  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.
