Implementing uniform reliable broadcast with binary consensus in systems with fair-lossy links

When implementing multivalued consensus using binary consensus, previous algorithms assume the availability of uniform reliable broadcast, which is not implementable in systems with fair-lossy links. In this paper, we show that with binary consensus we can implement uniform reliable broadcast directly in systems with fair-lossy links, and thus the separate assumption of the availability of uniform reliable broadcast is not necessary. We further prove that, when binary consensus instances are available only as black boxes, any implementation of uniform reliable broadcast in the fair-lossy link model requires the invocation of an infinite number of binary consensus instances even if no process ever broadcasts any messages, and this is true even when multivalued consensus is used.