A lower bound to transmission power for multicast in underwater networks using network coding

The purpose of this paper is to show that convexity of the underwater acoustic channel and that near-convexity of an approximate closed-form model for that channel holds, in order to use network optimization techniques. We obtain a lower bound on transmission power using subgraph selection to establish minimum-cost multicast connections in underwater acoustic networks with network coding. We solve this problem for a range of transmission distances that are of interest for practical systems and exploiting physical properties of the underwater acoustic channel. Since the complete model for the underwater channel is complex, an approximate model is used for numerical computations. We illustrate results numerically determining the lower bound on transmission power for different random two-dimensional deployment scenarios and unicast rates. Also, we quantify the performance gap of two practical network layer schemes with respect to the lower bound.