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 $(1+\pers)/(1+\smallO(1))$.
翻译：在我们的工作中,我们研究一个多源系统中的信息年龄($AoI$),在这个系统中,美元来源通过共同聚合器节点将时间变化过程的更新通过共享传送错误的频道向目的地节点传送。我们分析美元(AoI$),用于一个$(alpha,\beta,\epsilon_0,\epsilon_1美元),美元-Gilbert-Elliot($GE$) 包切除频道,使用圆环列表政策。我们在聚合器中采用最大距离(MDS$)计划($\MDS$),用于对多源更新进行编码。我们把大块长的 $\MDS编码系统的平均值定为$(oI$)。我们进一步显示,在未编码系统上实现最大/emph*%coding收益的 $(1-\pers)-SmallO(n) $($\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\
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