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

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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 suFces to take the minimum over connected cuts in the max-±ow min-cut theorem. 2. Show that it suFces 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. (b) Show that the cutset bound in part (a) is achievable via linear network coding.
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This note was uploaded on 01/08/2011 for the course ECE ece287b taught by Professor Cs during the Fall '10 term at UCSD.

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