Patent Publication Number: US-11641248-B2

Title: System, apparatus, and architecture for migrating an optical communication network

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     The present application claims the benefit of the filing date of U.S. Provisional Patent Application No. 63/155,003 filed Mar. 1, 2021, the disclosure of which is hereby incorporated herein by reference. 
    
    
     BACKGROUND 
     Coherent optical communications technology typically involves modulating the amplitude and phase of light, as well as transmission across two polarization states, in transporting information over a fiber optic cable. Coherent optical communications technology offers the potential to make use of more of the available bandwidth of a fiber optic cable or transmission path than competing technologies. Such communications typically make use of a coherent optical receiver. In such a receiver, the transmitted signal is interfered with using a local oscillator (LO) that provides for extraction of phase information and thus referred to as a coherent receiver. 
     As compared to other forms of optical transmission, such as intensity modulation and direct detection (IM-DD), coherent optical technology offers as possible advantages: higher receiver sensitivity, higher spectral efficiency (SE) and higher tolerance towards various linear optical impairments such as fiber chromatic dispersion (CD) and polarization mode dispersion (PMD). In applications where the state of polarization (SOP) is not maintained during transmission, a phase- and polarization-diversity four dimensional (4D) vector receiver is typically employed to detect and demodulate the coherently modulated signal. 4D refers the separate in-phase (I) and quadrature (Q) components of the X-polarized signal and Y-polarized signal (e.g., Ix, Qx for the X-polarized signal, and Iy, Qy for the Y-polarized signal, which when processed result in separate I, Q for each of the X and Y polarized signals). A 4D vector receiver is also typically used when the received signal is only a two dimensional (2D) modulated optical signal such as a single polarization (SP) quadrature amplitude modulated (QAM) (SP-QAM) signal or a 1D modulated signal such as a SP-pulse amplitude modulation (SP-PAM) signal. Thus, despite only receiving information encoded in two of the dimensions, the complexity of a 4D vector is typically required to process the transmitted signal. 
     SUMMARY 
     Aspects of the disclosed technology include methods, systems, and apparatuses that employ or use a two-dimensional (2D) or one-dimensional (1D) coherent receiver. For example, in relatively short reach transmission systems such a receiver can be used to detect and demodulate 2D or 1D coherent modulation formats and may be preferable over 4D vector receivers. Such receivers may be employed where the state of polarization (SOP) may change during transmission through a length of fiber. Such receivers may also be employed in short reach transmission systems where relatively high SE may be considered less critical than in, for instance, networks that span longer distances such as for example metropolitan or long haul optical networks. 
     Aspects of the disclosed technology include methods, systems, and apparatuses which can include any combination of the following features. 
     Aspects of the disclosed technology include an optical transmission system including (i) a polarization beam splitter having an input port, a first optical output port and a second optical output port, the input port coupled to an optical communication channel, the first optical output port providing a first optical signal derived from an encoded optical signal received over the optical communication channel and the second optical output port providing a second optical signal derived from the encoded optical signal, the first optical signal having a first polarization component and the second optical signal having a second polarization component; (ii) a delay element coupled to the second optical output port of the polarization beam splitter and configured to delay the second optical signal by a pre-determined time period to produce a delayed second optical signal; (iii) an optical coupler that includes a first input coupled to the first optical output of the polarization beam splitter and a second input coupled to the delay element so as to receive the delayed second optical signal, the optical coupled combining the first optical signal and the delayed second optical signal to form a combined optical signal, and (iv) a polarization rotator configured to rotate a polarization component of either the second optical signal or the delayed second optical signal into a polarization state corresponding to the first polarization component. The polarization beam splitter can include the polarization rotator and the second optical signal can be rotated into the polarization state corresponding to the first polarization component. The polarization rotator can be coupled to the delay element and configured to receive the delayed second optical signal and can rotate a polarization state of the delayed second optical signal into the polarization state corresponding to the first polarization component. The polarization rotator can be coupled to the delay element and can be configured to receive the delayed second optical signal and can rotate a polarization state of the delayed second optical signal into the polarization state corresponding to the first polarization component. The optical coupler can include a polarization rotator. The optical coupler can comprise a 3-dB coupler. The combined optical signal can comprise a folded optical signal in which the first optical signal can comprise a first X-polarized signal and the delayed second optical signal comprises a second X-polarized signal delayed by the predetermined time period. The predetermined time period can comprise a time period of one more symbol period. A symbol period can correspond to a time period it takes to transmit a predetermined number of bits. An X-polarized hybrid element can recover respective in-phase (I) and quadrature phase (Q) optical signals from the folded optical signal. A first and second photodetector/transimpedance amplifiers can receive the respective in-phase (I) and quadrature phase (Q) optical signals and can produce respective first and second electrical I and Q signals. First and second analog-to-digital converters can convert the respective first and second electrical I and Q signals into respective electrical digital signals. The system can include a multiplexer and/or a de-multiplexer. The multiplexer can be in direct or indirect optical communication with the de-multiplexer. The optical coupler can be a Mach-Zehnder interferometer. 
