Adaptive Coding for Information Freshness in a Two-user Broadcast Erasure Channel

In this paper, we investigate the impact of coding on the Age of Information (AoI) in a two-user broadcast symbol erasure channel with feedback. We assume each update consists of $K$ symbols and the source is able to broadcast one symbol in each time slot. Due to random channel noise, the intended symbol at each user will be erased according to an independent and identically distributed (i.i.d.) Bernoulli process. A user is able to successfully decode an update if it accumulates sufficient information and successfully decodes the $K$ symbols of the update. Assuming prefect feedback information at the source right after the transmission of each symbol, our objective is to design an adaptive coding scheme to achieve small AoI at both users. We propose a novel coding scheme to judiciously combine symbols from different updates together, and analyze the AoI at both users. Compared with a baseline greedy scheme, the proposed adaptive coding scheme improves the AoI at the weak user by orders of magnitude without compromising the AoI at the strong user.