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This paper studies feedback based instantly decodable network coding with the aim of minimizing decoding delay per transmission over wireless broadcast erasure channels with memory. We model such channels with a Gilbert-Elliott two-state Markov model with good and bad states. We first present a weighted sum generalized instantly decodable network coding (G-IDNC) scheme, where the aim is to service a subset of receivers with expected good channel state. We then propose an improved variation of the weighted sum G-IDNC that appropriately targets a broader set of receivers (while giving initial priority to receivers with expected good channel state) to reduce decoding delay over a wider range of erasure channels with memory. Simulation results show that our proposed improved weighted sum G-IDNC algorithm always considerably outperforms an earlier approach in the literature for erasure channels with memory, namely the weighted sum strict instantly decodable network coding (S-IDNC).