Abstract: A system/method for data transport, including encoding one or more streams of input data using one or more Low Density Parity Check (LDPC) encoders; employing one or more signal constellations obtained using an optimum signal constellation design (OSCD); determining an optimum mapping rule by comparing cost functions of each of a plurality of mapping rules; combining one or more LDPC-coded OSCD signal constellation data streams with coherent optical-orthogonal frequency division multiplexing (CO-OFDM) coded modulation to achieve channel capacity; and mode-multiplexing and transmitting one or more independent LDPC-coded optimum signal constellation design (OSCD) data streams over a transmission medium.

Abstract: Systems and methods for data transport are provided which encode streams of data using low density parity check (LDPC) encoders and map data streams to symbols, by assigning bits of symbols to a signal constellation and associating bits with constellation points. Constellation points are generated using a D-dimensional optimum signal constellation design (OSCD) method. The OSCD determines an optimum source distribution for an optical channel, generates D-dimensional training sequences from the optimum source distribution, determines new signal constellation points as the center of mass for each D-dimensional cluster of points, and repeats these steps until convergence or until a predetermined number of iterations is reached.

Abstract: A system and method for transmitting data, including one or more Low Density Parity Check (LDPC) encoders configured to encode one or more streams of input data; a signal constellation generation module configured to generate one or more signal constellations; one or more modulators configured to generate one or more signals using hybrid multidimensional coded modulation; a modified orthogonal polynomial generation module configured to generate modified orthogonal polynomials for use as electrical basis functions; and one or more mode-multiplexers and transmitters configured to mode-multiplex and transmit one or more LDPC-coded data streams over a transmission medium.

Abstract: Methods and systems for decoding a signal include compensating for impairments in a received signal using at least carrier phase estimation, where residual phase error remains after compensation; calculating symbol log-likelihood ratios (LLRs) for symbols in the compensated signal using Monte Carlo integration; demapping the symbols in the compensated signal using the symbol LLRs and extrinsic information from signal decoding to produce one or more estimated codewords; and decoding each estimated codeword with a decoder that generates a decoded codeword and extrinsic information.

Abstract: Systems and methods for data transport, including encoding streams of input data using generalized low-density parity check (GLDPC) encoders, the one or more GLDPC encoders being configured to generate GLDPC coded data streams using a plurality of component local codes to improve error correction strength, employ single-parity checks and two or more local block codes during generation of the GLDPC codes, and enable continuous tuning of code rate using the generated GLDPC codes. Signals may be generated using mappers, the mappers configured to assign bits of signals to signal constellations and to associate the bits of the signals with signal constellation points. The signal may be modulated using an I/Q or 4-D modulator composed of one polarization beam splitter, two I/Q modulators, and one polarization beam combiner. The modulated signals are multiplexed using a mode-multiplexer, transmitted over a transmission medium, and the signals are received and decoded using GLDPC decoders.

Abstract: Systems and methods for encoding streams of input data using at least two nonbinary low density parity check (NB-LDPC) encoders; generating NB-LDPC coded optimum signal constellations; performing orthogonal frequency division multiplexing (OFDM) on the NB-LDPC coded four-dimensional (4-D) optimum signal constellations; generating signals using mappers, the mappers configured to assign bits of signals to the signal constellations and to associate the bits of the one or more signals with signal constellation points. Output of the 4-D mappers is modulated using a 4-D OFDM transmitter and a 4-D modulator onto a transmission medium using block coded-modulation, and the modulated output is transmitted by mode-multiplexing independent 4-D OFDM data streams onto fiber.

Abstract: An optical transport network based on multimode/multicore fibers includes a mode-multiplexer to multiplex independent data streams from one or more transmitters; a multimode erbium-doped fiber amplifier (MM EDFA) to compensate for MMF loss; a multimode optical add-drop multiplexer (MM OADM) to add and/or drop multimode channels in multimode networks; a multimode optical cross-connect; and a mode-demultiplexer to separate various mode streams to one or more receivers.

Abstract: An optical network includes a multidimensional coder and modulator for handling multiple-in-multiple-out MIMO spatial lightpath properties and content of any specific supercarrier, a spatial mode multiplexer responsive to orthogonal frequency division multiplexing OFDM transmissions and the multidimensional coder, a spatial-spectral routing node coupled over a fiber link to the spatial mode multiplexer for performing switching granularity by a spatial mode reconnection, a multidimensional decoder and demodulator; and a spatial mode demultiplexer coupled over a fiber link to the spatial-spectral routing node and responsive to the multidimensional decoder and demodulator.

Abstract: Systems and methods for data transport, comprising encoding one or more streams of input data with one or more low density parity check (LDPC) encoders, corresponding to one or more polarization/spatial mode branches. One or more encoded data streams are mapped to symbols, wherein the mapper is configured to assign bits of the symbols to a signal constellation and to associate the bits of the symbols with signal constellation points. A signal constellation is formulated which minimizes a mean-square error of the signal constellation representing the source. The optimum signal constellation size is adjusted to improve transmission quality by adjusting the signal constellation an optical signal to noise ratio (OSNR), wherein the signal constellation is selected using a look-up table (LUT); and the symbols are modulated in accordance with the output of the mapper onto a transmission medium.

Abstract: Systems and methods for transmitting data, including encoding one or more streams of input data using one or more adaptive Low Density Parity Check (LDPC) encoders, wherein the encoders generate one or more signal constellations; modulate one or more signals using hybrid multidimensional coded modulation; apply orthogonal prolate spheroidal wave functions as electrical basis functions; generate one or more spectral band group signals by selecting and combining two or more spectral band groups with center frequencies that are orthogonal to each other; and spectral-mode-multiplex and transmit the one or more adaptive LDPC-coded data streams including the one or more spectral band group signals combined into corresponding spatial modes over a transmission medium.

