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On Multi-Source Networks: Enumeration, Rate Region Computation, and Hierarchy
Journal article   Open access   Peer reviewed

On Multi-Source Networks: Enumeration, Rate Region Computation, and Hierarchy

Congduan Congduan Li, Steven Weber and John MacLaren Walsh
IEEE transactions on information theory, v 63(11), pp 7283-7303
Nov 2017
url
https://doi.org/10.1109/tit.2017.2745620View
Accepted (AM)Open Access (Publisher-Specific) Open

Abstract

rate region Databases Software algorithms hierarchy Network coding Multi-source networks Encoding Random variables Complexity theory enumeration
Recent algorithmic developments have enabled computers to automatically determine and prove the capacity regions of small hypergraph networks under network coding. A structural theory relating network coding problems of different sizes is developed to make the best use of this newfound computational capability. A formal notion of network minimality is developed, which removes components of a network coding problem that are inessential to its core complexity. Equivalence between different network coding problems under relabeling is formalized via group actions, an algorithm which can directly list single representatives from each equivalence class of minimal networks up to a prescribed network size is presented. This algorithm, together with rate region software, is leveraged to create a database containing the rate regions for all minimal network coding problems with five or fewer sources and edges, a collection of 744119 equivalence classes representing more than 9 million networks. In order to best learn from this database, and to leverage it to infer rate regions and their characteristics of networks at scale, a hierarchy between different network coding problems is created with a new theory of combinations and embedding operators.

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Collaboration types
Domestic collaboration
International collaboration
Web of Science research areas
Computer Science, Information Systems
Computer Science, Theory & Methods
Engineering, Electrical & Electronic
Mathematics, Applied
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