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 optimality of the proposed IDNC scheme when the file sizes are sufficiently large.

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