Multiuser broadcast erasure channel with feedback - capacity and algorithms

Computer Science – Information Theory

Scientific paper

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45 pages, 3 figures, 3 tables, submitted to IEEE Transactions on Information Theory. Updated version to match reviewer comment

Scientific paper

We consider the N-user broadcast erasure channel with N unicast sessions (one for each user) where receiver feedback is regularly sent to the transmitter in the form of ACK/NACK messages. We first provide a generic outer bound to the capacity of this system; we then propose a virtual-queue-based inter-session mixing coding algorithm, determine its throughput region and show that it achieves capacity under certain conditions on channel statistics, assuming that instantaneous feedback is known to all users. Removing this assumption results in a throughput region that differs from the outer bound by a factor O(N/L), where L is the fixed packet length. For the case of arbitrary channel statistics, we present a modification of the previous algorithm whose throughput region is identical to the outer bound for N = 3, when instant feedback is known to all users, and differs from the bound by O(1/L), when the 3 users know only their own ACK. The proposed algorithms do not require any prior knowledge of channel statistics.

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