Constructing multicast networks where vector linear coding outperforms scalar linear coding

Vector linear network coding (LNC) is a generalization of the conventional scalar LNC, such that the data unit transmitted on every edge is an L-dimensional vector of data symbols over a base field GF(q). There are classical exemplifying multi-source networks that have simple vector linear solutions...

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Vydáno v:Proceedings / IEEE International Symposium on Information Theory s. 2633 - 2637
Hlavní autoři: Sun, Qifu, Yang, Xiaolong, Long, Keping, Li, Zongpeng
Médium: Konferenční příspěvek Journal Article
Jazyk:angličtina
Vydáno: IEEE 01.06.2015
Témata:
alphabet size
Coding
Construction
Data models
Kernel
Linear codes
Mathematical analysis
Mathematical model
Multicast
multicast networks
Network coding
Networks
Receivers
scalar network coding
Scalars
Symbols
Vector network coding
Vectors (mathematics)
ISSN:2157-8095, 2157-8117
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Popis
Shrnutí:Vector linear network coding (LNC) is a generalization of the conventional scalar LNC, such that the data unit transmitted on every edge is an L-dimensional vector of data symbols over a base field GF(q). There are classical exemplifying multi-source networks that have simple vector linear solutions but no scalar linear solutions over any field. For (single-source) multicast networks, a popular conjecture characterizes the following benefit of vector LNC over scalar LNC in terms of alphabet size of data units: there exist multicast networks that are vector linearly solvable of dimension L over GF(q) but not scalar linearly solvable over any field of size q' ≤ q L . This paper introduces a general method to construct such a network, and subsequently constructs the first examples to affirm the positive answer of this conjecture. Moreover, among these exemplifying networks vector linearly solvable of dimension L over GF(q), there are instances with the additional property that even for some extremely large q' > q L , they are still not scalar linearly solvable over GF(q').
Bibliografie:ObjectType-Article-2
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ObjectType-Conference-1
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SourceType-Conference Papers & Proceedings-2
ISSN:2157-8095
2157-8117
DOI:10.1109/ISIT.2015.7282933