In order to meet the requirements of the high bit-rate and the lower bit error-rate of the errorcorrection code in optical communication systems,based on the balanced incomplete block design(BIBD) and the circulant decomposition in this paper,a novel construction method of quasi-cyclic low-density parity-check(QC-LDPC)codes with the advantage of the simple implementation is proposed.A regular BIBDdes-QC-LDPC(6736,6316)code suitable for optical communication systems is constructed by applying the proposed method.The simulation results show that at the bit error rate(BER)of 10-6 and the same code rate of 93.7%,the net coding gain(NCG)of the constructed BIBDdes-QC-LDPC(6736,6316)code is 2.2dB more than that of the classic RS(255,239)code which has been widely used in optical communication systems,and 0.2dB more than that of the BIBD-QC-LDPC(6736,6315)code with the same code length and the same code-rate constructed only by the BIBD method and that of the irregular QC-LDPC(3843,3603)code with the same code-rate based on Galois field multiplicative group.Therefore,the novel BIBDdes-QC-LDPC(6736,6316)code has superior error-correction performance and is more suitable for the high-speed long-haul optical communication systems.And the novel construction method still has the advantage of the BIBD method which can flexibly adjust the code length and code rate.
In order to meet the requirements of the high bit-rate and the lower bit error-rate of the errorcorrection code in optical communication systems,based on the balanced incomplete block design(BIBD) and the circulant decomposition in this paper,a novel construction method of quasi-cyclic low-density parity-check(QC-LDPC)codes with the advantage of the simple implementation is proposed.A regular BIBDdes-QC-LDPC(6736,6316)code suitable for optical communication systems is constructed by applying the proposed method.The simulation results show that at the bit error rate(BER)of 10-6 and the same code rate of 93.7%,the net coding gain(NCG)of the constructed BIBDdes-QC-LDPC(6736,6316)code is 2.2dB more than that of the classic RS(255,239)code which has been widely used in optical communication systems,and 0.2dB more than that of the BIBD-QC-LDPC(6736,6315)code with the same code length and the same code-rate constructed only by the BIBD method and that of the irregular QC-LDPC(3843,3603)code with the same code-rate based on Galois field multiplicative group.Therefore,the novel BIBDdes-QC-LDPC(6736,6316)code has superior error-correction performance and is more suitable for the high-speed long-haul optical communication systems.And the novel construction method still has the advantage of the BIBD method which can flexibly adjust the code length and code rate.
Based on the Balanced Incomplete Block Design(BIBD),a novel construction method of Quasi-Cyclic Low-Density Parity-Check(QC-LDPC) codes is further analyzed and researched.And the three QC-LDPC codes with the same code-rate and different code-length are constructed by applying the proposed method.The simulation analysis shows that under the condition of the same code-rate,the QC-LDPC code with the longer code-length has better error-correction performance.Simultaneously,at the condition of the bit error rate(BER) of 10-6 and the same code rate of 93.7%,the net coding gain(NCG) of the constructed BIBD-QC-LDPC(5392,5056) code is respectively 2.13 dB and 1.41 dB higher than that of the classic RS(255,239) code widely used in optical communication systems and that of the LDPC(32640,30592) code in ITU-T G.975.1.Therefore,the BIBD-QC-LDPC(5392,5056) code has much superior error-correction performance and is better suitable for high-speed long-haul optical communication systems.
Based on finite field(GF(q)) additive group,a novel construction method with the advantages of simple construction and easy implementation of quasi-cyclic low-density parity-check(QC-LDPC) codes for optical communication systems is proposed in order to meet the increasing requirement on the transmission characteristics.The novel construction method can flexibly adjust the code-length and code-rate,and furthermore,the complexity of the encoding and decoding in lower.A regular QC-LDPC(4599,4307) code to be suitable for optical communication systems is constructed by applying the proposed method.The simulation results show that at the condition of the bit error rate(BER) of 10-7 and the same code rate of 93.7%,the net coding gain(NCG) of the constructed QC-LDPC(4599,4307) code is 2.2 dB more than that of the classic RS(255,239) code which has widely been applied in optical communication systems,and 0.47 dB and 0.25 dB more than those of the SCG-LDPC(3969,3720) code constructed by the systematically constructed gallager(SCG) construction method and the irregular QC-LDPC(3843,3603) code respectively,and is 1 dB away from the Shannon limit.Therefore,the novel QC-LDPC(4599,4307) code has superior error-correction performance and is more suitable for the high-speed long-haul optical communication systems.
