  In this paper, we investigate the problem of minimizing the frame completion
delay for Instantly Decodable Network Coding (IDNC) in relay-assisted wireless
multicast networks. We first propose a packet recovery algorithm in the single
relay topology which employs generalized IDNC instead of strict IDNC previously
proposed in the literature for the same relay-assisted topology. This use of
generalized IDNC is supported by showing that it is a super-set of the strict
IDNC scheme, and thus can generate coding combinations that are at least as
efficient as strict IDNC in reducing the average completion delay. We then
extend our study to the multiple relay topology and propose a joint generalized
IDNC and relay selection algorithm. This proposed algorithm benefits from the
reception diversity of the multiple relays to further reduce the average
completion delay in the network. Simulation results show that our proposed
solutions achieve much better performance compared to previous solutions in the
literature.
