Conservative Network Coding

Motivated by practical networking scenarios, we introduce a notion of restricted communication called conservative networking. Consider a network of lossless links and a number of independent sources. Each node needs to recover a certain subset of the sources. However, each node is conservative in that all information it receives can only be a function of the sources it will ultimately recover. For acyclic networks, we show that conservative networking admits a clean characterization: (i) the rates achievable by integer routing, factional routing, and network coding are equal, and (ii) this rate is determined by a simple cut bound. However, this clean characterization does not extend to cyclic networks. We present cyclic examples showing that (i) fractional routing can be strictly better than integer routing, and (ii) network coding can be strictly better than fractional routing. This work underscores the difficulties generally encountered in cyclic networks.