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

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.