On $\ell_p$-norm Computation over Multiple-Access Channels

TL;DR

This paper explores how to efficiently compute $ ext{ell}_p$-norms over multiple access channels in wireless networks, emphasizing the integration of communication and computation for dynamic, task-specific information transfer.

Contribution

It introduces a novel approach to joint communication and distributed function computation, specifically for $ ext{ell}_p$-norms, highlighting the role of information theory in network design.

Findings

Demonstrates the importance of coupling communication and computation in wireless networks.

Proposes strategies for $ ext{ell}_p$-norm computation over multiple access channels.

Shows potential for improved efficiency in distributed function computation.

Abstract

This paper addresses some aspects of the general problem of information transfer and distributed function computation in wireless networks. Many applications of wireless technology foresee networks of autonomous devices executing tasks that can be posed as distributed function computation. In today's wireless networks, the tasks of communication and (distributed) computation are performed separately, although an efficient network operation calls for approaches in which the information transfer is dynamically adapted to time-varying computation objectives. Thus, wireless communications and function computation must be tightly coupled and it is shown in this paper that information theory may play a crucial role in the design of efficient computation-aware wireless communication and networking strategies. This is explained in more detail by considering the problem of computing $\ell_p$-norms over multiple access channels.