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In user cooperative communications, time offsets among the relay nodes may distort the structure of a distributed space-time code, and therefore impair the diversity gain. In this paper, we first recall some of the existing schemes for dealing with this problem and then introduce a distributed linear space- time convolutional coding scheme for asynchronous scenario. We present a systematic construction of distributed linear space- time convolutional codes that can achieve the full diversity under any delay profile. Furthermore, we show that with the MMSE decision feedback equalizer (MMSE-DFE) receiver, our proposed codes also achieve the asynchronous full diversity.