Codes on Graphs: Models for Elementary Algebraic Topology and Statistical Physics

This paper is mainly a semi-tutorial introduction to elementary algebraic topology and its applications to Ising-type models of statistical physics, using graphical models of linear and group codes. It contains new material on systematic (n, k) group codes and their information sets; normal realiz...

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Veröffentlicht in:	IEEE transactions on information theory 2018-12, Vol.64 (12), p.7465-7487
1. Verfasser:	Forney, G. David
Format:	Artikel
Sprache:	eng
Schlagworte:	Aerospace electronics Algebra Algebraic topology Computational modeling Controllability Graphical models group codes Homology Ising model Ising models Observability (systems) Physics Statistical physics Systematics Topology
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Beschreibung
Zusammenfassung:	This paper is mainly a semi-tutorial introduction to elementary algebraic topology and its applications to Ising-type models of statistical physics, using graphical models of linear and group codes. It contains new material on systematic (n, k) group codes and their information sets; normal realizations of homology and cohomology spaces; dual and hybrid models; and connections with system-theoretic concepts, such as observability, controllability, and input/output realizations.
ISSN:	0018-9448 1557-9654
DOI:	10.1109/TIT.2018.2866577