Design LDPC Codes with Good Characteristic Parity Check Matrix

Abstract

Considered essential for their favorable characteristics, Low-Density Parity-Check codes (LDPC codes) are widely used in various applications such as fourth and fifth-generation mobile communication systems, wireless internet connections, digital radio, and digital TV via satellite or cable. This widespread usage has prompted numerous research efforts dedicated to addressing LDPC code-related issues.

 In this paper, we introduce an effective algorithm to design parity check matrices for LDPC codes. This algorithm balances between the code’s

minimum distance and the sparsity of its matrix. Moreover, the generator matrix is produced directly from the parity check matrix, making encoding straightforward. Hence, there is no need for solving equations. Furthermore, these matrices are full rank