Energy Efficient Distributed Coding for Data Collection in a Noisy Sparse Network

We consider the problem of data collection in a two-layer network consisting of (1) links between $N$ distributed agents and a remote sink node; (2) a sparse network formed by these distributed agents. We study the effect of inter-agent communications on the overall energy consumption. Despite the sparse connections between agents, we provide an in-network coding scheme that reduces the overall energy consumption by a factor of $\Theta(\log N)$ compared to a naive scheme which neglects inter-agent communications. By providing lower bounds on both the energy consumption and the sparseness (number of links) of the network, we show that are energy-optimal except for a factor of $\Theta(\log\log N)$. The proposed scheme extends a previous work of Gallager on noisy broadcasting from a complete graph to a sparse graph, while bringing in new techniques from error control coding and noisy circuits.Comment: arXiv admin note: substantial text overlap with arXiv:1508.0155

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

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.Comment: 60 pages. Submitted for publicatio