A random construction of LDPC codes using a sub-optimal search algorithm

In this paper, a method for constructing low-density parity-check (LDPC) codes of good performance in terms of bit error rate (BER) using a computer search algorithm is presented. First, LDPC codes and encoding along with its Tanner graph representation is described. Then, a detailed description of the proposed construction algorithm is given. A modified shortest-path (MSP) algorithm of lower complexity is applied to obtain a code graph of the desired structure. The proposed algorithm works directly on the parity-check matrix of the LDPC code. The parity-check matrix of the code is constructed column by column subject to the bit-degree and girth constraints. Using the proposed algorithm, both regular and irregular LDPC codes have been constructed. Furthermore, not only have the girth been improved but also the rate of LDPC codes. Finally, by simulation results the constructed codes were shown to perform well over an additive white Gaussian noise (AWGN) channel.