  In this paper, we show how to construct a factor graph from a network code.
This provides a systematic framework for decoding using message passing
algorithms. The proposed message passing decoder exploits knowledge of the
underlying communications network topology to simplify decoding. For uniquely
decodeable linear network codes on networks with error-free links, only the
message supports (rather than the message values themselves) are required to be
passed. This proposed simplified support message algorithm is an instance of
the sum-product algorithm. Our message-passing framework provides a basis for
the design of network codes and control of network topology with a view toward
quantifiable complexity reduction in the sink terminals.
