  In this paper, we study the convergence behavior of distributed iterative
algorithms with quantized message passing. We first introduce general iterative
function evaluation algorithms for solving fixed point problems distributively.
We then analyze the convergence of the distributed algorithms, e.g. Jacobi
scheme and Gauss-Seidel scheme, under the quantized message passing. Based on
the closed-form convergence performance derived, we propose two quantizer
designs, namely the time invariant convergence-optimal quantizer (TICOQ) and
the time varying convergence-optimal quantizer (TVCOQ), to minimize the effect
of the quantization error on the convergence. We also study the tradeoff
between the convergence error and message passing overhead for both TICOQ and
TVCOQ. As an example, we apply the TICOQ and TVCOQ designs to the iterative
waterfilling algorithm of MIMO interference game.
