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Chinese Optics Letters

160-Gb/s NRZ-DQPSK optical transmission system employing QC-LDPC code

Sha Li, Chongxiu Yu Chongxiu Yu, Zhe Kang, Gerald Farrell, Qiang Wu

Published Jan 1, 2014• 2 citations
Publisher

Abstract

A quasi-cyclic low-density parity check (QC-LDPC) code is constructed by an improved stability of the shortest cycle algorithm for 160-Gb/s non-return zero differential quadrature phase shift keying (NRZ-DQPSK) optical transmission system with the fiber-based optical parametric amplifier (FOPA).The QC-LDPC code with stability of the shortest cycle reduces the bit error ratio (BER) to 10 -14 and restrains the error floor effectively.

DOI
10.3788/col201412.010604

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A quasi-cyclic low-density parity check (QC-LDPC) code is constructed by an improved stability of the shortest cycle algorithm for 160-Gb/s non-return zero differential quadrature phase shift keying (NRZ-DQPSK) optical transmission system with the fiber-based optical parametric amplifier (FOPA).The QC-LDPC code with stability of the shortest cycle reduces the bit error ratio (BER) to 10 -14 and restrains the error floor effectively.
In this letter, we investigate quasi-cyclic low-density parity-check (QC-LDPC) codes in a 40-Gb/s nonreturn-to-zero differential phase-shift keying (NRZ-DPSK) signal transmission system based on a fiberbased optical parametric amplifier (FOPA).A constructed algorithm of QC-LDPC codes according to the optimizing set of shift values on the circulant permutation matrix (CPM) of the basis matrix is proposed.Simulation results prove that the coding gain in the encoded system can be realized at 10.2 dB under QC-LDPC codes with a code rate of 5/6 when the bit error rate (BER) is 10 -9 .In addition, the error-floor level originating from the uncoded system is suppressed.
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.
Forward error correction is as one of the key technologies enabling the next-generation high-speed fiber optical communications. Quasi-cyclic (QC) low-density parity-check (LDPC) codes have been considered as one of the promising candidates due to their large coding gain performance and low implementation complexity. In this paper, we present our designed QC-LDPC code with girth 10 and 25% overhead based on pairwise balanced design. By FPGAbased emulation, we demonstrate that the 5-bit soft-decision LDPC decoder can achieve 11.8dB net coding gain with no error floor at BER of 10-15 avoiding using any outer code or post-processing method. We believe that the proposed single QC-LDPC code is a promising solution for 400Gb/s optical communication systems and beyond.
Quasi-cyclic low-density parity-check (QC-LDPC) codes with low-complexity hardware implementation and excellent performance have become a hot research topic in many optical communication systems. To meet the different requirements of code lengths in optical communication systems, lifting methods which remove all the short cycles equally are usually used to construct long QC-LDPC codes of larger lengths by lifting short QC-LDPC codes. A lifting method is proposed, which considers both length and connectivity of short cycles. The proposed lifting method reduces the complexity of calculating the approximated cycle extrinsic message degree -related metrics and improves connectivity of the Tanner graph. The numerical results prove that, by employing our proposed lifting method, the lifted long QC-LDPC codes have better bit error rate performance compared with the lifted codes employing the traditional lifting method.