Communication via Sensing

TL;DR

This paper explores the limits of using sensing capabilities at the receiver for communication, formulating capacity bounds for finite-state channels with practical constraints, and providing a closed-form upper bound for a specific case.

Contribution

It introduces a novel framework for communication via sensing, deriving tight capacity upper bounds and a single-letter formula for a two-state noisy sensing scenario.

Findings

Derived a cost-constrained capacity upper bound for communication via sensing.

Converted the capacity bound into a single-letter formulation using graph cycle decomposition.

Obtained a closed-form expression for the capacity upper bound in a two-state BSC sensing model.

Abstract

We present an alternative take on the recently popularized concept of `\textit{joint sensing and communications}', which focuses on using communication resources also for sensing. Here, we propose the opposite, where we utilize the receiver's sensing capabilities for communication. Our goal is to characterize the fundamental limits of communication over such a channel, which we call `\textit{communication via sensing}'. We assume that changes in the sensed attributes, such as location and speed, are limited due to practical constraints, which are captured by assuming a finite-state channel (FSC) with an input cost constraint. We first formulate an upper bound on the \(N\)-letter capacity as a cost-constrained optimization problem over the input sequence distribution, and then convert it to an equivalent problem over the state sequence distribution. Moreover, by breaking a walk on the underlying Markov chain into a weighted sum of traversed graph cycles in the long walk limit, we obtain a compact single-letter formulation of the capacity upper bound. Finally, for a specific case of a two-state FSC with noisy sensing characterized by a binary symmetric channel (BSC), we obtain a closed-form expression for the capacity upper bound. Comparison with an existing numerical lower bound shows that our proposed upper bound is very tight for all crossover probabilities.