A novel construction method with the advantages of simple construction and easy implementation encoding for quasi-cyclic low-density parity-check(QC-LDPC) codes based on Galois field(GF(q)) multiplicative group is proposed.This algorithm can flexibly adjust code length and code rate Furthermore,the complexity of the encoding and decoding is low.An irregular QC-LDPC(3843,3603) code suitable for optical communication systems is constructed by applying the proposed construction method.The simulation results show that the error-correction performance of the QC-LDPC(3843,3603) code is better than that of the classic RS(255,239) code,the LDPC code constructed by the SCG construction method,and the regular QC-LDPC(4221,3956) code.So the QC-LDPC(3843,3603) code is suitable for the high-speed long-haul optical communication systems.
A construction method of Quasi-Cyclic Low-Density Parity-Check(QC-LDPC) codes based on cyclic subgroups of finite field is proposed.The method owns the advantages such as easier construction,more flexible adjustment on code-length and code-rate and lower encoding/ decoding complexity.Moreover,a regular QC-LDPC(5334,4955)code suitable for optical communication systems is constructed by this construction method.The simulation results show that the code can gain good performance under the condition of additive white Gaussian noise(AWGN)channel with iterative decoding sum-product algorithm(SPA).The error-correction performance of the QC-LDPC(5334,4955)code is better than that of the classic RS(255,239) code which is widely used in optical communication system.Therefore,the constructed QC-LDPC(5334,4955)code can be better suitable for the long-haul and high-speed optical communication systems.
To meet the increasing requirement on the transmission characteristics of optical communication systems,based on the structure of parity-check matrix of Richardson-Urbanke algorithm,a lowercomplexity constructing method is proposed for the quasi-cyclic low-density parity-check(QC-LDPC) codes in the optical communication systems,and a QC-LDPC(4288,4020) code with 93.7% higher code-rate is also constructed.Simulation shows that the constructed QC-LDPC(4288,4020) code has net coding gain of about 1.7 dB over the classic RS(255,239) code which has been widely used for optical communication systems and 0.3 dB more than that of SCG-LDPC(3969,3720) code with the same 93.7% higher code-rate,and the NCG of the QC-LDPC(4288,4020) code is about 1.3 dB away from the Shannon limit at bit error rate BER of 10-7;furthermore,the error floor of QC-LDPC(4288,4020) code is lower than that of the randomly constructed LDPC(4288,4020) with the column weight of 3.
A novel construction method of Quasi-Cyclic Low-Density Parity-Check (QC-LDPC) code is proposed in this paper, which is based on protograph and Balanced Block Design (BIBD) in combinational mathematics.The method is to fill the base matrix of protograph with the base set elements of BIBD in accordance with certain mathematical rules.And the base matrix of protograph proposed in the paper has special double diagonal structure, which overcomes the low weight code words in general structure and achieves rapid encoding at the same time.The QC-LDPC code in this paper possesses lower encoding complexity and less memory occupation; therefore it is easy for hardware implementation.In addition, it effectively avoids girth 4. Simulation results show that when the Bit Error Rate (BER) is 10 -7 , QC-LDPC codes based on Protograph and BIBD (PBIBD-LDPC) proposed in this paper has 0.5dB Net Coding Gain (NCG) compared with the protograph QC-LDPC codes that based on Vander monde matrix and PEG algorithm structure, and has 0.15dB NCG compared with the excellent code QC-LDPC that based on the lifting structure.