Three Randomized Construction Methods for LDPC Codes

This article introduces three randomized construction methods for LDPC codes: PEG, MacKay, and Gallager. These methods can be implemented using MATLAB through corresponding code development.

The PEG (Progressive Edge-Growth) method is a graph-based construction approach that generates LDPC codes through an iterative process. In MATLAB implementation, this typically involves creating Tanner graphs by progressively adding edges while maximizing the girth, using functions like peg_ldpc for matrix generation.

The MacKay method utilizes matrix operations for LDPC code construction, where sparse parity-check matrices are built using combinatorial mathematics. MATLAB implementation often employs sparse matrix functions and random permutation techniques to create irregular code structures with optimized performance.

The Gallager method is based on permutation matrix operations, constructing regular LDPC codes through systematic arrangements of submatrices. In MATLAB, this can be implemented using permutation matrices and block-wise concatenation functions to ensure the required code properties.

Implementing these methods in MATLAB provides deeper understanding of LDPC code construction processes and facilitates further research and analysis through customizable parameter adjustments and performance simulations.