Factor graphs: constructions, classification, and bounds

The representation of codes by factor graphs provides a general framework for iterative decoding, and has become a subject of much research. We address the following problem: given a factor graph G and a code C how can one construct the set of local behaviors for G so that G represents C in the most efficient manner? In this context, we introduce the notion of trellis formations, and obtain a classification of factor graphs into several types, based on this notion. We then describe a general construction of local behaviors for trellis formations, which generalizes the product construction for conventional trellises. In both cases, the goal of the construction is to obtain state-space sizes that are as small as possible. We also investigate bounds on the size of trellis formations and the size of local behaviors in factor graphs.