Abstract: Consistent with the present disclosure, an encoder circuit is provided at a transmit side of an optical fiber link that maps an input sequence of bits of fixed length k a sequence of symbols of a codeword of length n, such that the symbols of the codeword define a predetermined transmission probability distribution. Preferably, each symbol of the codeword is generated during a corresponding clock cycle, such that after n clock cycles, a complete codeword corresponding to the input bit sequence is output. On a receive end of the link, a decoder is provided that outputs the k-bit sequence every n clock cycles. Accordingly, buffers need not be provided at the output of the encoder and the input of the decoder, such that processing of the input sequence, codewords, and output sequence may be achieved efficiently without large buffers and complicated circuitry. Moreover, the input sequence, with any binary alphabet may be matched to a desired output distribution with any arbitrary alphabet.

Abstract: Constant modulus multi-dimensional modulation system and methods are disclosed herein, employing multi-intensity quadrature amplitude modulation (QAM) to generate a dual-polarization symbol. j bits may be mapped to one of a plurality of dual-polarization symbols having a same constant power modulus on a two-level constellation including first and second intensity rings in a four-dimensional (4D) space including in-phase (I), quadrature (Q), X polarization (Xpol) and Y polarization (Ypol). A first bit of the j bits may indicate that the symbol is on the first intensity ring for the Xpol and the second intensity ring for the Ypol, a next k bits may indicate a location of the symbol on the first intensity ring in the Xpol, and a remaining j?k?1 bits may indicate a location of the symbol on the second intensity ring in the Ypol. Maximum correlation decoding may be used to decode the first symbol at the receiver.

Abstract: Various apparatus and methods may use iterative de-mapping/decoding to on received symbol estimates corresponding to interleaved coded modulation (ICM) using low-density parity check convolutional coding (LPDC-CC). The iterative de-mapping/decoding, may take the form of a multi-stage feed-forward arrangement that may include multiple identically designed stages, and the stages may use parallelism to increase speed and efficiency.

Abstract: Constant modulus multi-dimensional modulation system and methods are disclosed herein, employing multi-intensity quadrature amplitude modulation (QAM) to generate a dual-polarization symbol. j bits may be mapped to one of a plurality of dual-polarization symbols having a same constant power modulus on a two-level constellation including first and second intensity rings in a four-dimensional (4D) space including in-phase (I), quadrature (Q), X polarization (Xpol) and Y polarization (Ypol). A first bit of the j bits may indicate that the symbol is on the first intensity ring for the Xpol and the second intensity ring for the Ypol, a next k bits may indicate a location of the symbol on the first intensity ring in the Xpol, and a remaining j?k?1 bits may indicate a location of the symbol on the second intensity ring in the Ypol. Maximum correlation decoding may be used to decode the first symbol at the receiver.

Abstract: An optical system includes a transmitter module and/or a receiver module. The transmitter module is configured to receive input data, map the input data to a set of subcarriers associated with an optical communication channel, independently apply spectral shaping to each of the subcarriers, generate input values based on the spectral shaping of each of the subcarriers, generate voltage signals based on the input values, modulate light based on the voltage signals to generate an output optical signal that includes the subcarriers, and output the output optical signal. The receiver module is configured to receive the output optical signal, convert the output optical signal to a set of voltage signals, generate digital samples based on the set of voltage signals, independently process the digital samples for each of the subcarriers, map the processed digital samples to produce output data, and output the output data.

Abstract: Apparatus and methods may provide improved equalizer performance, e.g., for optical-fiber-based communication systems. A least-mean-square (LMS) equalizer may include a decision feedback path containing feedback carrier recovery (FBCR), which may have low latency, and which may thus enable high-speed tap updating in the equalizer. Feed-forward carrier recovery (FFCR) may be applied, in parallel with the FBCR, to provide equalizer output by compensating, e.g., for phase noise, with improved carrier recovery/compensation, versus using FBCR to generate the output.

