Age-Optimal Transmission of Rateless Codes in an Erasure Channel

Abstract: In this paper, we examine a status updating system where updates generated by the source are sent to the monitor through an erasure channel. We assume each update consists of $k$ symbols and the symbol erasure in each time slot follows an independent and identically distributed (i.i.d.) Bernoulli process. We assume rateless coding scheme is adopted at the transmitter and an update can be successfully decoded if $k$ coded symbols are received successfully. We assume perfect feedback available at the source, so that it knows whether a transmitted symbol has been erased instantly. Then, at the beginning of each time slot, the source has the choice to start transmitting a new update, or continue with the transmission of the previous update if it is not delivered yet. We adopt the metric "Age of Information" (AoI) to measure the freshness of information at the destination, where the AoI is defined as the age of the latest decoded update at the destination. Our objective is to design an optimal online transmission scheme to minimize the time-average AoI. The transmission decision is based on the instantaneous AoI, the age of the update being transmitted, as well as the number of successfully delivered symbols of the update. We formulate the problem as a Markov Decision Process (MDP) and identify the monotonic threshold structure of the optimal policy. Numerical results corroborate the structural properties of the optimal solution.