     Aspects of the disclosed technology include a method for transmission of signals. The method can include deriving for output, from an encoded optical signal received at a polarization beam splitter (PBS), a first optical signal at a first output port of the PBS and a second optical signal at a second output port of the PBS, the first optical signal having a first polarization component and the second optical signal having a second polarization component; delaying the second optical signal by a pre-determined time period to produce a delayed second optical signal; combining the first optical signal and the delayed optical signal at an optical coupler; and rotating a polarization component of either the second optical signal or the delayed second optical signal. The method can include a polarization beam splitter which can rotate, combine, or rotate and combine either the second optical signal or the delayed second optical signal. The optical coupler can include a polarization rotator. The optical coupler can include a 3-db coupler or other coupler. The combined optical signal can comprise a folded optical signal in which the first optical signal comprises a first X-polarized signal and the delayed second optical signal comprises a second X-polarized signal delayed by the predetermined time period. The predetermined time period can comprise a time period of one more symbol period. A symbol period can correspond to a time period it takes to transmit a predetermined number of bits. An X-polarized hybrid element can be configured for respective in-phase (I) and quadrature phase (Q) optical signals from the folded optical signal. A first and a second photodetector/transimpedance amplifiers can be configured for receiving the respective in-phase (I) and quadrature phase (Q) optical signals and produce respective first and second electrical I and Q signals. A first and a second analog-to-digital converters can be configured for converting the respective first and second electrical I and Q signals into respective electrical digital signals. The system can include a multiplexer and/or a de-multiplexer. The multiplexer can be in direct or indirect optical communication with the de-multiplexer. The optical coupler can be a Mach-Zehnder interferometer. 
     Aspects of the disclosed technology include an optical system comprising an optical modulator that can outputs an in-phase (I) signal and a quadrature phase (Q) signal; a delay element for delaying the in-phase (I) signal and the quadrature phase (Q) signal by a pre-determined time period to produce a delayed in-phase (I) signal and a delayed quadrature phase (Q) signal; a polarization beam combiner (PBC) that can output the in-phase (I) signal, the quadrature phase (Q) signal, the delayed in-phase (I) signal, and the delayed quadrature phase (Q) signal as a folded optical signal having polarized light corresponding to a first polarization component; and a receiver that can receive the optical signal, the receiver including a polarization beam splitter (PBS) that separates the received optical signal into the first polarization component and a second polarization component. The receiver can comprise a polarized hybrid element for recovering respective in-phase (I) and quadrature phase (Q) optical signals from the folded optical signal. The first polarization component can corresponds to X-polarized light and the second polarization component corresponds to Y-polarized light. The polarized hybrid element can comprise a X-polarized hybrid element. The first and second photodetector/transimpedance amplifiers can be coupled to an output of for receiving the respective in-phase (I) and quadrature phase (Q) optical signals and produce respective first and second electrical I and Q signals. First and second analog-to-digital converters can convert the respective first and second electrical I and Q signals into respective electrical digital signals. 
     Aspects of the disclosed technology can include a method for transmission of optical signals. The method can include modulating a baseband information signal to produce an in-phase (I) signal and a quadrature phase (Q) signal; delaying the in-phase (I) signal and the quadrature phase (Q) signal by a pre-determined time period to produce a delayed in-phase (I) signal and a delayed quadrature phase (Q) signal; combining the in-phase (I) signal, the quadrature phase (Q) signal, the delayed in-phase (I) signal, and the delayed quadrature phase (Q) signal as a folded optical signal having polarized light corresponding to a first polarization component; and separating the received optical signal into the first polarization component and a second polarization component. The method can include recovering respective in-phase (I) and quadrature phase (Q) optical signals from the folded optical signal at a receiver containing a polarized hybrid element. The method can include the first polarization component corresponding to X-polarized light and the second polarization component corresponds to Y-polarized light. The method can include the polarized hybrid element comprising an X-polarized hybrid element. The method can include receiving the respective in-phase (I) and quadrature phase (Q) optical signals and produce respective first and second electrical I and Q signals occurs at a first and a second photodetector/transimpedance amplifiers are coupled to an output. The method can include converting the respective first and second electrical I and Q signals into respective electrical digital signals occurs at a first and a second analog-to-digital converters. The method can further include the use of a de-multiplexer. The de-multiplexer can demultiplex signals. The method can include the use of a multiplexer in direct or indirect optical communication with the de-multiplexer. The method can include multiplexing an optical signal within a transmitter. The method can include de-multiplexing an optical signal or a signal derived therefrom within a receiver. 
