The extraction and complexity limits of graphical models for linear codes. (English summary) IEEE Trans. Inform. Theory 54 (2008), no. 9, 3884–3906. Summary: “Two broad classes of graphical modeling problems for codes can be identified in the literature: constructive and extractive. The former class of problems concerns the construction of a graphical model in order to define a new code. The latter class of problems concerns the extraction of a graphical model for a (fixed) given code. The design of a new low-density parity-check code for some given criteria (e.g., target block length and code rate) is an example of a constructive problem. The determination of a graphical model for a classical linear block code that implies a decoding algorithm with desired performance and complexity characteristics is an example of an extractive problem. This work focuses on extractive graphical model problems and aims to lay out some of the foundations of the theory of such problems for linear codes. The primary focus of this work is a study of the space of all graphical models for a (fixed) given code. The tradeoff between cyclic topology and complexity in this space is characterized via the introduction of a new bound: the forest-inducing cut-set bound (FI-CSB). The proposed bound provides a mor
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