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Cooperative communication is an important technology in next generation wireless networks. Aside from conventional amplify-and-forward (AF) and decode-and-forward (DF) protocols, the partial decode-and-forward (PDF) protocol is an alternative relaying scheme that is especially promising for scenarios in which the relay node cannot reliably decode the complete source message. However, there are several important issues to be addressed regarding the application of PDF protocols. In this paper, we propose a PDF protocol and MIMO precoder designs at the source and relay nodes. The precoder designs are adapted based on statistical channel state information for correlated MIMO channels, and matched to practical minimum mean-square-error successive interference cancelation (MMSE-SIC) receivers at the relay and destination nodes. We show that under similar settings, the proposed MIMO precoder design with PDF protocol and MMSE-SIC receivers achieves substantial performance enhancement compared with conventional baselines.