Convergence-Optimal Quantizer Design of Distributed Contraction-based Iterative Algorithms with Quantized Message Passing

TL;DR

This paper investigates how quantized message passing affects the convergence of distributed iterative algorithms and proposes optimal quantizer designs to minimize convergence errors while balancing communication overhead.

Contribution

It introduces convergence-optimal quantizer designs (TICOQ and TVCOQ) for distributed algorithms, enhancing convergence performance under quantized message passing.

Findings

Proposed TICOQ and TVCOQ improve convergence accuracy.

Analyzed tradeoff between convergence error and message overhead.

Validated designs with iterative waterfilling in MIMO interference.

Abstract

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.