The statistical mechanics of turbo codes

TL;DR

This paper models turbo codes using statistical mechanics, identifying a threshold signal-to-noise ratio above which error probability vanishes for long sequences, with computed thresholds for specific codes and comparison to simulations.

Contribution

It introduces a spin Hamiltonian framework for turbo codes and calculates thresholds, revealing code-dependent performance limits.

Findings

Threshold ratio Theta exists for turbo codes.

Error probability vanishes above the threshold in the thermodynamic limit.

Threshold values depend on the specific turbo code analyzed.

Abstract

The "turbo codes", recently proposed by Berrou et. al. are written as a disordered spin Hamiltonian. It is shown that there is a threshold Theta such that for signal to noise ratios v^2 / w^2 > Theta, the error probability per bit vanishes in the thermodynamic limit, i.e. the limit of infinitly long sequences. The value of the threshold has been computed for two particular turbo codes. It is found that it depends on the code. These results are compared with numerical simulations.