High Stopping-distance \(LDPC\) Product Codes based on Hamming and Finite Geometry Codes

Abstract

High stopping-distance low-density parity-check \((LDPC)\) product codes with finite geometry \(LDPC\) and Hamming codes as the constituent codes are constructed. These codes have high stopping distance compared to some well-known LDPC codes. As examples, linear \((511, 180, 30)\), \((945, 407, 27)\), \((2263, 1170, 30)\), and \((4095, 2101, 54)\) LDPC codes are designed with stopping distances \(30\), \(27\), \(30\), and \(54\), respectively. Due to their good stopping redundancy, they can be considered as low-complexity codes with very good performance when iterative decoding algorithms are used.