Structural Routability of n-Pairs Information Networks

Information does not generally behave like a conservative fluid flow in communication networks with multiple sources and sinks. However, it is often conceptually and practically useful to be able to associate separate data streams with each source-sink pair, with only routing and no coding performed at the network nodes. This raises the question of whether there is a nontrivial class of network topologies for which achievability is always equivalent to routability, for any combination of source signals and positive channel capacities. This chapter considers possibly cyclic, directed, errorless networks with n source-sink pairs and mutually independent source signals. The concept of downward dominance is introduced and it is shown that, if the network topology is downward dominated, then the achievability of a given combination of source signals and channel capacities implies the existence of a feasible multicommodity flow.Comment: The final publication is available at link.springer.com http://link.springer.com/chapter/10.1007/978-3-319-02150-8_

Achievable schemes for cost/performance trade-offs in networks

A common pattern in communication networks (both wired and wireless) is the collection of distributed state information from various network elements. This network state is needed for both analytics and operator policy and its collection consumes network resources, both to measure the relevant state and to transmit the measurements back to the data sink. The design of simple achievable schemes are considered with the goal of minimizing the overhead from data collection and/or trading off performance for overhead. Where possible, these schemes are compared with the optimal trade-off curve. The optimal transmission of distributed correlated discrete memoryless sources across a network with capacity constraints is considered first. Previously unreported properties of jointly optimal compression rates and transmission schemes are established. Additionally, an explicit relationship between the conditional independence relationships of the distributed sources and the number of vertices for the Slepian-Wolf rate region is given. Motivated by recent work applying rate-distortion theory to computing the optimal performance-overhead trade-off, the use of distributed scalar quantization is investigated for lossy encoding of state, where a central estimation officer (CEO) wishes to compute an extremization function of a collection of sources. The superiority of a simple heterogeneous (across users) quantizer design over the optimal homogeneous quantizer design is proven. Interactive communication enables an alternative framework where communicating parties can send messages back-and-forth over multiple rounds. This back-and-forth messaging can reduce the rate required to compute an extremum/extrema of the sources at the cost of increased delay. Again scalar quantization followed by entropy encoding is considered as an achievable scheme for a collection of distributed users talking to a CEO in the context of interactive communication. The design of optimal quantizers is formulated as the solution of a minimum cost dynamic program. It is established that, asymptotically, the costs for the CEO to compute the different extremization functions are equal. The existence of a simpler search space, which is asymptotically sufficient for minimizing the cost of computing the selected extremization functions, is proven.Ph.D., Electrical Engineering -- Drexel University, 201