# Computing and Communicating Functions in Disorganized Wireless Networks

## TL;DR

This paper proposes a hierarchical approach combining computation over multi-access channels and orthogonal communication to efficiently compute functions in disorganized wireless networks with multiple relays, improving data aggregation.

## Contribution

It introduces a novel hierarchical network model and multi-layer function computation method that integrates CoMAC and orthogonal communication for disorganized wireless networks.

## Key findings

- Derived the general computation rate for the proposed scheme.
- Optimized time allocation and power control improve performance.
- Closed-form solutions for optimization demonstrate scheme generality.

## Abstract

For future wireless networks, enormous numbers of interconnections are required, creating a disorganized topology and leading to a great challenge in data aggregation. Instead of collecting data individually, a more efficient technique, computation over multi-access channels (CoMAC), has emerged to compute functions by exploiting the signal-superposition property of wireless channels. However, the implementation of CoMAC in disorganized networks with multiple relays (hops) is still an open problem. In this paper, we combine CoMAC and orthogonal communication in the disorganized network to attain the computation of functions at the fusion center. First, to make the disorganized network more tractable, we reorganize the disorganized network into a hierarchical network with multiple layers that consists of subgroups and groups. In the hierarchical network, we propose multi-layer function computation where CoMAC is applied to each subgroup and orthogonal communication is adopted within each group. By computing and communicating subgroup and group functions over layers, the desired functions are reconstructed at the fusion center. The general computation rate is derived and the performance is further improved through time allocation and power control. The closed-form solutions to optimization are obtained, which suggest that existing CoMAC and orthogonal communication schemes can be generalized.