Low Latency Allcast Over Broadcast Erasure Channels

Mark A. Graham, Ayalvadi J. Ganesh, Robert J. Piechocki

Abstract: Consider <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$n$ </tex-math></inline-formula> nodes communicating over an unreliable broadcast channel. Each node has a single packet that needs to be communicated to all other nodes. Time is slotted, and a time slot is long enough for each node to broadcast one packet. Each broadcast reaches a random subset of nodes. The objective is to minimise the time until all nodes have received all packets. We study two schemes, (i) random relaying, and (ii) random linear network coding, and analyse their performance in an asymptotic regime in which <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$n$ </tex-math></inline-formula> tends to infinity. Simulation results for a wide range of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$n$ </tex-math></inline-formula> are also presented.