Study And Design Of Low-Density Parity-Check Codes

Low-Density Parity-Check Codes(LDPC) is currently pop topic in communication field.It is one of the strongest candidates in the 4^th generation communication system since it is one of the best channel codes.There are two most significant reasons for its excellent performance.One is its good distance spectrum,the other is that LDPC codes are decoded by iterative probability decoding algorithm.What's more,the complexity of the decoding algorithm is linearity with the code's length because of the sparse check matrix.And LDPC codes are propitious to be implemented by hardware because the decoding algorithm is parallel in essence and can reduce the decoding delay time.It can make certain that whether the codes are decoded in the iterative decoding process and whether the process can be finished before reaching the maximum number of the iterative decoding.Bit error rate(BER) of LDPC codes can be decreased arbitrarily along with the increase of signal to noise rate(SNR).And the errors can be detected;the error floor phenomenon will not be happened.Of course there is a drawback about LDPC codes,which is the high complexity of encoding.Since the complexity of encoding is not linearity with the code's length,it is unacceptable when the length reaches very large.But now,many scholars devote themselves into the research of LDPC encoding,and many feasible schemes are brought forward.This paper gives a systematic investigation of LDPC codes.Firstly,the structure of LDPC codes and Tanner graph are introduced.Then,the algorithms about encoding are introduced,including traditional encoding algorithm and efficient algorithm.The encoding can be finished in linearity by efficient algorithm.After that,several decoding algorithms,such as probability domain BP algorithm,Log-Likelihood Ration BP algorithm,minimum sum algorithm,bit flipping and weighted bit flipping algorithm, are expounded.Comparing the simulation results,the performance of the algorithms varies a lot.Accordingly,the complexity of them varies a lot too.Then,some factors affecting the performance of LDPC codes are presented.They can be some hints by some degrees when constructing LDPC codes.Finally,the construction of LDPC codes is studied.There are mainly two types of construction scheme.Random method is from the point of performance,while structure method is from the point of encoding and the structure of LDPC codes.Several typical methods are summarized in this paper and the comparison of performance between them is brought forward in the end.