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Journal of Optoelectronics·laser

A novel construction method of quasi-cyclic non-binary LDPC codes in optical communication

Huang Shen

Published Jan 1, 2014• 0 citations
OpenAlex

Abstract

This paper presents a construction method of quasi-cyclic non-binary low density parity-check(NB-LDPC)code based on the finite field three-dimensional construction.After construction of base matrix based on the finite field,a cyclic matrix is constructed with the method of three-dimensional extension.Finally,non-binary parity check matrix with quasi-cyclic feature is constructed.Compared with the GF(29)-based RS(511,305)and NB-LDPC code constructed by the three-dimensional construction can increase 3.3dB net code gain(NCG)at the bit error rate(BER)of 10-7.Compared with the binary QC-LDPC codes constructed by the traditional way,the binary LDPC codes randomly constructed,the32-ary QC-LDPC codes constructed based on finite fields and the 64-ary cyclic LDPC codes constructed based on Euclidean geometry,the NB-LDPC code constructed by the three-dimensional construction can increase 0.56dB,0.56dB,0.03dB and 0.83dB NCGrespectively at the BERof 10-7.Through performance simulation of the NB-LDPC code constructed based on this three-dimensional construction,it shows that such an NB-LDPC code not only has quasi-cyclic feature,conducive to hardware implementation,but also shows better error correction performance in the short code length.

Related papers

A novel construction method of the QC-LDPC code based on finite field additive group for optical communications

Yong Wang

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.

Journal of Optoelectronics·laser•Jan 1, 2013•0 citations

High-Rate Nonbinary Regular Quasi-Cyclic LDPC Codes for Optical Communications

Murat Arabaci, Ivan B. Djordjević, Ross Saunders +1 more

The parity-check matrix of a nonbinary (NB) low-density parity-check (LDPC) code over Galois field GF(q) is constructed by assigning nonzero elements from GF(q) to the 1s in corresponding binary LDPC code. In this paper, we state and prove a theorem that establishes a necessary and sufficient condition that an NB matrix over GF(q), constructed by assigning nonzero elements from GF(q) to the 1s in the parity-check matrix of a binary quasi-cyclic (QC) LDPC code, must satisfy in order for its null-space to define a nonbinary QC-LDPC (NB-QC-LDPC) code. We also provide a general scheme for constructing NB-QC-LDPC codes along with some other code construction schemes targeting different goals, e.g., a scheme that can be used to construct codes for which the fast-Fourier-transform-based decoding algorithm does not contain any intermediary permutation blocks between bit node processing and check node processing steps. Via Monte Carlo simulations, we demonstrate that NB-QC-LDPC codes can achieve a net effective coding gain of 10.8 dB at an output bit error rate of 10-12. Due to their structural properties that can be exploited during encoding/decoding and impressive error rate performance, NB-QC-LDPC codes are strong candidates for application in optical communications.

Journal of Lightwave Technology•Aug 7, 2009•42 citations

Performance Analysis of NB-QC-LDPC Code for High-Speed Optical Communication Systems

Zhiqiang Lin, Jianyong Zhang

In the paper, we construct the non-binary quasi-cyclic low-density parity check (NB-QC-LDPC) code from the quasi-cyclic low-density parity check (QC-LDPC) code. The NB-QC-LDPC code over the Galois field GF(4) is suitable for 100Gb/s optical communication systems with QPSK or DQPSK modulation formats. We also study the bit error ratio (BER) performance of the NB-QC-LDPC code by using the Log-Fourier Sum and Product decoding algorithm (LFSPA). The numerical results show that the NB-QC-LDPC code with code length 500 can provide approximately 5.5dB coding gain at the BER of 910- and outperform QC-LDPC code by 0.7dB.

International Conference on Electronics, Communications and Control•Oct 16, 2012•0 citations

Construction Method of QC-LDPC Codes in Optical Communication Systems

Yong Wang

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.

Beijing Youdian Xueyuan xuebao•Jan 1, 2013•0 citations

Study on QC-LDPC Codes Based on BIBD for Optical Communication Systems

Yong Wang

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.

