Abstract: A receiver and method are provided. The receiver includes a detector configured to receive polarization multiplexed coded orthogonal frequency division multiplexing input sequences and generate estimates of unknown transmitted symbols in the input sequences for x- and y-polarization channels with respect to laser phase noise and PMD. A demapper coupled to the detector is configured to partially cancel polarization mode dispersion (PMD) in the input sequences by computing symbol probabilities for the estimates with respect to the laser phase noise, and averaging the symbol probabilities with respect to the laser phase noise. One or more low-density parity-check (LDPC) decoders coupled to the demapper are configured to receive bit probabilities derived from the averaged symbol probabilities and output code words based at least on the bit probabilities. The one or more LDPC decoders iteratively provide extrinsic soft information feedback to the demapper to compensate for the PMD.

Abstract: A receiver and method are provided for mitigation of finer non-linearities in multilevel coded-modulation schemes. The receiver includes a multilevel Bahl-Cocke-Jelinek-Raviv (BCJR) equalizer configured to receive channel samples of an input signal, partially mitigate fiber non-linearities, and provide symbol reliabilities. The receiver further includes a bit probabilities module coupled to the BCJR equalizer configured to calculate soft bit reliabilities from the symbol reliabilities. The receiver also includes one or more low-density parity-check (LDPC) decoders coupled to the bit probabilities module and the BCJR equalizer, configured to receive the soft bit reliabilities and output code words. The one or more LDPC decoders iteratively provide extrinsic soft information feedback to the BCJR equalizer to compensate for the fiber non-linearities.

Abstract: A transmitter, a receiver, and corresponding methods are provided. The transmitter includes encoders configured to encode source bit streams from L information sources into bytes of codewords. Each encoder includes different (n, k) multidimensional turbo-product codes of code rate R=k/n, where k is a number of information bytes, and n is code word length. The encoders operate in at least two phases. A first phase involves operating ky column-encoders in parallel on kx bytes per column to generate the code words for a current dimension. A second phase involves operating nx row-encoders in parallel on ky memory locations per rows to generate the code words for the current dimension. The first and second phases are repeated for remaining layers of the current dimension and layers of other dimensions.

Abstract: Multilevel soft-equalizer detectors, such as a maximum a posteriori probability (MAP) detector, suitable for use in polarization multiplexed optical communications using multilevel modulations and coherent detection are disclosed. Detection systems and methods may consider two symbols transmitted over two orthogonal polarization states as a two-component symbol, which is effective in eliminating the bit error ratio (BER) floor phenomenon introduced by conventional soft equalizers.

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: Methods and systems for optical communication using hybrid subcarrier/amplitude/phase/polarization modulation are shown that include LDPC encoding a plurality of groups of bitstreams. The groups of bitstreams are mapped to the points of a three-dimensional constellation that is represented by the vertices of a regular polyhedron and its dual. Each group of bitstreams is then modulated onto a respective subcarrier beam and the subcarrier beams are combined into a carrier beam using a power combiner.

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: A method for error correction and a decoder using low density parity check (LDPC) codes includes initializing extrinsic probability information between variable nodes and check nodes in a bipartite graph including generating a Bernoulli sequence according to a probability of a bit having a value one. Parity checking is performed in accordance with a parity check equation. If the parity check equation is not satisfied, then extrinsic information is updated in check nodes from variable nodes using a parity node update logic circuit in a first half iteration, extrinsic information is updated in variable nodes from check nodes using a variable node update logic circuit in a second half iteration, and the variable nodes are updated with a probability based upon the extrinsic information passed between check nodes and variable nodes wherein the probability represents a likelihood that an ith bit is a one.

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: A turbo equalizer includes a Bahl-Cocke-Jelinek-Raviv (BCJR) equalizer configured to receive a transmitted signal and partially cancel inter-symbol interference (ISI) due to polarization-mode dispersion (PMD). A low-density parity check (LDPC) decoder is coupled to the BCJR equalizer to receive channel bit reliabilities therefrom. The LDPC decoder iteratively provides extrinsic soft information feedback to the BCJR equalizer to compensate for PMD.

