This paper considers the downlink traffic from a base station to two different clients. When assuming infinite backlog, it is known that inter-session network coding (INC) can significantly increase the throughput of each flow. However, the corresponding scheduling solution (when assuming dynamic arrivals instead and requiring bounded delay) is still nascent. For the 2-flow downlink scenario, we propose the first opportunistic INC + scheduling solution that is provably optimal for time-varying channels, i.e., the corresponding stability region matches the optimal Shannon capacity. Specifically, we first introduce a new binary INC operation, which is distinctly different from the traditional wisdom of XORing two overheard packets. We then develop a queue-length-based scheduling scheme, which, with the help of the new INC operation, can robustly and optimally adapt to time-varying channel quality. We then show that the proposed algorithm can be easily extended for rate adaptation and it again robustly achieves the optimal throughput. A byproduct of our results is a scheduling scheme for stochastic processing networks (SPNs) with random departure, which relaxes the assumption of deterministic departure in the existing results. The new SPN scheduler could thus further broaden the applications of SPN scheduling to other real-world scenarios.

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