Bandaoti guangdian•Jan 1, 2013•0 citations

A method for constructing parity-check matrices of non-binary quasi-cyclic LDPC codes

Stanislav Kruglik, Valeriya Potapova, Alexey Frolov

An algorithm for constructing parity-check matrices of non-binary quasi-cyclic low-density parity-check (NB QC-LDPC) codes is proposed. The algorithm finds short cycles in the base matrix and tries to eliminate them by selecting the circulants and the elements of GF(q). Firstly the algorithm tries to eliminate the cycles with the smallest number edges going outside the cycle. The efficiency of the algorithm is demonstrated by means of simulations. In particular, it was shown that NB QC-LDPC codes constructed with use of our algorithm loose less that 0.1 dB in comparison to the best NB LDPC codes.

arXiv:1705.10717•May 30, 2017•0 citations
This paper presents a construction method of quasi-cyclic non-binary low density parity-check(NB-LDPC)code based on the finite field three-dimensional construction.After construction of base matrix based on the finite field,a cyclic matrix is constructed with the method of three-dimensional extension.Finally,non-binary parity check matrix with quasi-cyclic feature is constructed.Compared with the GF(29)-based RS(511,305)and NB-LDPC code constructed by the three-dimensional construction can increase 3.3dB net code gain(NCG)at the bit error rate(BER)of 10-7.Compared with the binary QC-LDPC codes constructed by the traditional way,the binary LDPC codes randomly constructed,the32-ary QC-LDPC codes constructed based on finite fields and the 64-ary cyclic LDPC codes constructed based on Euclidean geometry,the NB-LDPC code constructed by the three-dimensional construction can increase 0.56dB,0.56dB,0.03dB and 0.83dB NCGrespectively at the BERof 10-7.Through performance simulation of the NB-LDPC code constructed based on this three-dimensional construction,it shows that such an NB-LDPC code not only has quasi-cyclic feature,conducive to hardware implementation,but also shows better error correction performance in the short code length.
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.
The parity-check matrix of a nonbinary (NB) low-density parity-check (LDPC) code over Galois field GF(q) is constructed by assigning nonzero elements from GF(q) to the 1s in corresponding binary LDPC code. In this paper, we state and prove a theorem that establishes a necessary and sufficient condition that an NB matrix over GF(q), constructed by assigning nonzero elements from GF(q) to the 1s in the parity-check matrix of a binary quasi-cyclic (QC) LDPC code, must satisfy in order for its null-space to define a nonbinary QC-LDPC (NB-QC-LDPC) code. We also provide a general scheme for constructing NB-QC-LDPC codes along with some other code construction schemes targeting different goals, e.g., a scheme that can be used to construct codes for which the fast-Fourier-transform-based decoding algorithm does not contain any intermediary permutation blocks between bit node processing and check node processing steps. Via Monte Carlo simulations, we demonstrate that NB-QC-LDPC codes can achieve a net effective coding gain of 10.8 dB at an output bit error rate of 10-12. Due to their structural properties that can be exploited during encoding/decoding and impressive error rate performance, NB-QC-LDPC codes are strong candidates for application in optical communications.
In the paper, we construct the non-binary quasi-cyclic low-density parity check (NB-QC-LDPC) code from the quasi-cyclic low-density parity check (QC-LDPC) code. The NB-QC-LDPC code over the Galois field GF(4) is suitable for 100Gb/s optical communication systems with QPSK or DQPSK modulation formats. We also study the bit error ratio (BER) performance of the NB-QC-LDPC code by using the Log-Fourier Sum and Product decoding algorithm (LFSPA). The numerical results show that the NB-QC-LDPC code with code length 500 can provide approximately 5.5dB coding gain at the BER of 910- and outperform QC-LDPC code by 0.7dB.
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.
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.
An algorithm for constructing parity-check matrices of non-binary quasi-cyclic low-density parity-check (NB QC-LDPC) codes is proposed. The algorithm finds short cycles in the base matrix and tries to eliminate them by selecting the circulants and the elements of GF(q). Firstly the algorithm tries to eliminate the cycles with the smallest number edges going outside the cycle. The efficiency of the algorithm is demonstrated by means of simulations. In particular, it was shown that NB QC-LDPC codes constructed with use of our algorithm loose less that 0.1 dB in comparison to the best NB LDPC codes.