×

Representations of the multicast network problem. (English) Zbl 1391.94866

Howe, Everett W. (ed.) et al., Algebraic geometry for coding theory and cryptography, IPAM, Los Angeles, CA, USA, February 2016. Cham: Springer (ISBN 978-3-319-63930-7/hbk; 978-3-319-63931-4/ebook). Association for Women in Mathematics Series 9, 1-23 (2017).
Summary: We approach the problem of linear network coding for multicast networks from different perspectives. We introduce the notion of the coding points of a network, which are edges of the network where messages combine and coding occurs. We give an integer linear program that leads to choices of paths through the network that minimize the number of coding points. We introduce the code graph of a network, a simplified directed graph that maintains the information essential to understanding the coding properties of the network. One of the main problems in network coding is to understand when the capacity of a multicast network is achieved with linear network coding over a finite field of size \(q\). We explain how this problem can be interpreted in terms of rational points on certain algebraic varieties.
For the entire collection see [Zbl 1387.14013].

MSC:

94B27 Geometric methods (including applications of algebraic geometry) applied to coding theory
05C90 Applications of graph theory
14G50 Applications to coding theory and cryptography of arithmetic geometry
90B18 Communication networks in operations research
PDFBibTeX XMLCite
Full Text: DOI arXiv