     Aspects of the disclosed technology can include an optical transmission system comprising a transmitter and a receiver. The transmitter can comprise a laser; at least one Mach Zehnder modulator optically coupled to the laser; a multiplexer optically coupled to the at least one mach zender modulator; a polarization beam combiner coupled to the multiplexer and configured to output an encoded signal received from the multiplexer onto an optical fiber. The receiver can comprise a polarization beam splitter configured to receive the encoded signal; at least one of an optical coupler or a Mach-Zehnder interferometer optically coupled to the polarization beam splitter; a de-multiplexer optically coupled to the at least one optical coupler or Mach-Zehnder interferometer to receive an optical signal comprising the encoded signal; and a 90 degree hybrid coupled to a local oscillator signal generated at the transmitter and configured to receive the folded optical signal from the de-multiplexer. The system can comprise a digital signal processor configured to perform a single tap partial response signal recovery. The polarization beam splitter outputs a first optical signal on a first optical output port and a second optical signal on a second optical output port, the first optical signal having a first polarization component and the second optical signal having a second polarization component. A time delay module can receive the first optical signal or the second optical signal from the polarization beam splitter and transmits a time delayed optical signal to the Mach-Zehnder interferometer. The polarization rotator can be configured to rotate a polarization component of either the second optical signal or the delayed second optical signal into a polarization state corresponding to the first polarization component. 
     Aspects of the disclosed technology can include an optical transmission system comprising a transmitter and a receiver. The transmitter can comprise a laser; at least one mach zehnder modulator optically coupled to the laser; a multiplexer optically coupled to the at least one Mach Zender modulator; a polarization beam combiner coupled to a multiplexer and configured to output an encoded signal received from the multiplexer onto an optical fiber; a phase shifter. The receiver can comprise a polarization beam splitter configured to receive the encoded signal; at least one of an optical coupler or a Mach-Zehnder interferometer optically coupled to the polarization beam spliter; a de-multiplexer optically coupled to the at least one optical coupler or Mach-Zehnder interferometer to receive an optical signal comprising the encoded signal; and a 90 degree hybrid coupled to a local oscillator signal generated at the transmitter and configured to receive the folded optical signal from the de-multiplexer. The system can comprise a digital signal processor configured to perform a single tap partial response signal recovery. The polarization beam splitter can output a first optical signal on a first optical output port and a second optical signal on a second optical output port, the first optical signal having a first polarization component and the second optical signal having a second polarization component. The time delay module can receive the first optical signal or the second optical signal from the polarization beam splitter and transmits a time delayed optical signal to the Mach-Zehnder interferometer. The polarization rotator can be configured to rotate a polarization component of either the second optical signal or the delayed second optical signal into a polarization state corresponding to the first polarization component. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The accompanying drawings are not intended to be drawn to scale. Like reference numbers and designations in the various drawings indicate like elements. For purposes of clarity, not every component may be labeled in every drawing. In the drawings: 
         FIG.  1    illustrates a schematic example system of a possible 4D receiver. 
         FIG.  2    illustrates a schematic example system according to aspects of the disclosure which can be used for 2D modulation formats. 
         FIG.  3    illustrates a schematic example system according to aspects of the disclosure which can be used for 1D modulation formats. 
         FIG.  4    illustrates a schematic example system according to aspects of the disclosure. 
         FIG.  5    illustrates a schematic example system according to aspects of the disclosure. 
         FIG.  6    illustrates an example digital signal processor according to aspects of the disclosure. 
         FIG.  7    is an example schematic view of a method of forward propagation maximum likelihood sequence estimation according to aspects of the disclosure. 
         FIG.  8    is an example schematic view of a method of backward propagation maximum likelihood sequence estimation according to aspects of the disclosure. 
         FIG.  9    illustrates example aspects of performance of aspects of the disclosure. 
         FIG.  10    is a schematic example system according to aspects of the disclosure which in some examples can be used for 1D modulation formats. 
         FIG.  11    is a schematic example system according to aspects of the disclosure which in some examples can be used for QAM modulation formats. 
         FIG.  12    is a schematic example system according to aspects of the disclosure which in some examples can be used for multiple modulation formats, including PAM or QAM. 
         FIG.  13    is a schematic example computer system according to aspects of the disclosure. 
     
