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In this paper, we study optimum SNR threshold based partial decode-and-forward (PDF) schemes where relays may choose to forward the demodulated symbols in form of distributed space-time coding (DSTC) or to remain silent according to instantaneous link qualities of the source to relays. Considering the possible error of Maximum likelihood decoding at intermediate relays, we model a general noise in the received signal-noise ratio (SNR) expression at the destination. First, we analyze a centralized scheme, called Centralized Selecting, where the relaying decisions are based on all average SNRs of the source-relays and relays-destiantion. The SNR threshold vector are calculated in a central way. Then, a distributed scheme, Distributed Selecting, is proposed to let every relay individually make its decision based on two related average SNRs, i.e., source-ith relay and ith relay-destination. We show that both proposed selective PDF relaying schemes have better performances than traditional partial decode-and-forward scheme, and the centralized selecting is better than distributed selecting. However, distributed selecting approaches the centralized selecting closely with a far lower system cost.