Age of Incorrect Information With Hybrid ARQ Under a Resource Constraint for N-ary Symmetric Markov Sources

TL;DR

This paper investigates optimal transmission policies to minimize the Age of Incorrect Information (AoII) in remote monitoring systems with resource constraints, using a Markov decision process framework and hybrid ARQ protocols.

Contribution

It formulates the AoII optimization as a constrained MDP for N-ary symmetric Markov sources and derives conditions under which transmission should be avoided or randomized based on source dynamics.

Findings

Optimal policy may involve never transmitting in certain source states.

When transmission occurs, the policy is a randomized threshold-based strategy.

Numerical results show how source dynamics and channel conditions affect AoII.

Abstract

The Age of Incorrect Information (AoII) is a recently proposed metric for real-time remote monitoring systems. In particular, AoII measures the time the information at the monitor is incorrect, weighted by the magnitude of this incorrectness, thereby combining the notions of freshness and distortion. This paper addresses the definition of an AoII-optimal transmission policy in a discrete-time communication scheme with a resource constraint and a hybrid automatic repeat request (HARQ) protocol. Considering an $N$-ary symmetric Markov source, the problem is formulated as an infinite-horizon average-cost constrained Markov decision process (CMDP). Interestingly, it is proved that, under some conditions, the optimal transmission policy is to never transmit. This reveals a region of the source dynamics where communication is inadequate in reducing the AoII. Elsewhere, there exists an optimal transmission policy, which is a randomized mixture of two discrete threshold-based policies that randomize on at most one state. The optimal threshold and the randomization component are derived analytically. Numerical results illustrate the impact of the source dynamics, channel conditions, and resource constraints on the average AoII.