    
    
     DETAILED DESCRIPTION 
     Overview 
     Aspects of the disclosed technology enable the transmission of certain 2D and 1D modulation formats, such as QAM, PAM, and other optical transmission formats, without the use of a 4D receiver through the introduction of a methods, systems, and apparatuses related to a class of polarization-folding based coherent optical technology. 
     For example, aspects of the disclosed technology may comprise a coherent optical receiver that processes a received optical signal by separating the X- and Y-polarization components, rotates the Y-polarization component into the X-polarization space, delays the rotated Y-polarization component by one or more symbol periods (e.g., one or more T) before recombining or folding, through a 3 dB optical coupler, the delayed Y-component into the X-component. In other examples, the concept of folding may be considered the acts of rotating the Y-polarization component into X-polarization space or state and combining the rotated Y-component with the X-component via a 3-dB optical coupler. The folded Y-component may be detected as a delayed, by one or more symbol periods, X-polarized signal. The resulting combined or folded signal may be detected using a phase diversity 2D coherent receiver, which employs less electronic components, such as for example photo detectors (PDs), transimpedance amplifiers (TIAs), analog-to-digital converters (ADCs), than a 4D vector coherent receiver. In some examples, the 2D coherent optical receiver may require only about one-half the number of electronic components as a 4D vector receiver. 
     In another example, aspects of the disclosed technology may be employed at a transmitter and a receiver in an optical network. For instance, a QAM transmitter may be configured such that both outputs of the in-phase/quadrature (I/Q) modulator are utilized. More specifically, one output of the I/Q modulator may be delayed by one or more symbol period T and combined with the other output using a polarization beam combiner (PBC). In this example, the transmitted Y-polarization component is essentially a delayed copy of the I/Q-folded X-polarization component, implying a redundant signal being carried over the Y-polarization component. In this example, a receiver comprises a PBS to generate the X- and Y-polarized signals. Because the Y-component was folded at the transmitter, the received X-polarized signal includes both the original X-polarized optical signal component and Y-polarized optical signal component. Thus, only processing of the X-polarized signals at the receiver may be necessary. This example may result in a 3 dB link budget gain. In addition, in this example, the receiver need not employ polarization folding functionality. 
     Aspects of the disclosed technology may thus enable a less complex receiver design for coherent detection and demodulation of 2D and 1D modulated optical signals as compared to a 4D vector coherent receiver. 
     Aspects of the disclosed technology enable the use of a 2D vector coherent optical receiver to detect and demodulate 2D or 1D modulated optical signals without using an external endless optical polarization controllers. Aspects of the disclosed technology allow for polarization folding. Aspects of the disclosed technology include improved transmitter, receiver and digital signal processors, which can in some examples, be configured to work with polarization folded signals. For instance, in accordance with an aspect of the disclosed technology, digital signal processors may implement a state-reduced and multiplier-free algorithm in processing the signals output from a receiver configured to detect the polarization folded signals. Such digital signal processors may likely exhibit reduced power consumption. 
     In addition, the disclosed technology may avoid the use of external endless optical polarization controllers. The disclosed technology may also avoid an extra optical loss from an optical polarization controller and uses a simplified coherent receiver “front end.” 
     Aspects of the disclosed technology may also increase robustness against random link polarization changes. The disclosed technology, as compared to techniques employing polarization and phase diversity 4D vector coherent receivers, may reduce the required number of photodetectors (PDs), transimpedance amplifiers (TIAs) and analog-to-digital converters (ADCs) by one-half. 
     Aspects of the disclosed technology may enable smoother direct detection to coherent detection transition in DC interconnection networks as well as lower cost mobile front/middle haul and fiber access networks. Furthermore, the disclosed technology may meet or resolve the polarization diversity requirements for technologies such as photonic integrated circuits, such as for example, silicon, Indium Phosphide based, or others circuits, which are inherently polarization sensitive. 
