A New Computational Approach for Determining Rate Regions and Optimal Codes for Coded Networks
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. The authors 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.