Age-optimal Transmission Policy for Markov Source with Differential Encoding

Abstract

In this paper, we consider a status update system, in which the source monitors a dynamic Markov process. The status updates are generated with a fixed rate, and delivered to the receiver over an unreliable channel instantaneously. The timeliness of the status updates is characterized by a recent metric, age of information (AoI). In this setting, error would occur in the transmission, deteriorating the reliability of updates. Thus, once an update is not decoded successfully, one should decide whether to retransmit the stale update or switch to transmit the newly generated one. Especially, differential encoding scheme is applied to the considered system to exploit the temporal correlations of the source. By differential encoding, each update can be actual or differential, based on the differential encoding level. To minimize the long-term average age, we formulate a Markov Decision Process (MDP). We prove that the optimal transmission policy has a threshold structure. We also show the existence of the optimal differential encoding level that minimizes the long-term average age under the optimal transmission policy. Numerical results are provided to validate our analytical results. Furthermore, numerical results show that the optimal differential encoding level is decreasing with higher erasure probability of the channel.