This work studies the performance of a cooperative network which consists of two channel-coded sources, multiple relays, and one destination. Due to spectral efficiency constraint, we assume only one time slot is dedicated for relaying. Conventional network coding based cooperation (NCC) selects the best relay which uses network coding to serve two sources simultaneously. The performance in terms of bit error rate (BER) of NCC, however, is not available in the literature. In this paper, we first derive the closed-form expression for the BER of NCC and analytically show that NCC always achieves diversity of order two regardless the number of available relays and the channel code. Secondly, motivated by a loss in diversity in NCC, we propose a novel relaying scheme based on partial relaying cooperation (PARC) in which two best relays are selected, each forwarding half of the codeword to help one source. Closed-form expression for BER and system diversity order of the proposed scheme are derived. Analytical results show that the diversity order of PARC is a function of the operating signal-to-noise ratio (SNR) and the minimum distance of the channel code. More importantly, full diversity order in PARC can be achieved for practically operating finite SNRs with the proper channel code. Finally, intensive simulations present a huge SNR gain of PARC over NCC and reference schemes without relay selection.