Optimal Age over Erasure Channels
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Previous works on age of information and erasure channels have dealt with specific models and computed the average age or average peak age for certain settings. In this paper, we ask a more fundamental question: Given a single source and an erasure channel, what is the optimal coding scheme from an age point of view and what is the optimal achievable age? We answer these questions in the following two scenarios: (i) the source alphabet and the erasure-channel input-alphabet are the same, and (ii) the source alphabet and the channel input-alphabet are different. We show that, in the first case, no coding is required and we derive a closed form formula for the average age. Whereas, in the second case, we use a random coding argument to bound the average age and show that the average age achieved using random codes converges to the optimal average age as the source alphabet becomes large.
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