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In this paper, we examine a status updating system where updates generated bythe source are sent to the monitor through an erasure channel. We assume eachupdate consists of $k$ symbols and the symbol erasure in each time slot followsan independent and identically distributed (i.i.d.) Bernoulli process. Weassume rateless coding scheme is adopted at the transmitter and an update canbe successfully decoded if $k$ coded symbols are received successfully. Weassume perfect feedback available at the source, so that it knows whether atransmitted symbol has been erased instantly. Then, at the beginning of eachtime slot, the source has the choice to start transmitting a new update, orcontinue with the transmission of the previous update if it is not deliveredyet. We adopt the metric "Age of Information" (AoI) to measure the freshness ofinformation at the destination, where the AoI is defined as the age of thelatest decoded update at the destination. Our objective is to design an optimalonline transmission scheme to minimize the time-average AoI. The transmissiondecision is based on the instantaneous AoI, the age of the update beingtransmitted, as well as the number of successfully delivered symbols of theupdate. We formulate the problem as a Markov Decision Process (MDP) andidentify the monotonic threshold structure of the optimal policy. Numericalresults corroborate the structural properties of the optimal solution.

Age-Optimal Transmission of Rateless Codes in an Erasure Channel