Contents I. Introduction
Monitoring the state of remotely-deployed nodes in a wire-less sensor network is one of the possible applications of Internet of Things (IoT) systems. Due to potentially large node populations and the sporadic and unpredictable nature of transmissions, the use of random access (RA) as multiple access channel (MAC) protocol is a viable option. In this paper, we consider a system in which nodes monitoring two-state Markov sources communicate towards a common receiver over a slotted ALOHA RA channel without feedback [1]. Under the assumption of destructive collisions we investigate the ability of the system to acquire accurate estimates of the state of the sources at the receiver. As performance metric, we adopt the state estimation entropy (SEE) [2], which quantifies the uncertainty in the knowledge of sources’ state at the sink, based on current and past channel outputs as well as on the source model. Two transmission strategies are considered: a random transmission strategy, where the nodes send updates of their state with a fixed probability in each slot according to a Bernoulli process, and a reactive transmission strategy, where the nodes send updates only when a change of state in the underlying Markov source is detected. We show that both strategies can be studied using two distinct hidden Markov models (HMMs) and provide an efficient evaluation of their performance in terms of SEE via density evolution (DE) [3][4, Chapter 4] analysis with a complexity that grows only quadratically with the number of nodes. We validate our analytical results with simulations for both symmetric and asymmetric sources. The DE analysis shows that the reactive transmission strategy can drastically reduce the SEE when compared to the random transmission strategy. The intuition underlying the result follows the observation that, when collisions are rare, transmitting upon a state change is sufficient to accurately track the state of the sources. This result is in stark contrast with what happens for the age of information (AoI) [5], [6], for which random transmissions are preferable.
