Research On The Construction Methods Of QC-LDPC Codes Based On Integer Sequence

In the structured Low-Density Parity-Check(LDPC)codes,Quasi-Cyclic Low-Density Parity-Check(QC-LDPC)codes are promising because they have easier hardware implementation due to the special quasi-cyclic properties of their check matrices.Among construction methods of QC-LDPC codes,not only do the construction methods of QC-LDPC codes based on integer sequences have low encoding complexity due to the simple mathematical basis,but also the codes constructed by these methods have excellent error correction performance,so the research of QC-LDPC codes’ construction methods based on integer sequences has become a hot topic in recent years.The construction methods of QC-LDPC codes based on Hoey sequence(HS)and Fibonacci sequence(FS)are researched in this thesis.The error correction performance,the encoding complexity and the code rate flexibility of QC-LDPC codes are mainly discussed.And the error correction performance is discussed by the girth and the minimum distance of check matrices.The main research work is as follows:1.To solve the poor error correction performance caused by the short girth of QC-LDPC codes,two construction methods of QC-LDPC codes with girth eight and low column weight based on HS and FS respectively are proposed.Two methods are both the structural construction methods whose column weights are three,so these methods can be used in some special systems that require the column weight to be three,such as China mobile multimedia broadcasting system.Among the construction methods that use generate matrices to encode,the two methods both have the low encoding complexity due to the low column weight and the similar error correction performance.It is theoretically proved that the girth of the check matrices constructed by the two methods is at least eight.The QC-LDPC(3249,2168)code that has the code rate of 0.67 and can be used in deep space communications,satellite digital video broadcasting and other fields is constructed based on HS,and the QC-LDPC(900,452)code that has the code rate of 0.50 and can be used in deep space communications,satellite digital video broadcasting,wireless communication,China mobile multimedia broadcasting and other fields is constructed based on FS.The simulation results show that at the bit error rate of 10-6,the coding gain of the HS-QC-LDPC(3249,2168)code is respectively about O.lOdB,0.14dB and 0.18dB more than those of the DS-QC-LDPC(3249,2168)code constructed by Dayan sequence(DS),the Mackay-LDPC(3249,2168)code constructed by computer searching and the IEEE 802.16e-LDPC(3264,2176)code constructed by IEEE 802.16e standard method,the coding gain of the FS-QC-LDPC(900,452)code is respectively about 0.13dB,0.25dB and 0.27dB more than those of the APS-QC-LDPC(900,452)code constructed by arithmetic progression sequence(APS),the IEEE 802.16e-LDPC(912,456)code and the PEG-LDPC(900,450)code constructed by progressive edge growth(PEG)construction method,and the coding gain of the FS-QC-LDPC(900,452)code is only about 0.02dB less than that of the HS-QC-LDPC(900,452)code.2.To solve the poor error correction performance caused by the short minimum distance of QC-LDPC codes,a construction method of irregular Type-II QC-LDPC codes based on HS is proposed.It is theoretically proved that the girth of the check matrix constructed by this method is at least six,and the QC-LDPC(5226,3484)code that has the same code rate of 0.67 is constructed.The simulation results show that at the bit error rate of 10-6,the coding gain of the HS-Type-II QC-LDPC(5226,3484)code is respectively about 0.09dB,0.21dB,0.32dB and 0.35dB more than those of the HS-QC-LDPC(5229,3488)code,the CDS-Type-II QC-LDPC(5226,3486)code constructed by cyclic difference set(CDS),the SS-Type-II QC-LDPC(5226,3486)code constructed by Sidon sequence(SS)and IEEE 802.16e-LDPC(5232,3488)code.In addition,the encoding complexity of the two construction methods based on HS is analyzed,and it can be known that the encoding complexity of the two construction methods based on HS is lower than those of three classic construction methods of LDPC codes.Among the construction methods that use generate matrices to encode,the encoding complexity of the construction method of QC-LDPC codes with low column weight is very low and lower than that of the construction method of Type-II QC-LDPC codes.3.To solve the high encoding complexity and the stiff choice of code rate of QC-LDPC codes,a construction method of irregular QC-LDPC codes with fast encoding based on FS is proposed and the codes constructed by this method have excellent error correction performance.It is theoretically proved that the girth of the check matrix constructed by this method is at least six,and the encoding algorithm that use the check matrix to encode directly is given.The encoding complexity is also analyzed in detail,and it can be known that the operand is only about O(n)and the number of storage parameters in encoding is small.Then the QC-LDPC(1224,612)code that has the same code rate of 0.50 is constructed.The simulation results show that at the bit error rate of 10-6,the coding gain of the FS-irregular QC-LDPC(1224,612)code is respectively about 0.13dB,013dB,0.13dB and 0.34dB more than those of the FS-QC-LDPC(1224,614)code,the GCD-QC-LDPC(1430,715)code constructed by greatest common divisor(GCD),the IEEE 802.16e-LDPC(1224,612)code and the irregular QC-LDPC(1224,612)code constructed by masking method.Finally,the choice of code rate is analyzed and it can be known that the choice of code rate in this construction method is more flexible than those in the construction methods of QC-LDPC codes with fixed low column weight or rows of check matrices.