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While the capacity, feasibility and methods to obtain codes for networkcoding problems are well studied, the decoding procedure and complexity havenot garnered much attention. In this work, we pose the decoding problem at asink node in a network as a marginalize a product function (MPF) problem over aBoolean semiring and use the sum-product (SP) algorithm on a suitablyconstructed factor graph to perform iterative decoding. We use\textit{traceback} to reduce the number of operations required for SP decodingat sink node with general demands and obtain the number of operations requiredfor decoding using SP algorithm with and without traceback. For sinks demandingall messages, we define \textit{fast decodability} of a network code andidentify a sufficient condition for the same. Next, we consider the in-networkfunction computation problem wherein the sink nodes do not demand the sourcemessages, but are only interested in computing a function of the messages. Wepresent an MPF formulation for function computation at the sink nodes in thissetting and use the SP algorithm to obtain the value of the demanded function.The proposed method can be used for both linear and nonlinear as well as scalarand vector codes for both decoding of messages in a network coding problem andcomputing linear and nonlinear functions in an in-network function computationproblem.

Reduced Complexity Sum-Product Algorithm for Decoding Network Codes and In-Network Function Computation