Coding Gain for Age of Information in a Multi-source System with Erasure Channel

In our work, we study the age of information ($\AoI$) in a multi-source system where $K$ sources transmit updates of their time-varying processes via a common-aggregator node to a destination node through a channel with packet delivery errors. We analyze $\AoI$ for an $(\alpha, \beta, \epsilon_0, \epsilon_1)$-Gilbert-Elliot ($\GE$) packet erasure channel with a round-robin scheduling policy. We employ maximum distance separable ($\MDS$) scheme at aggregator for encoding the multi-source updates. We characterize the mean $\AoI$ for the $\MDS$ coded system for the case of large blocklengths. We further show that the \emph{optimal coding rate} that achieves maximum \emph{coding gain} over the uncoded system is $n(1-\pers)-\smallO(n)$, where $\pers \triangleq \frac{\beta}{\alpha+\beta}\epsilon_0 + \frac{\alpha}{\alpha+\beta}\epsilon_1$, and this maximum coding gain is $(1+\pers)/(1+\smallO(1))$.