Robust Multidimensional Optical Modulation Based on Hybrid Subcarrier/Amplitude/Phase/Dual Polarization for Wavelength-Division Multiplexing Systems

—Here, we propose a novel scheme based on advanced techniques of digital modulation in optical communications to achieve a single-channel transmission rate above 100 Gb/s. We utilize a hybrid scheme amplitude/phase/frequency/dual polarization, combined with multidimensional dual lattice and a low-density parity-check-coded modulation. The Stokes parameters are applied to the proposed scheme to map the four-dimensional classical polarization I X , Q X , I Y , Q Y in a three- dimensional space. In addition, in the proposed system, the packing theory is applied to the bit interleaver process. Three wavelengths are packaged before being transmitted over a wavelength-division multiplexing optical channel. This modulation process is carried out using symmetrical geometric shapes, such as a hypercube or a polyhedron, based on the molecular links theory using a grouping of 12 and 13/15 bits for the cubic and spherical lattices, respectively. The proposed technique is evaluated in the context of long-distance communications over distances up to 100km. The bit error rate (BER) results showed that the optical signal-to-noise ratio was approximately 4dB over a distance of 50km. In addition, the power spectral efficiency was found to be 3 lambdas, which is considered good performance considering the effects of distance and the non-linear effects influencing the number of lambdas. Also, we use an optical time-division multiplexing scheme (OTDM) in order to achieve a transmission rate beyond 1Tbit/s, where the speed effect is evaluated, taking into consideration that the power spectral efficiency is degraded.


Index
Terms-Coherent Optical Communications; Polyhedron; Hypercube; Multidimensional Modulations; Stokes parameters; Poincaré sphere Resumen-En este documento propone un nuevo esquema basado en las técnicas avanzadas de modulación digital en comunicaciones ópticas para lograr una velocidad de transmisión de un solo canal sobre los 100 Gb/s. Utilizamos un esquema híbrido de amplitud/fase/frecuencia/doble polarización, combinado con un doble enmallado multidimensional y una modulación codificada por verificación de paridad de baja densidad. Los parámetros de Stokes se aplican al esquema propuesto para mapear la polarización clásica de cuatro dimensiones I X , Q X , I Y , Q Y en un espacio tridimensional. Además, en el sistema propuesto, la teoría de empaquetamiento se aplica al proceso de entrelazado de bits. Se empaquetan tres longitudes de onda antes de transmitirse a través de un canal óptico de multiplexación por división de longitud de onda. Este proceso de modulación se lleva a cabo utilizando formas geométricas simétricas, como un hipercubo o un poliedro, basado en la teoría de enlaces moleculares que utiliza una agrupación de 12 y 13/15 bits para los enmallados cúbicos y esféricos, respectivamente. La técnica propuesta se evalúa en el contexto de las comunicaciones a larga distancia en distancias de hasta 100 km. Los resultados de la tasa de error de bits (BER) mostraron que la relación señal/ruido óptico era de aproximadamente 4 dB en una distancia de 50 km. Además, se encontró que la eficiencia espectral de potencia con 3 lambdas, lo que se considera un buen rendimiento teniendo en cuenta los efectos de la distancia y los efectos no lineales que influyen en el número de lambdas. Además, utilizamos un esquema de multiplexación óptica por división de tiempo (OTDM) para lograr una velocidad de transmisión más allá de 1Tbit/s, donde se evalúa el efecto de la velocidad, tomando en consideración que la eficiencia espectral de potencia se degrada. N RECENT years, network operators have been considering and installing network infrastructures even more robust than those before them. The rapidly increasing demand for transmission capacity and the ineffective use of optical fiber links have led to many studies to develop advanced schemes that achieve transmission rate beyond 240 Gb/s per wavelength channel.

Robust Multidimensional Optical Modulation
A promising approach to improving the transmission performance of future access networks, called multidimensional modulations was discovered a long time ago by Wei [1]. This technique involves the use of a rectangular or cross-lattice grouping technique to provide other modulations formats, being compatibility with traditional formats. This strategy improves the peak-to-average power ratio (PAPR) and SNR efficiency due to shaping component constellationexpansion-ratio (CER) that depends only on the shape of the constellation. Consequently, the shape gain (dB) is evaluated in terms of PAPR and CER, where cross constellations achieve better results in comparison with rectangular constellations.
The increase in PAPR is considered primarily as a negative effect of OFDM systems. However, this technique has more recently been applied to modern mobile access networks, such as sparse code multiple access networks (SCMA) [2] to achieve the high capacity needed to support large volumes of information and massive connectivity.
