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Real-valued average consensus over noisy quantized channels
This paper concerns the average consensus problem
with the constraint of quantized communication between
nodes. A broad class of algorithms is analyzed, in which the
transmission strategy, which decides what value to communicate
to the neighbours, can include various kinds of rounding, probabilistic
quantization, and bounded noise. The arbitrariness
of the transmission strategy is compensated by a feedback
mechanism which can be interpreted as a self-inhibitory action.
The result is that the average of the nodes state is not conserved
across iterations, and the nodes do not converge to a consensus;
however, we show that both errors can be made as small
as desired. Bounds on these quantities involve the spectral
properties of the graph and can be proved by employing
elementary techniques of LTI systems analysis
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