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Chinese Optics Letters

Fiber-based optical parametric amplif ier for 40-Gb/s NRZ-DPSK signal transmission system employing QC-LDPC codes

Jian Zheng, Hongxia Bie, Xuekun Zhang, Chunyang Lei, Ming Lun Fang, Sha Li, Zhe Kang

Published Jan 1, 2013• 1 citation
Publisher

Abstract

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.

DOI
10.3788/col201311.110601

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IEEE Latin-American Conference on Communications•Nov 1, 2016•1 citation
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.
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.
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.
We study the decoding performance of low-density parity-check (LDPC) code based on Watermark scheme under different percentages of water-mark bits over 100 Gb/s differential quadrature phase shift keying (DQPSK) high-speed optical communication system. We also find the optimum percentage of water-mark bits according to the performance comparison. Simulation result shows an improvement of 0.5 dB net code gain by using the optimum Watermark scheme at a post-forward error correction bit error rate (BER) of 10-9, comparing with the traditional log-likelihood ratios belief propagation decoding algorithm. Also, for the same BER, there is a decrease in the number of iterations used in LDPC decoding.
Powerful forward error correction codes such as quasi-cyclic low density parity check (QC-LDPC) are required in next-generation coherent optical communication systems [1]. This work describes the design and experimental verification of a high net coding gain (NCG), low complexity QC-LDPC code. Towards this end, we develop a field programmable gate array (FPGA) based platform specially designed for optimization and performance evaluation of LDPC codes. The proposed FPGA framework includes several features such as the capability of changing the internal resolution of the decoder algorithm or capturing error patterns for error-floor analysis. Experimental results derived from the FPGA platform show that the designed QC-LDPC code is able to achieve an NCG of 11.6 dB at a bit-error-rate (BER) of 10-15with an overhead of 25% and a codeword length of only 16K bits.