Content Delivery Over Broadcast Erasure Channels With Distributed Random Cache

We study the content delivery problem between a transmitter and two receivers through erasure links, when each receiver has access to some random side-information about the files requested by the other user. The random side-information is cached at the receiver via the decentralized content placement. The distributed nature of the receiving terminals may also make it harder for the transmitter to learn the erasure state of the two links and indices of the cached files. We thus investigate the capacity gain due to various levels of availability of channel state and cache index information at the transmitter. More precisely, we cover a wide range of settings from global delayed channel state knowledge and a non-blind transmitter (i.e., one that knows the exact cache index information at each receiver) all the way to no channel state information and a blind transmitter (i.e., one that only statistically knows cache index information at the receivers). We derive new inner and outer bounds for the problem under various settings and provide the conditions under which the two match and the capacity region is characterized. Surprisingly, for some interesting cases, the capacity region remains unchanged even with only single-user channel state or single-user cache index information at the transmitter.