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Representations of the Multicast Network Problem

Anderson, Sarah E. and Halbawi, Wael and Kaplan, Nathan and López, Hiram H. and Manganiello, Felice and Soljanin, Emina and Walker, Judy L. (2017) Representations of the Multicast Network Problem. In: Algebraic Geometry for Coding Theory and Cryptography. Association for Women in Mathematics Series. No.9. Springer , Cham, Switzerland, pp. 1-23. ISBN 978-3-319-63930-7. http://resolver.caltech.edu/CaltechAUTHORS:20171128-092215927

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Abstract

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.


Item Type:Book Section
Related URLs:
URLURL TypeDescription
https://doi.org/10.1007/978-3-319-63931-4_1DOIArticle
https://link.springer.com/chapter/10.1007%2F978-3-319-63931-4_1PublisherArticle
http://rdcu.be/zKUmPublisherFree ReadCube access
Additional Information:© 2017 The Author(s) and the Association for Women in Mathematics. First Online: 16 November 2017. The authors would like to acknowledge the hospitality of IPAM and the organizers of its Algebraic Geometry for Coding Theory and Cryptography Workshop: Everett Howe, Kristin Lauter, and Judy Walker. The third author was supported by NSA Young Investigator Grant H98230-16-10305 and by an AMS–Simons Travel Grant. The fourth author was partially supported by CONACyT, CVU No. 268999 project “Network Codes,” and Universidad Autónoma de Aguascalientes. The fifth author was partially supported by the National Science Foundation under grant DMS-1547399.
Funders:
Funding AgencyGrant Number
National Security AgencyH98230-16-10305
American Mathematical SocietyUNSPECIFIED
Consejo Nacional de Ciencia y Tecnología (CONACYT)268999
Universidad Autónoma de AguascalientesUNSPECIFIED
NSFDMS-1547399
Simons FoundationUNSPECIFIED
Record Number:CaltechAUTHORS:20171128-092215927
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20171128-092215927
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:83490
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:28 Nov 2017 17:38
Last Modified:28 Nov 2017 17:38

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