Achievable schemes for cost/performance tradeoffs 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. In this thesis, I consider the design of simple achievable schemes that minimize the overhead from data collection and/or tradeoff performance for overhead. Where possible, these schemes are compared with the optimal tradeoff curve.

I first consider the optimal transmission of distributed correlated discrete memoryless sources across a network with capacity constraints and establish previously unreported properties of jointly optimal compression rates and transmission schemes. Additionally, an explicit relationship between the conditional independence relationships of the distributed sources and the number of vertices for the Slepian-Wolf rate region are given.

Motivated by recent work applying rate distortion theory to computing the optimal performance-overhead tradeoff, I also investigate the use of distributed scalar quantization for lossy encoding of state, where a central estimation officer (CEO) wishes to compute an extremization function (e.g. max, argmax) of a collection of sources. The superiority of a simple heterogeneous (across users) quantizer design over the optimal homogeneous quantizer design is proven.