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arXiv · 1707.06621

Codes on graphs: Models for elementary algebraic topology and statistical physics

G. David Forney Jr
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Abstract

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.

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G. David Forney Jr. 2017-07-20. Codes on graphs: Models for elementary algebraic topology and statistical physics. https://doi.org/10.1109/tit.2018.2866577

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