Decoding network codes by message passing

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.