Publications and Research
Document Type
Article
Publication Date
2026
Abstract
We consider the problem of multiple parties iteratively solving a system of linear equations in a decentralized manner. Specifically, we solve for $\negr{x} \in \R^n$, the $n \times n$ system of linear equations $M\negr{x} = \negr{b}$ when each party only knows their row of the matrix $M$ and a single component of $\negr{b} \in \R^n$. Our objective is to determine the tradeoff between the accuracy of the solution and the total communication cost measured in bits. A fully connected, reliable mesh network is assumed to connect the different parties. We develop a general formulation that applies to a large class of standard linear solvers, and provide a rate-distortion analysis. Furthermore, we analyze the security of the distributed system, demonstrating that the quantized iterative framework inherently acts as a privacy shield against malicious parameter inference. We establish a fundamental trade-off showing that faster convergence yields stronger algebraic privacy for the local nodes. The results of numerical experiments are also provided.
