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In this paper, we consider the problem of coding for the half-duplex nonorthogonal amplify-and-forward (NAF) cooperative channel where the transmitter to relay and the interrelay links are highly reliable. We derive bounds on the diversity order of the NAF protocol that are achieved by a distributed space-time bit-interleaved coded modulation (D-ST-BICM) scheme under iterative APP detection and decoding. These bounds lead to the design of space-time precoders that ensure maximum diversity order and high coding gains. The word error rate performance of D-ST-BICM are also compared to outage probability limits.