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: A transmitter and method include a LDPC encoder configured to encode source data, and a mapper configured to generate three coordinates in accordance with a 3D signal constellation where the coordinates include an amplitude coordinate and two phase coordinates. A laser source is modulated in accordance with each of the three coordinates to provide a transmission signal. A receiver, includes a demapper receives an input signal from three branches to demap the input signal using a three-dimensional signal constellation having three coordinates. The three branches include a direct detection branch, and two coherent detection branches such that the direct detection branch detects an amplitude coordinate of the input signal and the two coherent detection branches detect in-phase and quadrature coordinates of the input signal. A bit prediction module and at least one LDPC decoder are configured to iteratively decode bits by feeding back extrinsic LLRs to the demapper.

Abstract: A transmitter includes a plurality of encoders configured to receive source bit streams from m information sources, each of the plurality encoders including identical (n,k) low-density parity check (LDPC) codes of code rate r=k/n, where k is a number of information bits and n is codeword length. An interleaver is configured to collect m row-wise codewords from the plurality of encoders, and a mapper is configured to receive m bits at a time column-wise from the interleaver and to determine an M-ary signal constellation point. A modulator is configured to modulate a light source in accordance with the output of the mapper at a transmission rate Rs/r (Rs—the symbol rate, r—-the code rate). A receiver and transmission and receiving methods are also disclosed.

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: Multilevel soft-equalizer detectors, such as a maximum a posteriori probability (MAP) detector, suitable for use in polarization multiplexed optical communications using multilevel modulations and coherent detection are disclosed. Detection systems and methods may consider two symbols transmitted over two orthogonal polarization states as a two-component symbol, which is effective in eliminating the bit error ratio (BER) floor phenomenon introduced by conventional soft equalizers.

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: A receiver and method are provided for mitigation of finer non-linearities in multilevel coded-modulation schemes. The receiver includes a multilevel Bahl-Cocke-Jelinek-Raviv (BCJR) equalizer configured to receive channel samples of an input signal, partially mitigate fiber non-linearities, and provide symbol reliabilities. The receiver further includes a bit probabilities module coupled to the BCJR equalizer configured to calculate soft bit reliabilities from the symbol reliabilities. The receiver also includes one or more low-density parity-check (LDPC) decoders coupled to the bit probabilities module and the BCJR equalizer, configured to receive the soft bit reliabilities and output code words. The one or more LDPC decoders iteratively provide extrinsic soft information feedback to the BCJR equalizer to compensate for the fiber non-linearities.

Abstract: A transmitter, a receiver, and corresponding methods are provided. The transmitter includes encoders configured to encode source bit streams from L information sources into bytes of codewords. Each encoder includes different (n, k) multidimensional turbo-product codes of code rate R=k/n, where k is a number of information bytes, and n is code word length. The encoders operate in at least two phases. A first phase involves operating ky column-encoders in parallel on kx bytes per column to generate the code words for a current dimension. A second phase involves operating nx row-encoders in parallel on ky memory locations per rows to generate the code words for the current dimension. The first and second phases are repeated for remaining layers of the current dimension and layers of other dimensions.

Abstract: A method for error correction and a decoder using low density parity check (LDPC) codes includes initializing extrinsic probability information between variable nodes and check nodes in a bipartite graph including generating a Bernoulli sequence according to a probability of a bit having a value one. Parity checking is performed in accordance with a parity check equation. If the parity check equation is not satisfied, then extrinsic information is updated in check nodes from variable nodes using a parity node update logic circuit in a first half iteration, extrinsic information is updated in variable nodes from check nodes using a variable node update logic circuit in a second half iteration, and the variable nodes are updated with a probability based upon the extrinsic information passed between check nodes and variable nodes wherein the probability represents a likelihood that an ith bit is a one.

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.