networkcoding encourages the mixing of information flows at intermediate nodes of a network for enhanced network capacity, especially for one-to-many multicast applications. A fundamental problem in multicastnetwork...
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ISBN:
(纸本)9781479933617
networkcoding encourages the mixing of information flows at intermediate nodes of a network for enhanced network capacity, especially for one-to-many multicast applications. A fundamental problem in multicast network coding is to construct a feasible solution such that encoding and decoding are performed over a finite field of size as small as possible. coding operations over very small finite fields (e.g., F2) enable low computational complexity in theory and ease of implementation in practice. In this work, we propose a new approach based on matroid theory to study multicast network coding and its minimum field size requirements. Applying this new approach that translates multicastnetworks into matroids, we derive the first upper-bounds on the field size requirement based on the number of relay nodes in the network, and make new progresses along the direction of proving that coding over very small fields (F2 and F3) suffices for multicast network coding in planar networks.
Using tools from algebraic geometry and Grobner basis theory we solve two problems in networkcoding. First we present a method to determine the smallest field size for which linear networkcoding is feasible. Second ...
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ISBN:
(纸本)9783540694984
Using tools from algebraic geometry and Grobner basis theory we solve two problems in networkcoding. First we present a method to determine the smallest field size for which linear networkcoding is feasible. Second we derive improved estimates on the success probability of random linear networkcoding. These estimates take into account which monomials occur in the support of the determinant of the product of Edmonds matrices. Therefore we finally investigate which monomials can occur in the determinant of the Edmonds matrix.
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