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Traditional approaches to reliably transmit information over an error-prone network employ either forward error correction (FEC) or retransmission techniques. In this paper, we propose some network coding schemes to reduce the number of broadcast transmissions from one sender to multiple receivers. The main idea is to allow the sender to combine and retransmit the lost packets in a certain way so that with one transmission, multiple receivers are able to recover their own lost packets. For comparison, we derive a few theoretical results on the bandwidth efficiency of the proposed network coding and traditional automatic repeat-request (ARQ) schemes. Both simulations and theoretical analysis confirm the advantages of the proposed network coding schemes over the ARQ ones.