Remote Tracking of Distributed Dynamic Sources Over a Random Access Channel With One-Bit Updates

In this work, we consider a network, where distributed information sources whose states evolve according to a random process transmit their time-varying states to a remote estimator over a shared wireless channel. Each source generates packets in a decentralized manner and employs a slotted random access mechanism to transmit the packets. In particular, we are interested in networks with a large number of low-complexity devices that share low-capacity random access channels. Accordingly, we investigate update strategies for remote tracking of source states that require each update to constitute as few bits as possible. To that end, we develop update strategies requiring only one-bit of information per update that employ a local cancellation strategy. We further analytically compare the performance of the cancellation-enabled update policy to the optimal policy that does not restrict the number of bits for each update, which show that an asymptotic upper bound of the optimality ratio is $\frac{13\sqrt{2}}{12}$. Through simulations, we compare the proposed cancellation-enabled one-bit update policy with zero-wait sampling and threshold-based sampling policies that require more than one-bit of information per update. The comparisons show that the cancellation-enabled update policy at its optimal threshold level outperforms the multi-bit update policies.