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 |
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| container_title | IEEE transactions on information theory |
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| creator | Forney, G. David |
| description | 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. |
| doi_str_mv | 10.1109/TIT.2018.2866577 |
| format | Article |
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| ispartof | IEEE transactions on information theory, 2018-12, Vol.64 (12), p.7465-7487 |
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| language | eng |
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| source | IEEE Electronic Library (IEL) |
| subjects | Aerospace electronics Algebra Algebraic topology Computational modeling Controllability Graphical models group codes Homology Ising model Ising models Observability (systems) Physics Statistical physics Systematics Topology |
| title | Codes on Graphs: Models for Elementary Algebraic Topology and Statistical Physics |
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