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Most of existing distributed coding schemes assume a perfect detection at relays. In this paper, we propose a distributed space time trellis coding (DSTTC) scheme by taking into account the imperfect detections at relays. We propose a detection metric to address the effect of decoding errors. In particular, we consider an equivalent one-hop link model for the source-relay-destination path and use it to modify the maximum likelihood detection metric by taking into account the equivalent signal to noise ratio (SNR) of the link model. The upper bound of the pairwise error probability (PEP) is then derived for both slow and quasi-slow Rayleigh fading channels, and the design criteria for the distributed space-time trellis codes are formulated accordingly. Based on the proposed design criteria, the optimal QPSK 4-state, 8-state, 16 -state and 32- state DSTTCs are constructed. The results are validated by computer simulations.