  Network coding and cooperative communication have received considerable
attention from the research community recently in order to mitigate the adverse
effects of fading in wireless transmissions and at the same time to achieve
high throughput and better spectral efficiency. In this work, we design and
analyze deterministic and random network coding schemes for a cooperative
communication setup with multiple sources and destinations. We show that our
schemes outperform conventional cooperation in terms of the
diversity-multiplexing tradeoff (DMT). Specifically, it achieves the
full-diversity order at the expense of a slightly reduced multiplexing rate. We
establish the link between the parity-check matrix for a $(N+M,M,N+1)$
systematic MDS code and the network coding coefficients in a cooperative
communication system of $N$ source-destination pairs and $M$ relays. We present
two ways to generate the network coding matrix: using the Cauchy matrices and
the Vandermonde matrices, and establish that they both offer the maximum
diversity order.
