  In this paper, we dynamically select the transmission rate and design
wireless network coding to improve the quality of services such as delay for
time critical applications. With low transmission rate, and hence longer
transmission range, more packets may be encoded together, which increases the
coding opportunity. However, low transmission rate may incur extra transmission
delay, which is intolerable for time critical applications. We design a novel
joint rate selection and wireless network coding (RSNC) scheme with delay
constraint, so as to minimize the total number of packets that miss their
deadlines at the destination nodes. We prove that the proposed problem is
NPhard, and propose a novel graph model and transmission metric which consider
both the heterogenous transmission rates and the packet deadline constraints
during the graph construction. Using the graph model, we mathematically
formulate the problem and design an efficient algorithm to determine the
transmission rate and coding strategy for each transmission. Finally,
simulation results demonstrate the superiority of the RSNC scheme.
