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

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