Representations of codes by factor graphs provide a general framework for iterative decoding and has attracted much interest recently. A natural problem to investigate is the efficient representation of a given code, or linear system, in a given graph. This problem has been studied extensively if the graph is a simple path (trellis representations of codes), and, more recently, if the underlying graph is a cycle (tail-biting trellises). For general graphs the subject is just emerging and has led to the notions of trellis formations and Forney's Generalized State Realizations (GSRs), where both can be seen as an attempt to normalize the overly rich framework of factor graphs and as a generalization of conventional trellises. We review connections between conventional trellises, GSRs, trellis formations, and network information theory.

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