Abstract: A system and method for transmitting data, including one or more Low Density Parity Check (LDPC) encoders configured to encode one or more streams of input data; a signal constellation generation module configured to generate one or more signal constellations; one or more modulators configured to generate one or more signals using hybrid multidimensional coded modulation; a modified orthogonal polynomial generation module configured to generate modified orthogonal polynomials for use as electrical basis functions; and one or more mode-multiplexers and transmitters configured to mode-multiplex and transmit one or more LDPC-coded data streams over a transmission medium.

Abstract: Systems and methods for data transport are provided which encode streams of data using low density parity check (LDPC) encoders and map data streams to symbols, by assigning bits of symbols to a signal constellation and associating bits with constellation points. Constellation points are generated using a D-dimensional optimum signal constellation design (OSCD) method. The OSCD determines an optimum source distribution for an optical channel, generates D-dimensional training sequences from the optimum source distribution, determines new signal constellation points as the center of mass for each D-dimensional cluster of points, and repeats these steps until convergence or until a predetermined number of iterations is reached.

Abstract: Systems and methods for data transport include encoding one or more streams of input data using one or more Quasi-Cyclic Low Density Parity Check (QC-LDPC) encoders; controlling irregularity of the QC-LDPC encoded data while preserving the quasi-cyclic nature of the LDPC encoded data and eliminating the error floor phenomenon. A parity-check matrix may be partially reconfigured to adapt one or more code rates; and one or more signals are generated using a mapper, wherein the output of the mapper is modulated onto a transmission medium. One or more streams of input data are received, and the streams are decoded using one or more QC-LDPC decoders.

Abstract: Systems and methods are disclosed to perform four-dimensional optical multiband OFDM communication by organizing an N-dimensional (ND) signal constellation points as a signal matrix; performing 2D-inverse FFT and 2D-FFT to perform modulation and demodulation, respectively; and applying both orthogonal polarizations in the OFDM communication to deal with chromatic dispersion, PMD and PDL effects, and multidimensional signal constellation to improve optical signal-to-noise ratio (OSNR) sensitivity.

Abstract: Systems and methods are disclosed to provide optical communication by using subcarriers as individual bases functions, obtaining signal constellation points of an N-dimensional pulse amplitude modulation (ND-PAM) constellation diagram as an N-dimensional Cartesian product of a one-dimensional PAM; and transmitting the N-dimensional signal constellation point over all N orthogonal subcarriers serving as individual bases functions.

Abstract: Systems and methods are disclosed with a spatial-domain-based multi-dimensional coded-modulation scheme that improves dramatically OSNR sensitivity and tolerance to fiber nonlinearities by using D-dimensional signal constellations, where D=2(2+M)N. The factor 2 originates from two polarizations, 2+M electrical basis functions are selected (2 in-phase/quadrature channels and M pulse-position like basis functions), and N represents the number of orbital angular momentum (OAM) states used in FMFs/MMFs. For single mode fiber applications N is 1.

Abstract: Systems and methods are disclosed for communicating signals, by receiving a K-symbol-long input block from a 2m-ary source channel; encoding the input block into a 2m-ary non-binary low-density parity-check (LDPC) codeword of length N; and mapping each 2m-ary symbol to a point in a signal constellation comprised of 2m points, wherein a non-binary LDPC code is used as the component code for forward error correction in a coded modulation scheme capable of achieving optical fiber communication at rates beyond 100 Gb/s.

Abstract: A coded multidimensional modulation system called generalized OFDM (GOFDM) uses orthogonal subcarriers as bases functions, and the signal constellation points of corresponding multidimensional constellation diagram are obtained as N-dimensional Cartesian product of one-dimensional PAM/two-dimensional QAM. In GOFDM, the N-dimensional/2N-dimensional signal constellation point is transmitted over all N subcarriers/2N-subcarriers, which serve as individual bases functions. Even if some of the subcarriers are severely affected by channel distortion, the overall signal constellation point will face only small distortion, when strong channel capacity achieving channel codes are used. In addition, because the channel capacity is a linear function of number of dimensions, the spectral efficiency of optical transmission systems is significantly improved.

Abstract: Systems and methods of transmitting includes one or more low-density parity-check (LDPC) encoders configured to adaptively encode one or more streams of input data by adjusting error correction strength based upon channel conditions. One or more mappers are configured to map one or more encoded data streams to symbols by associating bits of the symbols to points of an optimum signal constellation design (OSCD) based on one or more encoded data streams, the OSCD being decomposed into two or more sub-constellations. A spectral multiplexer is configured to combine symbol streams for the one or more encoded data streams to provide a plurality of spectral band groups. A mode multiplexer is configured to combine spectral contents of the plurality of spectral band groups allocated to a plurality of spatial modes for transmission over a transmission medium.

Abstract: Methods and systems for decoding a signal include compensating for impairments in a received signal using at least carrier phase estimation, where residual phase error remains after compensation; calculating symbol log-likelihood ratios (LLRs) for symbols in the compensated signal using Monte Carlo integration; demapping the symbols in the compensated signal using the symbol LLRs and extrinsic information from signal decoding to produce one or more estimated codewords; and decoding each estimated codeword with a decoder that generates a decoded codeword and extrinsic information.