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hw278b - UCSD ECE287B Prof Young-Han Kim Homework Set#2 Due...

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UCSD ECE287B Handout #6 Prof. Young-Han Kim Thursday, October 7, 2010 Homework Set #2 Due: Thursday, October 14, 2010 1. Show that it suffices to take the minimum over connected cuts in the max-flow min-cut theorem. 2. Show that it suffices to take n ≤ ⌈ log( |D| R + 1) in the achievability proof of the network coding theorem in Subsection 16.3.2. 3. Prove the cutset bound for the general noiseless multi-message network in Theorem 16.4. 4. Noiseless multicast wireless networks. Consider a noiseless wireless network modeled by a weighted directed acyclic hypergraph H = ( N , E , C ), where E now consists of a set of hyperedges ( j, N j ) with capacity C j N j . Each hyperedge models a noiseless broadcast link from node j to a set of receiver nodes N j . Suppose source node 1 wishes to send the message M [1 : 2 nR ] to a set of destination nodes D . (a) Generalize the cutset bound for the noiseless multicast network to establish an upper bound on the capacity of the noiseless multicast wireless network.
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