Abstract: A method and apparatus employing statistical physics energy minimization methods to signal constellation design. By using statistical physics concepts, an energy-efficient signal constellation design algorithm (EE-SCDA) is described. In the presence of amplified spontaneous emission (ASE) noise and channel impairments, we use EE-SCDA to determine a source distribution, and represent the signal constellation design as a center of mass problem. Furthermore a discrete-time implementation of D-dimensional transceiver as well as corresponding EE polarization-division multiplexed (PDM) system is described.

Abstract: Methods and systems for transmitting and receiving data include reverse concatenated encoding and decoding. Reverse concatenated decoding includes inner decoding the encoded stream with an inner decoder that uses a low-complexity linear-block code to produce an inner-decoder output stream, outer decoding the inner-decoder output stream with an outer decoder that uses a low-density parity-check code to produce an information stream, and iterating extrinsic bit reliabilities from the outer decoding for use in subsequent inner decoding to improve decoding performance.

Abstract: Methods and systems for reduced-complexity decoding of low-density parity-check (LDPC) information. An encoded input stream is received. The received stream is decoded with one or more reduced-complexity min-sum or a posteriori probability LDPC decoders. A v-node update rule in the reduced complexity decoder is omitted.

Abstract: Systems and methods for optical communication that use a transmitter/receiver. The systems and methods include receiving a modulated, encoded input stream. Channel memory is reduced using coarse digital backpropagation and other channel impairments are removed using turbo equalization. Symbols are detected in the input stream that conform to a non-uniform, polar constellation having a Gaussian source distribution to produce a stream of encoded data. The stream of encoded data is decoded with one or more low density parity check (LDPC) decoders.

Abstract: In a polarization-multiplexing optical communications system, a method and system for coherent reception of polarization-multiplexed optical communications. Training and data sequences are recovered from a plurality of orthogonally polarized signals, such that training and data sequences may be used on a single channel without loss of spectral efficiency. This is accomplished by estimating a channel response for each orthogonally polarized signal based on the mean of the signal and distinguishing between a data sequence and a training sequence in each orthogonally polarized signal. Such distinguishing is accomplished according to an iterative linear minimum mean-square equalization based on the respective channel response estimate.

Abstract: Receivers and methods are provided for polarization mode dispersion compensation in multi-level coded-modulation schemes using a BLAST algorithm and iterative polarization cancellation. A receiver includes a vertical Bell Laboratories Layered Space-Time Architecture (V-BLAST) orthogonal frequency division multiplexing (OFDM) detector configured to receive input sequences and partially cancel polarization interference with respect to the input sequences to output symbol estimates for the input sequences. The receiver further includes one or more low-density parity-check (LDPC) decoders coupled to the V-BLAST OFDM detector configured to receive channel bit reliabilities and output code words. The channel bit reliabilities are indirectly calculated from the symbol estimates. The one or more LDPC decoders iteratively provide extrinsic soft information feedback to the V-BLAST OFDM detector to compensate for the polarization interference.

Abstract: A method of encoding for optical transmission of information includes encoding information with a generalized low-density parity-check (GLDPC) code for providing coding gains, and constructing the GLDPC code with a Reed-Muller RM code as a component code, the component code being decodable using a maximum posterior probability (MAP) decoding. In a preferred embodiment, the GLDPC code includes a codeword length of substantially 4096, an information word length of substantially 3201, a lower-bound on minimum distance of substantially greater than or equal to 16, a code rate of substantially 0.78 and the RM component code includes an order of substantially 4 and an r parameter of substantially 6.

Abstract: Systems and methods enabling ultra-high-speed optical transport The systems and methods include receiving a modulated, encoded input stream. Channel impairments are removed using MAP equalization. Symbols are detected in the input stream to produce a stream of encoded data. The stream of encoded data is decoded with one or more low density parity check (LDPC) decoders that use an LDPC code built by modified progressive edge growth. The LDPC code is built by iteratively expanding trees from each variable node until all check nodes are connected to the respective variable node, while controlling both the local girth and the global girth of the code.

Abstract: A method and apparatus employing statistical physics energy minimization methods to signal constellation design. By using statistical physics concepts, an energy-efficient signal constellation design algorithm (EE-SCDA) is described. In the presence of amplified spontaneous emission (ASE) noise and channel impairments, we use EE-SCDA to determine a source distribution, and represent the signal constellation design as a center of mass problem. Furthermore a discrete-time implementation of D-dimensional transceiver as well as corresponding EE polarization-division multiplexed (PDM) system is described.

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: 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 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 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: Methods and systems for soft-decision non-binary low-density parity-check (LDPC) coding for ultra-long-haul optical transoceanic transmissions are provided. A receiver includes one or more maximum a posteriori (MAP) equalizers configured to decode one or more symbols of an encoded input stream to provide one or more symbol log-likelihood ratios (LLRs). One or more LLR estimators are configured to estimate the log-likelihood ratios of the one or more symbol LLRs to provide one or more bit LLRs. One or more non-binary LDPC decoders are configured to decode the input stream using the one or more bit LLRs to recover an original input stream.

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 communication system includes a bit-interleaved coded modulation (BICM) coder; and a low-density parity-check (LDPC) coder coupled to the BICM coder to generate codes used as component codes and in combination with a coherent detector.

Abstract: Arbitrarily high data transmission rates may be achieved by the use of N-dimensional, LDPC-coded modulation. N orthonormal basis functions are employed using coherent reception, resulting in a proportional increase in transmission rate with only a modest increase in bit-error ratio.

Abstract: The invention provides methods, devices and a system for recovering the corrupted subcarrier at the local oscillator (LO) frequency in coherent optical OFDM transmission. The method includes performing advanced coding on a data signal to obtain an encoded signal; performing high order modulation on the encoded signal to obtain a high-order-modulated signal; performing OFDM modulation on the high-order-modulated signal to obtain an electrical OFDM signal; and performing up-conversion on the electrical OFDM signal to obtain an optical OFDM signal to be output.

Abstract: A transmitting device, a receiving device, an optical communication system, and associated methods are provided. The transmitting device transmits an optical signal containing data, and comprises: an optical tone generator for generating at least one optical tone; at least one encoder for performing advanced coding on at least one data signal respectively, each of the at least one data signal carrying a part of the data; at least one mapper for performing high order modulation on the at least one coded data signal; and an up-converter for up-converting the at least one high-order-modulated data signal into the optical signal to be outputted through the at least optical tone. Thereby, high speed (e.g., over 1-Tb/s) transmission per single channel over a long-haul distance (e.g. over 1000-km) with error-free recovery may be achieved.