Graph Codes for Distributed Instant Message Collection in an Arbitrary Noisy Broadcast Network

TL;DR

This paper studies the minimal number of broadcasts needed for sensor data collection in noisy networks, introducing graph codes and achieving bounds close to theoretical limits across various network types.

Contribution

It provides fundamental limits and practical in-network computing strategies using graph codes for arbitrary, geometric, and Erdős-Rényi networks, extending previous work.

Findings

Achieves upper bounds within logarithmic factor of fundamental limits for arbitrary networks.

Provides optimal in-network schemes for geometric and Erdős-Rényi networks.

Introduces novel graph coding techniques for distributed data gathering.

Abstract

We consider the problem of minimizing the number of broadcasts for collecting all sensor measurements at a sink node in a noisy broadcast sensor network. Focusing first on arbitrary network topologies, we provide (i) fundamental limits on the required number of broadcasts of data gathering, and (ii) a general in-network computing strategy to achieve an upper bound within factor $\log N$ of the fundamental limits, where $N$ is the number of agents in the network. Next, focusing on two example networks, namely, \textcolor{black}{arbitrary geometric networks and random Erd$\ddot{o}$s-R$\acute{e}$nyi networks}, we provide improved in-network computing schemes that are optimal in that they attain the fundamental limits, i.e., the lower and upper bounds are tight \textcolor{black}{in order sense}. Our main techniques are three distributed encoding techniques, called graph codes, which are designed respectively for the above-mentioned three scenarios. Our work thus extends and unifies previous works such as those of Gallager [1] and Karamchandani~\emph{et. al.} [2] on number of broadcasts for distributed function computation in special network topologies, while bringing in novel techniques, e.g., from error-control coding and noisy circuits, for both upper and lower bounds.