Optimal immediately-decodable inter-session network coding (IDNC) schemes for two unicast sessions with hard deadline constraints

In this paper, we study inter-session network coding for sending two unicast sessions over an unreliable wireless channel. Each unicast session transmits a stored video file, whose packets have hard sequential deadline constraints. We first characterize the capacity region (with inter-session network coding) for the transmission rates of the two unicast sessions under heterogeneous channel conditions and heterogeneous deadline constraints. We then develop immediately-decodable network coding (IDNC) schemes for controlling packet transmissions for the unicast sessions subject to hard deadline constraints. In contrast to our prior work that focuses on a single multicast session with homogeneous channel conditions and deadline constraints, the design and performance analysis of the IDNC scheme is much more complicated for unicast-sessions because of the asymmetry due to heterogeneous channel conditions and heterogeneous deadlines. Nonetheless, we establish the asymptotic optimality of the proposed IDNC scheme when the file sizes are sufficiently large.