In this paper, we considered the class of erasure channels, where symbols sent over the channel are received errorless or erased. We show why these channels are very relevant for modelling communication networks. We presented a review of known results in the context of erasure channe, decribing why they are different from more classical error channels. We give a glance at previous results in the context of erasure broadcast channels and we finally focused on the single relay erasure channel. For this last channel we developped a new converse theorem showing that for fixed random coding the cut-set bound is not attainable unless some virtually degradedness is ensured. To the best of our knowledge it is the first general converse theorem for relay channel.rnThis obtained converse theorem could be used for deriving tighter cut-set type bound for general multi-terminal erasure channels. However, these tighter bound have not been presented here because of lack of space.
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