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A new computational approach for determining rate regions and optimal codes for coded networks
Conference proceeding

A new computational approach for determining rate regions and optimal codes for coded networks

Congduan Li, Jayant Apte, John MacLaren Walsh, Steven Weber and IEEE
2013 International Symposium on Network Coding (NetCod)
Jun 2013
DOI: https://doi.org/10.1109/NetCod.2013.6570825

Abstract

Decoding Entropy Linear code Random variables Vectors
A new computational technique is presented for determining rate regions for coded networks. The technique directly manipulates the extreme ray representation of inner and outer bounds for the region of entropic vectors. We use new inner bounds on region of entropic vectors based on conic hull of ranks of representable matroids. In particular, the extreme-ray representations of these inner bounds are obtained via matroid enumeration and minor exclusion. This is followed by a novel use of iterations of the double description method to obtain the desired rate regions. Applications in multilevel diversity coding systems (MDCS) are discussed as an example. The special structure of the problem that makes this technique inherently fast along with being scalable is also discussed. Our results demonstrate that for each of the 31 2-level 3-encoder and the 69 3-level 3-encoder MDCS configurations, if scalar linear codes (over any field) suffice to achieve the rate region, then in fact binary scalar linear codes suffice. For the 31 2-level 3-encoder cases where scalar codes are insufficient we demonstrate that vector linear codes suffice and provide some explicit constructions of these codes.

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2 citations in Web of Science
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Computer Science, Theory & Methods
Engineering, Electrical & Electronic
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