     Aspects of the disclosed technology may be used in short-reach optical communication applications such as data center (DC) interconnects, mobile (5G/6G) front/middle haul as well as future high-speed fiber access networks. The disclosed technology enables a simpler receiver for coherent detection of 2- or 1-dimensionally (2D or 1D) modulated optical signals (as compared to the conventional phase- and polarization-diversity 4D vector coherent optical technique). The proposed new coherent optical technology can enable smoother direct detection to coherent detection transition in the DC interconnection networks (from 200 Gb/s per wavelength to 400 Gb/s per wavelength) as well as lower cost mobile front/middle haul and fiber access networks. 
     Aspects of the disclosed technology allow for use of a 2D or 1D coherent receiver in short reach transmission systems, or in systems where high SE may be less critical such as for example traditional metro and long-haul optical networks. As one example, to scale datacenter interconnects from 200 Gb/s per wavelength IM-DD based technology to 400 Gb/s per wavelength coherent technology, 2D single polarization (SP) 16QAM could be a better choice than the 4D polarization-multiplexed (PM)-16QAM, since the SP-16QAM requires only two Mach-Zehnder modulators (MZMs) while the PM-16QAM require 4 MZMs. For 5G/6G middle/front haul and fiber access networks where the required data rate is lower while fiber CD/PMD may still be a significant problem, 1D coherent PAM (or 2D SP-xQAM) may be a better choice than the 4D PM-xQAM, since the 1D PAM only requires 1 modulator while the PM-xQAM requires 4 modulators. Scaling of this magnitude is enabled by the disclosed technology. 
     Example Systems 
     The following example systems illustrate aspects of the disclosed technology. A person of skill in the art should understand that the various disclosed components can be coupled electronically by one or more of the disclosed electronics, processors, and computing devices to perform the methods and techniques disclosed herein. For simplicity and clarity, not every electronic or data link is illustrated. 
     With reference to the Figures below, rotation of an “X” and “Y” component of light are described. A person of skill in the art will appreciate that the “X” and “Y” components described are one formulation or convention to represent the transmission of light, and that further, either component can be rotated or “folded.” 
       FIG.  1    is a diagram illustrating an example polarization and phase diversity 4D vector coherent receiver, receiver  100 . Receiver  100  consists of a polarization beam splitter (PBS)  102  component or circuitry, local oscillator (LO)  104  circuitry, X-polarization hybrid  106  component or circuitry, Y-polarization hybrid  108  component or circuitry, photodetectors (PDs), transimpedance amplifiers (TIAs) components or circuitry  110 ,  112 ,  114 ,  116 , analog to digital convertors (ADCs) circuitry  118 ,  120 ,  122 , and  124 , and a digital signal processor (DSP) circuitry  126 . The hybrid is an optical device used to coherently mix the incoming optical signal and the local oscillator (LO) for coherent detection systems. The X-polarization hybrid is used for the X-polarization signal component while the Y-polarization hybrid is used for the Y-polarization signal components. The component or circuitry may comprise optical and/or electrical circuitry. A PBS may comprise an optical element that may change the polarization of light passing through it based on optical effects such as birefringence and could be considered an optical circuit element. Other components or circuitry such as TIAs and ADCs may comprise electrical components such as one or more resistors, transistors, capacitors, operational amplifiers, current or voltage supply, ground leads, comparators, digital processing elements, etc. configured to carry out their function as would be understood by those of skill the art. 
     PBS  102  can receive a signal which can be modulated or configured according to an encoding scheme. For example, the PBS may receive QAM encoded information as a light signal. PBS  102 , for example, may receive PM-QAM, SP-QAM or SP-PAM optical signals. PBS  102  may split a beam of light carrying such optical signals into two orthogonal polarization states or components, such as an “X” polarization and a “Y” polarization component. In some examples, PBS  102  may be a plate beamsplitter or a cube beamsplitter. 
     Local oscillator  104  provide a local reference signal which is provided to X-polarization hybrid  106  and Y-polarization hybrid  108 . At the X-polarization hybrid  106  and Y-polarization  108  circuitry, X-polarized component and Y-polarized component signals from PBS  102  are interfered with or mixed using the LO or reference signal so as to extract the phase information from the signal, e.g., the I and Q components. The signals from the X-pol. and Y-pol. hybrids  106 ,  108  comprises each of I and Q signals that are fed to PD/TIAs  110 - 116 . [Inventor Question: The eight lines going into the PD/TIAs are respective, I+, I−, Q+, Q− signals for each of the X- and Y-signals derived from the X- and Y-components. 
