  In this paper, we study the multicast completion and decoding delay
minimization problems of instantly decodable network coding (IDNC) in the case
of lossy feedback. In such environments, the sender falls into uncertainties
about packet reception at the different receivers, which forces it to perform
partially blind selections of packet combinations in subsequent transmissions.
To determine efficient partially blind policies that handle the completion and
decoding delays of IDNC in such environment, we first extend the perfect
feedback formulation in [2], [3] to the lossy feedback environment, by
incorporating the uncertainties resulting from unheard feedback events in these
formulations. For the completion delay problem, we use this formulation to
identify the maximum likelihood state of the network in events of unheard
feedback, and employ it to design a partially blind graph update extension to
the multicast IDNC algorithm in [3]. For the decoding delay problem, we derive
an expression for the expected decoding delay increment for any arbitrary
transmission. This expression is then used to derive the optimal policy to
reduce the decoding delay in such lossy feedback environment. Results show that
our proposed solution both outperforms other approaches and achieves a
tolerable degradation even at relatively high feedback loss rates.
