On The Stability Region of the Layered Packet Erasure Broadcast Channel with Output Feedback

Abstract

This paper studies the Layered Packet Erasure Broadcast Channel (LPE-BC) with Channel Output Feedback (COF), which is a high-SNR approximation of the fading Gaussian BC, proposed by Tse and Yates in 2012 for the case without COF. This model is also a multi-layer generalization of the Binary Erasure Channel (BEC). In a past work, the Authors derived inner and outer bounds to the rate region (set of achievable rates with backlogged arrivals) of the LPE-BC with COF; here, the arrival region (set of exogenous arrival rates for which packet arrival queues are stable) for the same model is analyzed. For the case of K=2 users and Q$\geq 1$ layers, the known achievable rate region and the derived arrival region coincide; both strategically employ a network-coding based retransmission protocol. For the case of Q = 2 layers, sufficient conditions are given for the achievable arrival region to coincide with the known converse rate region, thus showing that in those cases the optimal rate and arrival regions coincide.