Network coding for non-uniform demands

Abstract

Non-uniform demand networks are defined as a useful connection model, in between multicasts and general connections. In these networks, each sink demands a certain number of messages, without specifying their identities. We study the solvability of such networks and give a tight bound on the number of sinks for which the min cut condition is sufficient. This sufficiency result is unique to the non-uniform demand model and does not apply to general connection networks. We propose constructions to solve networks at, or slightly below capacity, and investigate the effect large alphabets have on the solvability of such networks. We also show that our efficient constructions are suboptimal when used in networks with more sinks, yet this comes with little surprise considering the fact that the general problem is shown to be NP-hard.

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