Source Coding Optimization for Distributed Average Consensus

TL;DR

This paper develops a model for quantized distributed average consensus, optimizing source coding to minimize communication load, and demonstrates the effectiveness of various quantization strategies through numerical results.

Contribution

It introduces a convex optimization framework for rate-distortion optimal quantization in distributed consensus, incorporating Gaussian assumptions and developing practical algorithms.

Findings

Convex optimization effectively minimizes communication rates.

Rate-distortion optimal quantization improves consensus accuracy.

Fixed-rate quantization matches exhaustive search results for small iterations.

Abstract

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.