Generic FG-SPA Update Rules Design of Linear Canonical Message Representation

This paper focuses an implementing issue of the sum-product algorithm on factor graphs (FGSPA) in a general system. The overall goal is to propose a message representation and corresponding update rules for both discretely and continuously valued variables with an acceptable exactness-complexity trade-off. We propose the update rules for a generic class of linear message representations with orthogonal canonical kernels. The proposed update rule design is combined with an already known message parameterization based on the KarhunenLoeve Transform (KLT) of the message. This combination of the proposed generic update rules with the KLT-message representation forms a generic implementation framework of the FG-SPA applicable whenever the KLT is defined. This framework preserves the properties of the KLTmessage representation that is the best linear approximation in the MSE sense. A particular example on a joint detection and phase estimation is shown to verify the framework and to compare the proposed method with a conventional solution.