AbstractWe derive graphical models for coded data transmission over channels introducing inter‐symbol interference. These models are factor graph descriptions of the transmitter section of the communication system, which serve at the same time as a framework to define the corresponding receiver. The graph structure governs the complexity and nature (e.g. non‐iterative, iterative) of the receiver algorithm. A particular graph yields several algorithms optimizing various cost functions depending on the choice of messages communicated along the edges of the graph. We study these different outcomes of message passing and how the corresponding receiver algorithms are related to existing ones. We also devise strategies to find suitable graphs for communication problems of interest. Copyright © 2004 AEI