Abstract: A digital signal processor (DSP) may include a receiver configured to receive an input signal. The DSP may include a processor component to perform carrier recovery on a set of digital signals representing a set of symbols associated with the input signal. The DSP may include an output component to provide information included in the set of digital signals representing the set of symbols. The DSP may be configured to perform, for the input signal, phase estimation with a latency of less than approximately 880 nanoseconds and having a power consumption of less than approximately 400 milliwatts at an update rate greater than approximately 4 Gigahertz. The latency being a propagation delay of the input signal.

Abstract: Consistent with the present disclosure, data, in digital form, is received by a transmit node of an optical communication system, and converted to an analog signal by a digital-to-analog converter (DAC) to drive a modulator. The modulator, in turn, modulates light at one of a plurality of wavelengths in accordance with the received data forming a plurality of corresponding carriers. The carriers are modulated according to one of a plurality of modulation formats and then optically combined to form a superchannel of a constant maximum capacity, for example. Accordingly, the number of carriers and the bit rate for each carrier remain constant for each modulation format to realize a constant maximum capacity. The superchannel is then transmitted over an optical communication path to a receive node. At the receive node, the superchannel is optically demultiplexed from a plurality of other superchannels.

Abstract: A transmitter is provided that transmits data in either a “quasi-DP-BPSK” (“QDP”) mode or in a DP-QPSK mode. In the QDP mode, data bits are transmitted as changes in phase between first and second phase states along a first axis or as changes in phase between third and fourth phase states along a second axis in the IQ plane. A sequence bit identifies which axis carries the data bit. The sequence bit is one of a series of sequence bits that may be generated by a pseudo-random number generator. The series of sequence bits can be relatively long to permit sufficiently random changes in the axis that carries the data. Thus, unlike conventional BPSK, in which data is transmitted between phase states along a single axis, the present disclosure provides an apparatus and related method for randomly selecting one of two axes, for example, for each transmitted bit.

Abstract: An optical receiver may include a digital signal processor to receive an input sample that includes transmitted data, transmitted by an optical transmitter, and nonlinear distortion. The digital signal processor may process the input sample to generate an estimated data value. The estimated data value may be an estimate of the transmitted data. The digital signal processor may remove the estimated data value from the input sample to generate a noise sample. The digital signal processor may determine a nonlinear distortion value based on the input sample, the estimated data value, and the noise sample. The nonlinear distortion value may be an estimate of the nonlinear distortion included in the input sample. The digital signal processor may remove the nonlinear distortion value from the input sample to generate an output sample, and may output the output sample.

Abstract: A system may include an optical transmitter and an optical receiver. The optical transmitter may generate optical signals associated with sub-carriers, and may provide the optical signals via an optical link. The optical receiver may receive the optical signals via the optical link, and may generate samples based on the optical signals. The samples may be associated with the sub-carriers. The optical receiver may combine the samples to form a time domain sample vector having a particular size, and may generate a frequency domain sample vector, having the particular size, based on the time domain sample vector. The optical receiver may demultiplex the frequency domain sample vector to generate domain sample vectors corresponding to the sub-carriers. The optical receiver may process the frequency domain sample vectors to generate equalized frequency domain sample vectors, and may output the equalized frequency domain sample vectors.

Abstract: Consistent with the present disclosure a transmitter is provided that transmits data in either a “quasi-DP-BPSK” (“QDP”) mode or in a DP-QPSK mode. In the QDP mode, data bits are transmitted as changes in phase between first and second phase states along a first axis or as changes in phase between third and fourth phase states along a second axis in the IQ plane. Although the transmitter outputs an optical signal that changes in phase between each of the four states, a sequence bit identifies which axis carries the data bit. The sequence bit is one of a series of sequence bits that may be generated by a pseudo-random number generator. The series of sequence bits can be relatively long, e.g., 32 bits, to permit sufficiently random changes in the axis that carries the data.

Abstract: An optical system includes an optical transmitter configured to modulate an optical signal to carry data, associated with an optical channel, via multiple sub-carriers in a quantity greater than four. The optical system further includes an optical receiver configured to demodulate the optical signal to recover the data from the multiple sub-carriers.

