Research On The Low Error Floor QC-LDPC Codes Based On The Hybrid Construction Methods

The error floor problem of Quasi-Cycle Low-Density Parity-Check?QC-LDPC?codes has always affected its error correction performance in high signal noise ratio areas.As people's requirements for communication quality become higer and higer,eliminating the error floor of QC-LDPC codes has become hot and difficult research in the field of encoding today.In this paper,the method of eliminating error floor is deeply studied through the codes construction methods.The main research work is as follows:1.In order to solve the problem of high encoding complexity when random constructing the low error floor codes with long lengths,the hybrid construction method based on random construction and structural construction is proposed.The Approximate Cycle Extrinsic message degree?ACE?algorithm is added to the method to improve the connectivity of cycle,in order to restrain the appearance of the small elementary trapping sets,so that achieve the effect of eliminating error floor.The basic matrix is composed of the Progressive Edge Growth?PEG?construction method and the ACE algorithm in this method.Then the Partition and Shift?PS?method is used to construct the cyclic shift matrix,and uses the cyclic shift matrix to extend the basic matrix in order to construct the check matrix with the girth of six,and finally construct the PEG-ACE-PS?PAP?-QC-LDPC?3024,1512?code with the code rate of 0.5.The simulation results show that with the increase of signal to noise ratio,the difference between the PAP-QC-LDPC?3024,1512?code and the comparison code will be larger,and there is no obvious the error floor phenomenon.In the communication system with strict requirements on the bit error rate?BER?,the PAP-QC-LDPC?3024,1512?code will be more applicable and more advantageous.2.In order to solve the problem that the low error floor codes constructed by the structural construction method is not flexible to select the codes rate,and further reduce the encoding complexity of the random construction method,and the QC-LDPC codes construction method of the low error floor based on the ACE algorithm and the Zig-Zag method is proposed.The PEG construction method and the ACE algorithm are used to construct the basic matrix,and using the Zig-Zag method to construct the cyclic shift matrix,the main advantage of the Zig-Zag method is that the cyclic shift matrix can be quickly construct Zig-Zag structure by simple algebraic expression.The cyclic shift matrix,and without the need of computer search,completely eliminates four cycle in the check matrix,reduces the hardware memory requirements of the communication system.Using the cyclic shift matrix to extend the basic matrix in order to construct the check matrix with the girth of six,and finally construct the PEG-ACE-Zig-Zag?PAZZ?-QC-LDPC?3024,1512?code with the code rate of 0.5,and construct the PAZZ-QC-LDPC?3024,2016?code with the code rate of 0.67 by adjusting the size of the basic matrix and the cyclic shift matrix.The simulation results show that at the BER of 10^-6,the coding gain of the PAZZ-QC-LDPC?3024,1512?code is respectively about 0.14dB,0.07dB and 0.06dB more than those of the PEG-LDPC?3024,1512?code,the PEG-Zig-Zag?PZZ?-QC-LDPC?3024,1512?code and the PEG-ACE?PA?-LDPC?3024,1512?code;the coding gain of the PAZZ-QC-LDPC?3024,2016?code is respectively about 0.20dB,0.15dB,and 0.10dB more than those of the PEG-LDPC?3024,2016?code,the PZZ-QC-LDPC?3024,2016?code and the PA-LDPC?3024,2016?code.As the increase of signal to noise ratio,the difference between the PAZZ-QC-LDPC code and the comparison code will be larger,the coding gain will increase more,and there will be no obvious the error floor phenomenon.3.In order to fundamentally eliminate the small elementary trapping sets and construct codes with excellent error correction performance,an improved Elimination Elementary Trapping Sets?EETS?algorithm is proposed to eliminate the small elementary trapping sets in the construction process,and the QC-LDPC codes construction method of the low error floor based on the improved EETS algorithm and the Zig-Zag method is proposed.The PEG construction method and the improved EETS algorithm are used to construct the basic matrix.Then the Zig-Zag method is used to construct the cyclic shift matrix,and uses the cyclic shift matrix extend the basic matrix in order to construct the check matrix with the girth of eight,and finally construct the PEG-EETS-Zig-Zag?PEZZ?-QC-LDPC?3024,1512?code with the code rate of 0.5.The simulation results show that the PEZZ-QC-LDPC?3024,1512?code compares with the PZZ-QC-LDPC?3024,1512?code and the PEG-LDPC?3024,1512?code,can respectively improve the coding gain of 0.10dB and 0.18dB at the BER of 10^-6;the coding gain of the PEZZ-QC-LDPC?3024,1512?code is respectively about 0.13dB more than that of the PEG-EETS?PE?-LDPC?3024,1512?code at BER=10^-7.With the increase of signal to noise ratio,the difference between the PEZZ-QC-LDPC?3024,1512?code and the comparison code will be larger,and there is no obvious the error floor phenomenon.