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On Network Coding for Funnel Networks

Network coding for non-multicast problems has been the subject of many recent studies. In this letter, we consider networks in which the total capacity of the incoming links to each intermediate node is not less than the total capacity of its outgoing links. We call these networks funnel networks and prove that any feasible non-multicast problem on funnel networks is solvable by routing (hence, by linear network coding, too). The desirability of network coding in funnel networks may be justified by the other benefits that coding offers. However, we see that in funnel networks, the conventional random approach to linear coding fails with high probability. Hence, we provide a new random linear network coding solution for these non-multicast problems.