A New Family Of IRA-LDPC Codes Based On Residue Class

Irregular Repeat-Accumulate Low-density parity-check (IRA-LDPC) codes, put forward by Hui Jin in his PhD dissertation, is made up of a low-density generate-matrix(LDGM) and a repeat-accumulator and the complexity of encoding are linear. When the code length Nâ†'∞, IRA codes can achieve the Shannon limit.This paper , supported by National Natural Science Foundation of China"The Research of Key Technology in Noncoherent MIMO Communication System", stdudies the IRA-LDPC codes used in DVB-S2 standard and deduce their structural feature. DVB-S2 standard does not show how H~ d matrixs are structured, and the form of those H~ d matrixs are not suitable to analysis their performance. But the simulation results show that the performance of those IRA-LDPC codes are pretty good, the code can work correctly at 0.9dB with code length 64800 and code rate 1/2. Based on the structure of IRA-LDPC codes used in DVB-S2 standard, this paper proposes a construction method for IRA-LDPC codes by using residue class pairs.After studing the girths of those new codes, we find that the value of residue class pairs can control the size of girths. In order to make the encoder of IRA-LDPC codes simple and with the girth larger than 4, the first element of residue class pairs is generated by the generator of cyclic multiplicative group and the second element of residue class pairs is generated under the principle that makes the girth in H~ d larger than 4. Using this construction method, a few parameters are needed to determine a H matrix, far less than that used in present standards. Simulation result shows that the performance of IRA-LDPC codes constructed by this method is close or even better than that of IEEE802.16e standard and DVB-S2 standard. After studing the encoding method, an encoder structure is proposed in this paper.