Abstract: An optical transmitter may receive and encode a first group of bits into first encoded data and second encoded data. The optical transmitter may supply a first sub-carrier carrying a first symbol and a second sub-carrier carrying a second symbol. The first symbol and the second symbol may be based on the first encoded data and the second encoded data, respectively, such that the first sub-carrier has a first polarization state comprising first and second polarization components, and the second sub-carrier has a second polarization state comprising first and second polarization components. The first polarization state may be substantially orthogonal to the second polarization state. An optical receiver may receive the first symbol via the first sub-carrier, may receive the second symbol via the second sub-carrier, may decode the first symbol and the second symbol into a second group of bits, and may output the second group of bits.

Abstract: Various apparatus and methods may use iterative de-mapping/decoding to on received symbol estimates corresponding to interleaved coded modulation (ICM) using low-density parity check convolutional coding (LPDC-CC). The iterative de-mapping/decoding, may take the form of a multi-stage feed-forward arrangement that may include multiple identically designed stages, and the stages may use parallelism to increase speed and efficiency.

Abstract: Consistent with the present disclosure, an optical communication system is provided in which data is carried over optical signals including subcarriers. The subcarriers may be modulated with the standard modulation formats noted above, but the modulation formats are selectively assigned to the subcarriers, such that some subcarriers are modulated with different standard modulation formats than others. As used herein, a “standard modulation format” is one of BPSK, and n-QAM, where n is an integer greater than one. Such n-QAM modulation formats include of 3-QAM, 4-QAM (QPSK), 8-QAM, 16-QAM, 64-QAM, 128-QAM, and 256-QAM. By selecting the number of subcarriers and the types of modulation formats employed, an optical signal with an effective SE that is between that of the standard modulation formats can be generated for transmission over a distances that more closely matches the link distance.

Abstract: A digital signal processor (DSP) may include a receiver configured to receive an input signal. The DSP may include a processor component to perform carrier recovery on a set of digital signals representing a set of symbols associated with the input signal. The DSP may include an output component to provide information included in the set of digital signals representing the set of symbols. The DSP may be configured to perform, for the input signal, phase estimation with a latency of less than approximately 880 nanoseconds and having a power consumption of less than approximately 400 milliwatts at an update rate greater than approximately 4 Gigahertz. The latency being a propagation delay of the input signal.

Abstract: An optical transmitter may receive and encode a first group of bits into first encoded data and second encoded data. The optical transmitter may supply a first sub-carrier carrying a first symbol and a second sub-carrier carrying a second symbol. The first symbol and the second symbol may be based on the first encoded data and the second encoded data, respectively, such that the first sub-carrier has a first polarization state comprising first and second polarization components, and the second sub-carrier has a second polarization state comprising first and second polarization components. The first polarization state may be substantially orthogonal to the second polarization state. An optical receiver may receive the first symbol via the first sub-carrier, may receive the second symbol via the second sub-carrier, may decode the first symbol and the second symbol into a second group of bits, and may output the second group of bits.

Abstract: An optical system includes an optical transmitter configured to modulate an optical signal to carry data, associated with an optical channel, via multiple sub-carriers in a quantity greater than four. The optical system further includes an optical receiver configured to demodulate the optical signal to recover the data from the multiple sub-carriers.

Abstract: A digital signal processor (DSP), may identify symbol values associated with a 5 quadrature amplitude modulation (5QAM) signal. The DSP may determine a first bit set based on the symbol values and a first particular bit value. The DSP may determine a second bit set based on the symbol values and a second particular bit value. The DSP may compute a first distance based on the first bit set and the symbol values. The DSP may compute a second distance based on the second bit set and the symbol values. The DSP may determine that the first distance is less than the second distance. The first distance being less than the second distance may indicate that the first bit set is a correctly decoded bit set. The DSP may provide an output associated with the correctly decoded bit set.