Low-Density-Parity-Check-Codes is currently one of the pop researches in communication field. It is the powerful competition in the 4th generation of mobile communication system. The decoding performance of LDPC is excellent and can be near the Shannon limit by iterative probability decoding algorithm. It has low complexity, the decoding algorithm is essentially parallel, so it is suitable to realize on hardware in parallel and reduce the decoding delay time. It can make certain that if the codes are decoded in the iterative decoding process and if the process can be finished in order to reduce iterative times, at the same time the decoding error can be detected. Bit error rate(BER) after decoding can be decreased arbitrarily along with the increase of Signal-to-Noise rate(SNR), and the error floor phenomenon can not occur. The complexity of encoding is high. Because the encoding process begins after receiving all needed signal bits, it brings certain delay time while the length of the codes is very long.
This paper gives a systematic investigation of LDPC codes. First, the definition of LDPC codes and the encoding methods are introduced. Then some parity check matrix construction methods of LDPC codes are illustrated; Finally, Gallager construction LDPC codes are simulated on MATLAB. The simulation results of BER performance of different length and rate for additive white Gaussian noise channels are presented.
Keywords: LDPC codes, encode, Gallager construction