Compute-and-forward: A novel strategy for cooperative networks

In recent work, we have shown that in a Gaussian network, nodes can often recover linear combinations of transmitted codewords much more efficiently than the codewords themselves. These nodes, after decoding their linear equations, simply send them towards the destination, which given enough equations, can recover the desired messages. This compute-and-forward strategy relies on a lattice-based coding framework. In this note, we show that by employing appropriately nested lattice codes, nodes can reliably recover linear combinations of the messages symbols themselves. This considerably simplifies the description of our scheme. We also consider superposition and successive cancellation within the compute-and-forward framework.