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：本文研究多源系统中的信息时效性（$\AoI$），其中$K$个信源通过公共聚合节点经具有数据包传输错误的信道向目的节点发送其时变过程更新。我们针对采用轮询调度策略的$(\alpha, \beta, \epsilon_0, \epsilon_1)$-吉尔伯特-艾略特（$\GE$）数据包擦除信道分析$\AoI$。在聚合节点处采用最大距离可分（$\MDS$）方案对多源更新进行编码。我们在长码块场景下刻画了$\MDS$编码系统的平均$\AoI$。进一步证明：相较于未编码系统，实现最大\emph{编码增益}的\emph{最优编码速率}为$n(1-\pers)-\smallO(n)$，其中$\pers \triangleq \frac{\beta}{\alpha+\beta}\epsilon_0 + \frac{\alpha}{\alpha+\beta}\epsilon_1$，且该最大编码增益为$(1+\pers)/(1+\smallO(1))$。