Generalized Belief Propagation for the Noiseless Capacity and Information Rates of Run-Length Limited Constraints

TL;DR

This paper investigates the effectiveness of generalized belief propagation in calculating the noiseless capacity and information rates of 2D and 3D run-length limited constraints, providing methods for region graph construction and analyzing convergence to Shannon capacity.

Contribution

It introduces a method for selecting basic regions and constructing region graphs for generalized belief propagation applied to multidimensional constraints.

Findings

Accurate capacity estimates for various constraints as channel size varies.

Mutual information rates computed as a function of SNR.

Discussion on convergence behavior towards Shannon capacity.

Abstract

The performance of the generalized belief propagation algorithm for computing the noiseless capacity and mutual information rates of finite-size two-dimensional and three-dimensional run-length limited constraints is investigated. For each constraint, a method is proposed to choose the basic regions and to construct the region graph. Simulation results for the capacity of different constraints as a function of the size of the channel and mutual information rates of different constraints as a function of signal-to-noise ratio are reported. Convergence to the Shannon capacity is also discussed.