     PD/TIAs components or circuitry  110 - 116  may comprise any combination of photodetectors and transimpedance amplifiers. In general, a photodetector may be any semiconductor device that converts light into an electrical current. Photodetectors may comprise a photodiode or a photosensor. The disclosed technology is not limited to any particular photodetector and any photodetector capable of converting light photons into electric current may be used in  FIG.  1    as well as in the other example systems where PDs are employed. A photodetector can also be made of an array of photodetectors. In general, a transimpedance amplifier (TIA) can be a current to voltage converter device which can be used to amplify the current output of a photodetector or other photon or light detection device. PD-TIAs can thus be used to detect both the in-phase (I) and quadrature (Q) components of the light signals output by the X-pol. and Y-pol. hybrids  106 ,  108  and output respective I and Q signals for associated with each of the X-polarized and Y-polarized components. 
     Signals outputted from PD-TIAs may be converted by ADCs  118 - 124  from analog signals to digital signals. These digital signals are digital representations of the respective I and Q signals. 
     Digital signal processor  126  receives the digital signals output from ADCs  118 - 124 . Digital signal processor  126  may then process the signals it receives to extract information encoded and transmitted over the fiber channel or cable from a transmitting station or transmitter. 
     As shown, receiver or system  100  employs two 90° hybrid blocks or circuitry, four PD/TIAs and four ADCs. Receiver  100  is an example of a 4D vector receiver. Such receivers are not only typically used to recover 4D signal formats, but also 2D and 1D. However, given the additional circuit components employed by such receivers, such receivers come at additional cost, even in deployments or applications, e.g., short range 2D and 1D, where using such 4D vector receivers may not be entirely necessary. 
       FIG.  2    depicts an example system  200  illustrating coherent optical technology in accordance with one or more aspects of the disclosed technology. The system  200  may be used for transmission and recovery of information encoding using 2D modulation formats. In  FIG.  2    a description is given for the use of the system  200  for 2D modulation, such as a QAM or APSK format. System  200  can also be modified to transport signals modulated in accordance with a 1D format, such as a 1D PAM format, as shown in  FIG.  3    and explained below. 
     System  200  may include a transmitter  210  and a receiver  230 . In some examples, transmitter  210  can comprise a light source, such as laser  212 . Laser  212  can be any light source, including but not limited to any combination of lasers, e.g., specially designed semiconductors, incandescent light, electrodeless lamps, or halogen lamps. As another example, laser  212  can be a distributed feedback laser. Laser  212  can be controlled with a controller or a computer to operate the laser in a manner to allow transmission of the modulated light. Laser  212  is coupled optically to modulator  214 . 
     In some examples, modulator  214  can be a QAM modulator or an amplitude-phase shift keying (APSK) modulator. In other examples, modulator  214  can produce other 2D modulation formats. Modulator  214  includes a first Mach-Zehnder modulator (MZM)  215  which receives a portion of an optical signal generated by laser  212  and a second MZM  216  which also receives a portion of the light generated by laser  212 . The first MZM  215  generates the in-phase or I signal, while the second MZM  216  and phase shifter  218  generate the quadrature or Q signal. In some examples, a Mach-Zehnder modulator (MZM) can be an interferometric structure which is made from materials with strong electro-optic effects, such as for example, LiNbO 3 , GaAs, and InP. Through the selective application of electric fields within the paths of the MZM, such as to the arms of the MZM, the optical lengths traveled by an optical signal can change, thus resulting in phase modulation of the optical signal. In some examples, combining the different phase modulation converts phase modulation into intensity modulation. 
     A 90° (π/2) phase shift is introduced to the signal output by MZM  216  by element  218 . Element  218  may comprise any 90° optical phase shifter. Some examples of such phase shifters include thermal phase shifter and electro-optical phase modulators. 
     The signals from MZM  215  and phase shifter  218  are combined through a 3-dB coupler (illustrated via combining the two lines into one at the output of transmitter  210 ) to form the output of modulator  214 , which output may be inserted into an optical fiber (illustratively depicted as the arrow from modulator  214 ) for transmission from the transmitter  210  to receiver  230 . 
