Improving the Performance of Protograph LDPC Codes by Using Different Transmission Energies

Irregular low-density parity-check (LDPC) codes constructed from small protographs are one of the most powerful LDPC codes. In this paper, we show that the performance of LDPC codes based on small protographs can be further improved by using different transmission energies for every variable node of the protograph. Thus, a protograph is now described by a set of variable nodes, a set of check nodes, edges connecting variable nodes and check nodes, and the transmission energy used for every variable node, which is called the energy distribution. We optimize the energy distribution of protographs by choosing the energy distribution with the highest threshold calculated with a generalization of the discretized density evolution. Furthermore, we show by simulations that the performance of long LDPC codes based on protographs can be improved as expected from the thresholds.