Changyu Lin

Multidimensional Signaling and Coding Enabling Multi-Tb\/s Optical Transport and Networking: Multidimensional aspects of coded modulation

The design of next-generation optical transmission systems and networks should address the concerns with respect to a limited bandwidth of information infrastructure, high energy consumption, as well as the need to support the network heterogeneity and demand for an elastic and dynamic bandwidth allocation. To address these concerns simultaneously, we propose an adaptive, software-defined, low-density parity check (LDPC)-coded multiband approach that involves spatial-multiple-input, multiple-output (MIMO) and an all-optical orthogonal frequency-division multiplexing (OFDM) scheme since it can enable energy efficient high-bandwidth delivery with fine granularity and elastic model of bandwidth utilization. The modulation is based on multidimensional signaling to improve the tolerance to fiber nonlinearities and imperfect compensation of channel impairments and has a hybrid nature with both electrical and optical degrees of freedom employed. Optical degrees of freedom include spatial and polarization modes in optical fibers supporting spatial-division multiplexing (SDM), while electrical degrees of freedom are based on 2M orthogonal basis functions. The adaptive coding has been performed by partial reconfiguration of the corresponding parity-check matrix. The proposed scheme is suitable for the conveyance of the information over optical fibers with bit rates exceeding 10 Tb/s. At the same time, the multitude of degrees of freedom will enable finer granularity and elasticity of the bandwidth, the features essential for next generation networking.

LDPC-coded mode-multiplexed CO-OFDM over 1000 km of few-mode fiber

We demonstrate by simulations that four independent LDPC-coded 80Gb/s QPSK OFDM signals can be transmitted by mode-multiplexing over 1000km of few-mode fiber using coherent detection with a powerful channel estimation technique.

Achievable information rates calculation for optical OFDM few-mode fiber long-haul transmission systems

We propose a method to estimate the lower bound of achievable information rates (AIRs) of high speed orthogonal frequency-division multiplexing (OFDM) in spatial division multiplexing (SDM) optical long-haul transmission systems. The estimation of AIR is based on the forward recursion of multidimensional super-symbol efficient sliding-window Bahl-Cocke-Jelinek-Raviv (BCJR) algorithm. We consider most of the degradations of fiber links including nonlinear effects in few-mode fiber (FMF). This method does not consider the SDM as a simple multiplexer of independent data streams, but provides a super-symbol version for AIR calculation over spatial channels. This super-symbol version of AIR calculation algorithm, in principle, can be used for arbitrary multiple-input-multiple-output (MIMO)-SDM system with channel memory consideration. We illustrate this method by performing Monte Carlo simulations in a complete FMF model. Both channel model and algorithm for calculation of the AIRs are described in details. We also compare the AIRs results for QPSK/16QAM in both single mode fiber (SMF)- and FMF-based optical OFDM transmission.

Nonbinary LDPC-Coded Mode-Multiplexed Coherent Optical OFDM 1.28-Tbit/s 16-QAM Signal Transmission Over 2000 km of Few-Mode Fibers With Mode-Dependent Loss

We demonstrate the possibility of nonbinary LDPC-coded mode-multiplexed coherent optical OFDM 1.28-Tbit/s 16-QAM signal transmission over 2000 km of few-mode fiber (FMF) with mode-dependent loss (MDL) by using an advanced mode-coupling compensation scheme. The performance of proposed coded-modulation scheme is evaluated for different number of spatial modes. The simulation results indicate that the MDL is the predominant effect in the long-haul optical transmission based on FMFs. Different pilot-aided OFDM based compensation methods are studied, and it has been found that minimum mean-square estimation with linear interpolation method is the most robust against mode coupling and MDL. We also show that the nonbinary LDPC-coded modulation provides about 1 dB improvement over binary LDPC-coded modulation (16 QAM OFDM and MDL of 25 dB). Finally, we study the degradation of increasing the number of modes and investigate the proposed scheme for different MDL values in both fourand eight-mode fibers.

Mode-Multiplexed Multi-Tb/s Superchannel Transmission With Advanced Multidimensional Signaling in the Presence of Fiber Nonlinearities

We have analyzed the possibility of long-haul superchannel transmission with an aggregate serial bit rate exceeding 1 Tb/s by using the mode-multiplexed multidimensional signaling. We considered nonbinary quasi-cyclic LDPC-coded OFDM signals transmitted over few-mode fibers (FMFs). The optimum vector-form nonlinear Schrödinger equation is developed to evaluate the performance of the proposed system. Both the impacts of nonlinear effects and nonlinear interaction between spatial modes have been included through the modified nonlinear Schrödinger equation we applied for the FMF case. Both two-dimensional and optimized four-dimensional (4D) signal constellations have been considered. To overcome the constraints imposed by the linear and nonlinear impairments in FMF, we proposed the use of block-coded modulation with advanced channel estimation and compensation techniques. We verified by means of simulation that the transmission of an aggregate serial bit rate of 1.2 Tb/s over 3000 km is achievable with a proposed LDPC-coded QPSK-OFDM format, whereas superchannel transmission with an aggregate serial rate of 2.4 Tb/s over 1800 km is achievable with the 16-QAM format. When a 4D 16-ary optimized constellation is used, we can extend the transmission distance of mode-multiplexed QPSK-OFDM by an additional 300 km.