     At receiver  230 , the transmitted signal first encounters PBS  232 . PBS  232  may be similar to PBS  102 . Thus, PBS  232  can separate the “X” and “Y” polarization components of the received optical signal and output those as separate signals X- and Y-components. In some examples, the PBS  102  also additionally rotates the Y-component so that it is also output as X-polarized signals. In such examples, the signals at both output of PBS  102  comprise X-polarized signals as a result of the rotation of the Y-component signal. However, the rotation of the “Y” component need not occur at or in the PBS and can, as explained below, occur at an optical coupler or after delay bock  234 . 
     The “Y” component signal (which has now been rotated into a X-polarization state) is fed to a time delay element  234 , which delays the signal it receives by one or more symbol periods T. In some examples, the time period ‘T’ can be related to a period of a frequency of the light which has been encoded and being transmitted that is determined so as to avoid destructive interference between a delayed portion of an optical signal and a portion which has not been delayed, such as for example, the X-polarization and Y-polarization components. The signals outputted from the PBS and the time delay module  234  are coupled to an optical coupler (OC)  236 , which then combines them into an output signal  239 . As a result of the rotating the Y-polarization component onto to X-polarized signals, delaying it by a symbol period T and combining or folding delayed signal X-polarized signal from the X-polarized component, output signal  239  includes two copies of the X-polarized signals, first X-polarized signals outputted from the output from a first port of PBS  232 , and second delayed X-polarized signals as a result of the polarization rotation within PBS  232  and folding within 3 dB coupler  236 . Output signal  239  may therefore be further processed as the I and Q components of only X-polarized signals, eliminating the need for a “4D” vector coherent receiver. 
     Collectively, PBS  232 , time delay module  234  and optical coupler  236  may be considered a polarization-folding unit  240 . In some examples, the concept of folding may be considered the act of combining, at OC  236 , the X-signals from one port of the PBS  232  with the Y-signals rotated into the X-polarized space from the other port of PBS  232  and delayed by delay element or block  234 . In other examples, the concept of folding may be considered the acts of rotating in PBS  232  and combining in OC  236 . Optical coupler  236  can lead to a decay in signal strength. In some examples, an optical coupler may cause a loss of signal strength on the order of 3 dBs. A person of skill in the art will appreciate that although a separate optical rotator has not been illustrated, polarization-folding unit  240  can contain a separate optical rotator at other locations along the optical path, such for example a rotator to rotate the Y-polarization component as part of delay element  234 , or as part of optical coupler  236 , as long polarization rotation occurs before combining via a coupler. In addition, in some examples, instead of rotating the Y-component into the X-polarization space, the X-component may be rotated into Y-polarization space, delayed by one or more symbol periods, and then combined in a coupler with the Y-signal associated with the Y-component. In this example, two signals appearing as Y-polarized light (one delayed and the other not delayed) may be processed as shown in  FIG.  2   . 
     The output from optical coupler  236  can be mixed or interfered with a signal from a local oscillator  238  so that the I and Q components of output signal  238  are recoverable (e.g., I(t), I(t−T), Q(t), Q(t−T) for the X-polarized signals). Local oscillator can be similar to local oscillator  104 . The signal from local oscillator  238  and output from optical coupler  236  can be transmitted to a 90 degree hybrid  242 . Although the 90 degree hybrid is receiving only “X” polarized signals, the “Y” component, referred to herein as the “Y” signal after arriving at a receiver, can recognized as it has been delayed by a period of “T.” Thus, it is possible to distinguish between the “X” and “Y” portion of the signal being transmitted by transmitter  210 . ‘T’ can be a constant or a multiple of a constant such that the two components of light do not destructively interfere with one another. 
     90 degree hybrid  242  outputs the X polarized light which contains both the information in the x and the y signal and can contain both the I and Q component of the light. The signal outputted from the 90 degree hybrid  242  is transmitted to PD/TIA  243  and PD/TIA  244 . PD/TIAs  243 - 244  can be similar to PD/TIAs  110 - 116 . PD/TIA  243  output analog electrical signals of the I and Q signals to respective ADCs  245  and  246  as shown. The output of ADCs  245  and  246  are then coupled to DSP  250 . 
     With reference to  FIG.  2   , the following equations may be used to describe the behavior of system  200 . For simplicity, the carrier phase is neglected in the formulations which follow. In this regard, the signal output of a QAM transmitter can be modeled by the following equation:
 
