Codes on graphs: Models for elementary algebraic topology and statistical physics
Information Theory
2018-12-20 v2 Statistical Mechanics
Systems and Control
math.IT
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.
Cite
@article{arxiv.1707.06621,
title = {Codes on graphs: Models for elementary algebraic topology and statistical physics},
author = {G. David Forney},
journal= {arXiv preprint arXiv:1707.06621},
year = {2018}
}
Comments
28 pages, 36 figures, 2 tables. Final version