Generalized Index Coding Problem and Discrete Polymatroids
نویسندگان
چکیده
منابع مشابه
Discrete Polymatroids
The discrete polymatroid is a multiset analogue of the matroid. Based on the polyhedral theory on integral polymatroids developed in late 1960’s and in early 1970’s, in the present paper the combinatorics and algebra on discrete polymatroids will be studied.
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Generalized polymatroids are a family of polyhedra with several nice properties and applications. One property of generalized polymatroids used widely in existing literature is “total dual laminarity;” we make this notion explicit and show that only generalized polymatroids have this property. Using this we give a polynomial-time algorithm to check whether a given linear program defines a gener...
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An optimal linear coding solution for index coding problem is established. Instead of network coding approach by focus on graph theoric and algebraic methods a linear coding program for solving both unicast and groupcast index coding problem is presented. The coding is proved to be the optimal solution from the linear perspective and can be easily utilize for any number of messages. The importa...
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We consider the vector linear solvability of networks over a field Fq. It is well known that a scalar linear solution over Fq exists for a network if and only if the network is matroidal with respect to a matroid representable over Fq. A discrete polymatroid is the multi-set analogue of a matroid. In this paper, a discrete polymatroidal network is defined and it is shown that a vector linear so...
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ژورنال
عنوان ژورنال: Entropy
سال: 2020
ISSN: 1099-4300
DOI: 10.3390/e22060646