Conference proceeding
Matroid Bounds on the Region of Entropic Vectors
2013 51ST ANNUAL ALLERTON CONFERENCE ON COMMUNICATION, CONTROL, AND COMPUTING (ALLERTON), pp.796-803
01 Jan 2013
Abstract
Several properties of the inner bound on the region of entropic vectors obtained from representable matroids are derived. In particular, it is shown that: I) It suffices to check size 2 minors of an integer-valued vector to determine if it is a valid matroid rank; II) the subset of the extreme rays of the Shannon outer bound (the extremal polymatroids) that are matroidal are also the extreme rays of the cone of matroids; III) All matroid ranks are convex independent; and IV) the extreme rays of the conic hull of the binary/ternary/quaternary representable matroid ranks inner bound are a subset of the extreme rays of the conic hull of matroid ranks. These properties are shown to allow for substantial reduction in the complexity of calculating important rate regions in multiterminal information theory, including multiple source multicast network coding capacity regions.
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Details
- Title
- Matroid Bounds on the Region of Entropic Vectors
- Creators
- Congduan Li - Drexel Univ, Dept ECE, Philadelphia, PA 19104 USAJohn MacLaren Walsh - Drexel UniversitySteven Weber - Drexel UniversityIEEE
- Publication Details
- 2013 51ST ANNUAL ALLERTON CONFERENCE ON COMMUNICATION, CONTROL, AND COMPUTING (ALLERTON), pp.796-803
- Conference
- 2013 51ST ANNUAL ALLERTON CONFERENCE ON COMMUNICATION, CONTROL, AND COMPUTING (ALLERTON), 51st
- Series
- Annual Allerton Conference on Communication Control and Computing
- Publisher
- IEEE
- Number of pages
- 8
- Resource Type
- Conference proceeding
- Language
- English
- Academic Unit
- Electrical and Computer Engineering
- Identifiers
- 991019170599704721
InCites Highlights
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- Automation & Control Systems
- Computer Science, Information Systems
- Telecommunications