Error-correcting codes and phase transitions

Details Error-correcting codes and phase transitions Error-correcting codes and phase transitions

2009-10-27

arxiv.org/abs/0910.5135v1

Computer Science

Information Theory

amstex 57 pages, 3 eps figures

Scientific paper

The theory of error-correcting codes is concerned with constructing codes that optimize simultaneously transmission rate and relative minimum distance. These conflicting requirements determine an asymptotic bound, which is a continuous curve in the space of parameters. The main goal of this paper is to relate the asymptotic bound to phase diagrams of quantum statistical mechanical systems. We first identify the code parameters with Hausdorff and von Neumann dimensions, by considering fractals consisting of infinite sequences of code words. We then construct operator algebras associated to individual codes. These are Toeplitz algebras with a time evolution for which the KMS state at critical temperature gives the Hausdorff measure on the corresponding fractal. We extend this construction to algebras associated to limit points of codes, with non-uniform multi-fractal measures, and to tensor products over varying parameters.

Affiliated with

Also associated with

No associations

Rating

Error-correcting codes and phase transitions does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Error-correcting codes and phase transitions, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Error-correcting codes and phase transitions will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-483240