It is widely known, that optical-fiber communication is a strong candidate for connecting the backbone with the end-users in future access networks. For this reason, research has been done to optimize optical channels by using advanced modulation formats so that they can transmit data at higher rates with flexible spectral and power efficiency. Furthermore, N-dimensional signal constellations may be incorporated to increase the system performance compared to that using traditional two-dimensional (2D) formats.
In this context, the spectrum allocation in conventional WDM Network is replaced for an elastic optical network (EON) which improves the spectral efficiency. EON is based on OFDM, they provide an alternative to single carrier modulation technique as the data stream divided and multiplexed onto multiple consecutive low rate subcarriers and hence increases the symbol duration and provides a higher data rate [3]. This approach leads us to think that our proposal is the key to the next generation of optical networks in order to obtain a flexible allocation of spectral resources improving in this way the spectral efficiency.
Incoherent detected optical transmission, polarizationdivision-multiplexing (POLMUX) can be used to generate two orthogonal polarization signals, X and Y, for transmission through a single-wavelength channel with a high SE and ultra-high-speed [4]. In this context, passive optical networks with two orthogonally polarized orthogonal frequencydivision multiple access signals have recently been proposed. This system can transmit data at a rate of 108 Gb/s after 20km SSMF in comparison with the back-to-back transmission. The fiber dispersion penalty is negligible due to distance of transmission, the attenuation (15dB) and the excellent Bit Error Rate (BER) achieved 1.4×10 -3 [5].
In this way, wavelength-division multiplexing (WDM) can facilitate the integration of coding (FEC, trellis, turbo code, LDPC) with code modulation together in order to improve the spectrum efficiency and coding gain. These are the promising solutions for 5G network access with optical communications known as 10-Gigabit-capable passive optical networks (XG-PON) [7] that should coexist with GPON and WDM-PON networks, and also guaranteeing an optimal allocation of wavelength bands in order to avoid the undesirable interference of GPON with XG-PON.
Another promising technology is the polarization switching system, which sends a three-dimensional (3D) constellation with an asynchronous in-phase/quadrature (IQ) polarization, which represents the transmitted symbol in 3D [8]. Dualpolarization (DP) modulation provides a lower SE but better performance for a long-distance transmission [9].
4D set-partitioning quadrature amplitude modulation (SP-QAM) is a special case of advanced optical modulation, in which a regular 4D cubic can be constructed by polarizationdivision multiplexing (PDM). A PDM-QAM model using a coherent detection scheme with Reed-Solomon encoding was shown to improve the SE and provide a data transmission rate of over 112 Gb/s [10]. In another study, the use of 4D 512-ary and 2048-ary SP-QAM signals and soft-decision forward error correction (FEC) with penalties resulted in BERs of 3.8×10 -3 and 2×10 -2 , respectively [11].
In addition to the use of spectrally efficient modulation formats low-density parity-check (LDPC) codes can be incorporated into the physical design for new schemes to make them compatible with 4D modulations and, thereby, enable coherent optical communications with high aggregate bit rates. LDPC codes offer significant benefits compared to other codes and hybrid codes like turbo-trellis code modulations. In this context, 4D bit-interleaved LDPC-coded modulation has been developed by connecting a distributed-feedback (DFB) laser to a polarization beam splitter (PBS) to combine two polarization (X and Y) for each IQ modulator, thus, forming the structure of a 4D modulator [12]. The aggregate information bit rates with 16-, 32-, and 64-QAM were measured as 160, 200, and 240 Gb/s, respectively; the best optical SNR of approximately 5 dB and a BER of 1×10 -8 was attained with 16-QAM. In another study, 320 Gb/s data transmission was achieved using an M-ary 3D constellation with LDPC coded modulation; an SNR of nearly 12dB and a BER of 1×10 -9 was achieved for 8-QAM [8]. I 10 MASKAY Therefore, the optimization of the power efficiency of an N-dimensional constellation that provides both flexible SE and high-power efficiency at the same time can be solved by considering it as a sphere-packing problem [13]. The number of degrees of freedom for optical transmission can be represented by the vertical axis, where the first and second dimensions represent the electrical field of the X-polarized IQ components, and the third and fourth dimensions represent the electrical field electrical of the Y-polarized IQ components. In this context, a 4D lattice is constructed, and optimized with respect to the discrete-time represented by the horizontal axis. This approach has been used to optimize a 3D constellation with four degrees of freedom, achieving data transmission of 224 Gb/s over a distance of 100km.
