Research Of Doubly-Generalized Low-Density Parity-Check(D-GLDPC) Codes’ Performance

Doubly-generalized low-density parity-check(D-GLDPC) code is an extension of the concept of LDPC code, where the check nodes and variable nodes are both allowed to be generic linear block codes instead of single parity-check(SPC) codes and repetition codes,respectively. If only the check nodes are allowed to be the generic linear block codes, then the code is called a generalized LDPC(GLDPC) codes. Compared with LDPC and GLDPC codes,D-GLDPC codes can offer better waterfall performance and lower error floor. Furthermore,the high code-rate of the component codes of D-GLDPC codes can compensate the overall rate loss of GLDPC codes. This research aims to design a class of high code-rate D-GLDPC codes that have a low decoding threshold and a better error correction performance.The minimum distance of D-GLDPC codes is increased exponentially with the girth of the code’s corresponding adjacency matrix. Moreover, the base of the exponent increases with the growth of the component codes’ minimum distance. In this paper, a class of D-GLDPC codes where the check component codes are 3-Dimensional(3-D) single-parity-check product-codes(SPC-PCs), whose minimum distance of eight, are proposed. Further, SPC codes are used at the super-variable nodes(SVNs) of the D-GLDPC code. The high code-rate of SPC codes can improve the overall code rate of D-GLDPC codes. The main research includes:First, the formular of calculating information function for the dual code of 3-D SPC-PC codes are put forward. Information function is an important parameter of extrinsic information transfer(EXIT) function of SCN decoder. From the viewpoint of definition, we should calculate the ranks of all possible sub-matrices and add them up, which is very time-consuming and requires computer has enough memory space. In order to solve this problem, we propose an efficient formula, which greatly simplifies the calculation steps and accelerates the computation speed.Second, the EXIT function of 3-D SPC-PCs using at the SCNs of D- GLDPC codes is concluded. According to the rule of constructing 3-D SPC-PCs, we can derive its parity-check matrix, namely the generator matrix of the dual code of 3-D SPC-PCs. The information function of the dual code of 3-D SPC-PCs is obtained by calculating above formular, then the EXIT function of 3-D SPC-PCs using at the SCNs of D- GLDPC codes can be derived by the duality proportity.Third, the decoding threshold performance of proposed D-GLDPC codes over Gussian channel is analyzed by using the EXIT chart.The simulation results show that the proposed D-GLDPC codes can offer better decoding threshold and higer code-rate than D-GLDPC codes with 2-Dimensional SPC-PCs at SCNs.