Evaluation of four-dimensional nonbinary LDPC-coded modulation for next-generation long-haul optical transport networks.

Leveraging the advanced coherent optical communication technologies, this paper explores the feasibility of using four-dimensional (4D) nonbinary LDPC-coded modulation (4D-NB-LDPC-CM) schemes for long-haul transmission in future optical transport networks. In contrast to our previous works on 4D-NB-LDPC-CM which considered amplified spontaneous emission (ASE) noise as the dominant impairment, this paper undertakes transmission in a more realistic optical fiber transmission environment, taking into account impairments due to dispersion effects, nonlinear phase noise, Kerr nonlinearities, and stimulated Raman scattering in addition to ASE noise. We first reveal the advantages of using 4D modulation formats in LDPC-coded modulation instead of conventional two-dimensional (2D) modulation formats used with polarization-division multiplexing (PDM). Then we demonstrate that 4D LDPC-coded modulation schemes with nonbinary LDPC component codes significantly outperform not only their conventional PDM-2D counterparts but also the corresponding 4D bit-interleaved LDPC-coded modulation (4D-BI-LDPC-CM) schemes, which employ binary LDPC codes as component codes. We also show that the transmission reach improvement offered by the 4D-NB-LDPC-CM over 4D-BI-LDPC-CM increases as the underlying constellation size and hence the spectral efficiency of transmission increases. Our results suggest that 4D-NB-LDPC-CM can be an excellent candidate for long-haul transmission in next-generation optical networks.

Experimental study of non-binary LDPC coding for long-haul coherent optical QPSK transmissions.

The performance of rate-0.8 4-ary LDPC code has been studied in a 50 GHz-spaced 40 Gb/s DWDM system with PDM-QPSK modulation. The net effective coding gain of 10 dB is obtained at BER of 10(-6). With the aid of time-interleaving polarization multiplexing and MAP detection, 10,560 km transmission over legacy dispersion managed fiber is achieved without any countable errors. The proposed nonbinary quasi-cyclic LDPC code achieves an uncoded BER threshold at 4×10(-2). Potential issues like phase ambiguity and coding length are also discussed when implementing LDPC in current coherent optical systems.

Spatial-domain-based multidimensional modulation for multi-Tb/s serial optical transmission.

The multidimensional channel capacity studies indicate that the employment of multiple photon degrees of freedom-such as subcarrier, amplitude, phase, polarization, and space-can improve the spectral efficiency by several orders of magnitude higher than that claimed in any fiber-optic experiment reported to date. This dramatic increase in spectral efficiency through multiple photon degrees of freedom can provide revolutionary capabilities for future optical networks. Moreover, photons can carry both spin angular momentum (SAM) associated with polarization, and orbital angular momentum (OAM) associated with the azimuthal phase of the complex electric field. Because OAM eigenstates are orthogonal, an arbitrary number of bits per photon can be transmitted in principle. The ability to generate the OAM modes, such as Bessel modes, in multimode fibers (MMFs) will allow realization of fiber-optic communication networks with ultra-high bits-per-photon efficiencies. To this end, we propose here a spatial-domain-based multidimensional coded-modulation scheme as an enabling technology for multi-Tb/s serial optical transport. To demonstrate the capabilities of the proposed scheme, we show that an eight-dimensional (8D) spatial-domain-based coded modulation scheme outperforms a prior-art 128-point 4D scheme by 3.88 dB at BER of 10(-8) while providing 120 Gb/s higher aggregate information bit rate. The proposed 8D scheme also outperforms its conventional polarization-multiplexed QAM counterpart by even a larger, and indeed striking, margin of 8.39 dB (also at the BER of 10(-8)).

Generalized OFDM (GOFDM) for ultra-high-speed optical transmission.

We propose a coded N-dimensional modulation scheme suitable for ultra-high-speed serial optical transport. The proposed scheme can be considered as a generalization of OFDM, and hence, we call it as generalized OFDM (GOFDM). In this scheme, the orthogonal subcarriers are used as basis functions and the signal constellation points are defined over this N-dimensional linear space. To facilitate implementation, we propose using N-dimensional pulse-amplitude modulation (ND-PAM) as the signal constellation diagram, which is obtained as the N-ary Cartesian product of one-dimensional PAM. In conventional OFDM, QAM/PSK signal constellation points are transmitted over orthogonal subcarriers and then they are multiplexed together in an OFDM stream. Individual subcarriers, therefore, carry N parallel QAM/PSK streams. In the proposed GOFDM scheme instead, an N-dimensional signal constellation point is transmitted over all N subcarriers simultaneously. When some of the subcarriers are severely affected by channel impairments, the constellation points carried by those subcarriers may be lost in the conventional OFDM. In comparison, under such conditions, the overall signal constellation point will face only small distortion in GOFDM and it can be recovered successfully using the information on the other high fidelity subcarriers. Furthermore, because the channel capacity is a logarithmic function of signal-to-noise ratio but a linear function of the number of dimensions, the spectral efficiency of optical transmission systems can be improved with GOFDM.

LDPC-coded orbital angular momentum (OAM) modulation for free-space optical communication.

An orbital angular momentum (OAM) based LDPC-coded modulation scheme suitable for use in FSO communication is proposed. We demonstrate that the proposed scheme can operate under strong atmospheric turbulence regime and enable 100 Gb/s optical transmission while employing 10 Gb/s components. Both binary and nonbinary LDPC-coded OAM modulations are studied. In addition to providing better BER performance, the nonbinary LDPC-coded modulation reduces overall decoder complexity and latency. The nonbinary LDPC-coded OAM modulation provides a net coding gain of 9.3 dB at the BER of 10(-8). The maximum-ratio combining scheme outperforms the corresponding equal-gain combining scheme by almost 2.5 dB.

Polarization-multiplexed rate-adaptive non-binary-quasi-cyclic-LDPC-coded multilevel modulation with coherent detection for optical transport networks.

In order to achieve high-speed transmission over optical transport networks (OTNs) and maximize its throughput, we propose using a rate-adaptive polarization-multiplexed coded multilevel modulation with coherent detection based on component non-binary quasi-cyclic (QC) LDPC codes. Compared to prior-art bit-interleaved LDPC-coded modulation (BI-LDPC-CM) scheme, the proposed non-binary LDPC-coded modulation (NB-LDPC-CM) scheme not only reduces latency due to symbol- instead of bit-level processing but also provides either impressive reduction in computational complexity or striking improvements in coding gain depending on the constellation size. As the paper presents, compared to its prior-art binary counterpart, the proposed NB-LDPC-CM scheme addresses the needs of future OTNs, which are achieving the target BER performance and providing maximum possible throughput both over the entire lifetime of the OTN, better.