The use of polarization-mode dispersion can improve the coding gain due to the error floor and the iterative exchange of extrinsic soft-bit reliabilities between posterior probabilities. Hussam developed a way to implement such a modulation with different sub-carriers in a 3D space using coded hybrid sub-carrier/amplitude/phase/polarization (H-SAPP) [14]. Using Stokes parameters, H-SAPP allows 20 points to be incorporated into a 3D constellation mapping in the form of a dodecahedron inscribed in a Poincaré sphere based on regular polyhedrons [15]. Numerical results using 20-HSAPP show that BER = 1×10 -6 with an OSNR of 0.5dB could be achieved with a back-to-back configuration.
Here, we propose a hybrid subcarrier/amplitude/phase/dual polarization (H-SAPDP) system for optical transmission of 300 Gb/s. To improve performance, the system is based on polyhedrons. We demonstrate that the proposed system can be significantly banked to the Shannon limit over optical channels of different distances using WDM techniques.
The use of multidimensional modulations is a novel technique that holds promise for future generations of communication systems with both enhanced SE and superior BER performance. The SE and BER performances are known to be inversely proportional to one another according to the Shannon theory. In addition, the system may suffer from distortion effects if larger amounts of information are transmitted. However, the use of multidimensional techniques mitigates these challenges because, if the amount of information increases, it can be packaged by an interleaving bit distribution process to generate an N-dimensional lattice. This approach reduces the bit error rate, the inter-symbol interference, and the power transmission and consequently increases the SE as if two different modulations were being used at the same time: high-index modulation to improve the SE and low-index modulation to enhance the BER performance.
The proposed technique is implemented with different lattice dimensions in the interleaver process: a hypercubic multidimensional lattice with 16 symbols for 12 bits in an even alignment, and a polyhedron-spherical lattice with 32 symbols for 13 or 15 bits in an odd alignment. 12_13 or 15 bits are allocated to each block and packed with three subcarriers composed of DP signals (I X , Q X , I Y , Q Y ) and aligned in parallel (i.e., they transmit at the same time). One bit is added to denote the change from even to odd alignment; thus, the packed block will have 5 bits and, consequently, the distribution packing can be set in the range of 13-15 bits.
Finally, this packaging is transformed into a 4D optical signal using Jones vectors and Pauli matrices designed according to the parameters of the polarized signal. Thus, the H-SAPDP system performs dual-lattice packing with multidimensional modulations at 50 Gsymbols/s. In this way, the binary input is divided among the 4D carriers for transmission over a distance of 50, 80, or 100km. This approach is compared with dodecahedral techniques based on the Poincaré technique and with different-dimensional packing.
Several possible constructions for the packing lattice have been proposed. However, unfortunately, this remains an unsolved problem in mathematics. The face-centered cubic lattice is obtained using a generator matrix in which the vectors represent the deep holes that arise from sphere packing (referred to as glue vectors). Another strategy is to consider the kissing number, which represents how many spheres can be arranged so that they all touch one central sphere of the same size [16]. In this study, we base the lattice on the theory of the sphere-packing problem which can be observed in the orange pyramid in fruit stands. Using this lattice configuration, the advantage of the triangles found in pyramids leads to geometrically equivalent packings.
To be precise, herein, we define the thickness (also called density, sparsity or coverage) as the number of spheres that contain a single point in space.
The remainder of this paper is organized as follows. Section II presents a description of the optical system considered here and the H-SAPDP coded modulation, the dual lattice used to build the cubic and spherical lattices (Section II-A), the interleaver process (Section II-B), the multidimensional modulator (Section II-B), and Stokes and polarized signal parameters (Section II-D). The numerical results of the simulation are presented in Section III. Finally, the conclusions are summarized in Section IV.

II. H-SAPDP CODED MODULATION
There are many ways of building a constellation lattice in order to optimize the signal constellations using Ndimensions. Fig. 1 shows different methods of polarization over an optical fiber. Previously, 4D formats with single-polarization and switch polarization were severely limited due to the synchronization of X and Y signals ( Fig.  1(b) and Fig. 1(c)) [17]. Today, it is possible to modulate different signals with orthogonal X and Y polarization with total dependency between them. Thus, we leveraged the four dimensions of the optical carrier field as shown in Fig. 1(d) in order to transport 16-point rectangular constellations and 28point circular constellations through a cube and hypercube respectively in the 3D with total independence among them. The proposed ources of n bit -SAPDP tran arrier, A λq . Th achieve diffe ubic or spheri ll the carriers mode optical f plitter divides t Fig. 4
M n our packing r-dimensional dimensional la next scheme
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