Decoding network codes using the sum-product algorithm

While feasibility and obtaining a solution of a given network coding problem are well studied, the decoding procedure and complexity have not garnered much attention. We consider the decoding problem in a network wherein the sources generate multiple messages and the sink nodes demand some or all of the source messages. We consider both linear and non-linear network codes over a finite field and propose to use the sum-product (SP) algorithm over the Boolean semiring for decoding at the sink nodes in order to reduce the computational complexity. We use traceback to further lower the computational cost incurred by SP decoding. For sinks demanding all the messages, we define fast decodability of a network code and identify a sufficient condition for the same.