  Consensus is a common method for computing a function of the data distributed
among the nodes of a network. Of particular interest is distributed average
consensus, whereby the nodes iteratively compute the sample average of the data
stored at all the nodes of the network using only near-neighbor communications.
In real-world scenarios, these communications must undergo quantization, which
introduces distortion to the internode messages. In this thesis, a model for
the evolution of the network state statistics at each iteration is developed
under the assumptions of Gaussian data and additive quantization error. It is
shown that minimization of the communication load in terms of aggregate source
coding rate can be posed as a generalized geometric program, for which an
equivalent convex optimization can efficiently solve for the global minimum.
Optimization procedures are developed for rate-distortion-optimal vector
quantization, uniform entropy-coded scalar quantization, and fixed-rate uniform
quantization. Numerical results demonstrate the performance of these
approaches. For small numbers of iterations, the fixed-rate optimizations are
verified using exhaustive search. Comparison to the prior art suggests
competitive performance under certain circumstances but strongly motivates the
incorporation of more sophisticated coding strategies, such as differential,
predictive, or Wyner-Ziv coding.
