Minimizing Age of Information in an Energy-Harvesting Scheduler with Rateless Codes

We consider a status update system consisting of a source, a sampler, a monitor, and an energy harvesting battery at the sampler. The capacity of the battery is 1 unit of energy and the energy generation time follows an independent and identically distributed (i.i.d.) Bernoulli process. The sampler aims to sample fresh update packets from the source and transmit them to the monitor. The communication channel between the sampler and the monitor is erroneous, with the probability of successful transmission being $q$. Each update packet consists of 2 sub-packets. At time slot $t$, the sampler can transmit only one sub-packet. The transmitter employs a rateless coding scheme, for which the monitor successfully decodes an update packet if and only if it receives both of the sub-packets. Transmission of a sub-packet requires 1 unit of energy. When there is no update packet available to transmit, the sampler has to decide whether to sample a fresh update packet or stay idle. When the monitor has received the first sub-packet, the sampler has to decide whether to sample a fresh packet and transmit the first sub-packet of the fresher update packet or transmit the second sub-packet of the staler update packet. We formulate this problem as a Markov decision process (MDP), and identify several structures of an optimal policy. We propose an optimal policy based on the studied structure of an optimal policy. Finally, we propose a low-complexity heuristic policy, by leveraging some of the structures of an optimal policy, and compare its performance with the actual optimal policy obtianed by the MDP.