Optimal Broadcast in Shared Spectrum Radio Networks

This paper studies single hop broadcast in a single hop shared spectrum radio network. The problem requires a source to deliver a message to n receivers, where only a polynomial upper bound on n is known. The model assumes that in each round, each device can participate on 1 out of \(\mathcal{C} \geq 1\) available communication channels, up to \(t < \mathcal{C}\) of which might be disrupted, preventing communication. This disruption captures the unpredictable message loss that plagues real shared spectrum networks. The best existing solution to the problem, which comes from the systems literature, requires \(O\big({\frac{\mathcal{C} t}{\mathcal{C}-t}}\log{n}\big)\) rounds. Our algorithm, by contrast, solves the problem in \(O\big(\frac{\mathcal{C}}{\mathcal{C}-t}\lceil\frac{t}{n}\rceil\log{n}\big)\) rounds, when \(\mathcal{C} \geq \log{n}\), and in \(O\big(\frac{\mathcal{C}}{\mathcal{C}-t}\log{n}\cdot\log{\rm log}{n}\big)\) rounds, when \(\mathcal{C}\) is smaller. It accomplishes this improvement by deploying a self-regulating relay strategy in which receivers that already know useful information coordinate themselves to efficiently assist the source’s broadcast. We conclude by proving these bounds tight for most cases.