Research On The Construction Of Quasi-cyclic LDPC Codes With Larger Girth

Low-density parity-check(LDPC)codes with low bit error rate,whose decoding performance can approach the shannon limit.Quasi-Cyclic Low-Density Parity-Check Codes is kinds of the LDPC codes with the character of cyclic shift,easy to coding and save storage space.The girth is one of the important factors that affect the performance of LDPC codes,so problem of how to construct the good performance codes will be transformed into the other problem of how to construct the large girth codes.Complexity is another important factor to be considered in coding.The performance of LDPC codes with random constructed is excellent,but the computational complexity is large,so it adopts the coding scheme of structured constrcuted.Therefore,it's a worthy issue to design the structured constrcuted LDPC codes with large girth and low complexity.The main works accomplished in this thesis are as follows:This thesis introduces the research background and related theories of low-density parity-check(LDPC)codes.At first,and then several common construction methods and encoding/decoding algorithms are analyzed in detail based on the basic theory of LDPC codes.At last,according to main factors affecting the performance of LDPC codes,two novel approaches to construct good performance QC-LDPC codes with larger girth and low complexity are proposed as following:1.In order to ensure the reliability of information transmission and communication quality requirements,an method to construct QC-LDPC codes with larger girth based on Binary polynomial function is proposed in this thesis.The elements of the index matrix are constructed using the coefficients in the polynomial.The process of construction is simple and has the characteristics of large girth.Simulation results indicate that our proposed codes reveal good error correction capability in AWGN(Additive White Gaussian Noise)channel,which can ensure the the reliability of information transmission and communication quality requirements and adapt to the communication those need quality requirements,long-distance transmission.2.In order to reduce the encoding complexity on the base of ensuring error correction performance,an approach to construct QC-LDPC codes with larger girth and low complexity characteristic is proposed in this thesis.The Chinese remainder theorem is adopted,using dual diagonal structure for fast coding,together with the Arithmetic Progression(AP)algorithm to construct the parity check matrix of QC-LDPC codes.Theory analysis and simulation results show that our proposed codes could use the parity check matrix to encode directly as the existence of dual diagonal structure,and the girth is eight,so it's suitable for practical communication system applications and easy to implement in hardware.