Codes on graphs: Models for elementary algebraic topology and statistical physics
arXiv:1707.06621 · doi:10.1109/TIT.2018.2866577
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.
28 pages, 36 figures, 2 tables. Final version