace codes.
In a sense, we are able to achieve for these codes what Sudan was able to
achieve for Reed-Solomon codes. In order to do so, we have to modify and
generalize the original Koetter-Kschischang construction in many important
respects. The end result is this: for any integer , our list- decoder
guarantees successful recovery of the message subspace provided that the
normalized dimension of the error is at most where
is the normalized packet rate. Just as in the case of Sudan's list-decoding
algorithm, this exceeds the previously best known error-correction radius
, demonstrated by Koetter and Kschischang, for low rates
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