  Network coding is a new and promising paradigm for modern communication
networks by allowing intermediate nodes to mix messages received from multiple
sources. Compute-and-forward strategy is one category of network coding in
which a relay will decode and forward a linear combination of source messages
according to the observed channel coefficients, based on the algebraic
structure of lattice codes. The destination will recover all transmitted
messages if enough linear equations are received. In this work, we design in a
system level, the compute-and-forward network coding coefficients by
Fincke-Pohst based candidate set searching algorithm and network coding system
matrix constructing algorithm, such that by those proposed algorithms, the
transmission rate of the multi-source multi-relay system is maximized.
Numerical results demonstrate the effectiveness of our proposed algorithms.
