An Application of Renormalization Group Techniques to Classical Information Theory

Abstract

We apply Renormalization Group (RG) techniques to Classical Information Theory, in the limit of large codeword size $n$. In particular, we apply RG techniques to (1) noiseless coding (i.e., a coding used for compression) and (2) noisy coding (i.e., a coding used for channel transmission). Shannon's "first" and "second" theorems refer to (1) and (2), respectively. Our RG technique uses composition class (CC) ideas, so we call our technique Composition Class Renormalization Group (CCRG). Often, CC's are called "types" instead of CC's, and their theory is referred to as the "Method of Types". For (1) and (2), we find that the probability of error can be expressed as an Error Function whose argument contains variables that obey renormalization group equations. We describe a computer program called WimpyRG-C1.0 that implements the ideas of this paper. C++ source code for WimpyRG-C1.0 is publicly available.