Quantum Few-Mode Fiber Communications Based on the Orbital Angular Momentum

We study a quantum few-mode fiber (FMF) communication scheme based on orbital angular momentum (OAM) modes and applied quantum information theory to develop the quantum FMF channel model and to calculate the quantum channel capacity. We assume a strong mode-coupling regime in FMF and an imperfect generation of OAM modes. The quantum FMF channel is modeled as a concatenation of many fiber sections describing the OAM eigenkets transitions as a Markov chain. The proposed model is suitable for the study of the multidimensional quantum key distribution and teleportation over FMFs. Numerical simulations are performed to demonstrate the ability of the model to determine the FMF output density state for a given input density state. It is shown that FMF quantum channel capacity decreases with distance in a strong coupling regime if OAM basekets are imperfectly generated.

Advanced GF(3^2) nonbinary LDPC coded modulation with non-uniform 9-QAM outperforming star 8-QAM

In this paper, we first describe a 9-symbol non-uniform signaling scheme based on Huffman code, in which different symbols are transmitted with different probabilities. By using the Huffman procedure, prefix code is designed to approach the optimal performance. Then, we introduce an algorithm to determine the optimal signal constellation sets for our proposed non-uniform scheme with the criterion of maximizing constellation figure of merit (CFM). The proposed nonuniform polarization multiplexed signaling 9-QAM scheme has the same spectral efficiency as the conventional 8-QAM. Additionally, we propose a specially designed GF(32) nonbinary quasi-cyclic LDPC code for the coded modulation system based on the 9-QAM non-uniform scheme. Further, we study the efficiency of our proposed non-uniform 9-QAM, combined with nonbinary LDPC coding, and demonstrate by Monte Carlo simulation that the proposed GF(23) nonbinary LDPC coded 9-QAM scheme outperforms nonbinary LDPC coded uniform 8-QAM by at least 0.8dB.

FPGA-based LDPC-coded APSK for optical communication systems

In this paper, with the aid of mutual information and generalized mutual information (GMI) capacity analyses, it is shown that the geometrically shaped APSK that mimics an optimal Gaussian distribution with equiprobable signaling together with the corresponding gray-mapping rules can approach the Shannon limit closer than conventional quadrature amplitude modulation (QAM) at certain range of FEC overhead for both 16-APSK and 64-APSK. The field programmable gate array (FPGA) based LDPC-coded APSK emulation is conducted on block interleaver-based and bit interleaver-based systems; the results verify a significant improvement in hardware efficient bit interleaver-based systems. In bit interleaver-based emulation, the LDPC-coded 64-APSK outperforms 64-QAM, in terms of symbol signal-to-noise ratio (SNR), by 0.1 dB, 0.2 dB, and 0.3 dB at spectral efficiencies of 4.8, 4.5, and 4.2 b/s/Hz, respectively. It is found by emulation that LDPC-coded 64-APSK for spectral efficiencies of 4.8, 4.5, and 4.2 b/s/Hz is 1.6 dB, 1.7 dB, and 2.2 dB away from the GMI capacity.

Capacity achieving nonbinary LDPC coded non-uniform shaping modulation for adaptive optical communications.

A mutual information inspired nonbinary coded modulation design with non-uniform shaping is proposed. Instead of traditional power of two signal constellation sizes, we design 5-QAM, 7-QAM and 9-QAM constellations, which can be used in adaptive optical networks. The non-uniform shaping and LDPC code rate are jointly considered in the design, which results in a better performance scheme for the same SNR values. The matched nonbinary (NB) LDPC code is used for this scheme, which further improves the coding gain and the overall performance. We analyze both coding performance and system SNR performance. We show that the proposed NB LDPC-coded 9-QAM has more than 2dB gain in symbol SNR compared to traditional LDPC-coded star-8-QAM. On the other hand, the proposed NB LDPC-coded 5-QAM and 7-QAM have even better performance than LDPC-coded QPSK.

Non-uniform signaling based LDPC coded modulation for high-speed optical transport networks

Different non-uniform (probability shaping) signaling schemes are introduced in this invited paper. By transmitting symbols with different probabilities, energy efficiency (shaping gain) of traditional schemes can be improved. With constellation points selected according to Maxwell-Boltzmann distribution, ultimate shaping gain of 1.53dB can be achieved.