{circumflex over ( E )}( t )=[ I ( t )+ jQ ( t )]) {circumflex over (x)}   (1)
 
where:
         Ê T : The outputted signal of a QAM transmitter as a function of time.   I(t): The “in-phase” component of the outputted signal as a function of time.   Q(t): The quadrature or perpendicular component of the outputted signal as a function of time.   j: An “imaginary” component related to phase.   {circumflex over (x)}: The ‘X’ component or ‘X’ polarization of the outputted signal.       

     For short-reach optical communications that use optical fiber as the communications medium, the state of polarization (SOP) of the transmitted signal may change during transmission. The relationship between the transmitted signals or signals input into the fiber and the received signals or signals output from the fiber after transmission can be represented by a polarization matrix. That matrix may be modeled as 2×2 unitary matrix with two independent angle parameters, α and θ as follows: 
     
       
         
           
             U 
             = 
             
               ( 
               
                 
                   
                     
                       cos 
                       ⁡ 
                       ( 
                       α 
                       ) 
                     
                   
                   
                     
                       
                         sin 
                         ⁡ 
                         ( 
                         α 
                         ) 
                       
                       ⁢ 
                       
                         e 
                         
                           
                             - 
                             j 
                           
                           ⁢ 
                           θ 
                         
                       
                     
                   
                 
                 
                   
                     
                       
                         - 
                         
                           sin 
                           ⁡ 
                           ( 
                           α 
                           ) 
                         
                       
                       ⁢ 
                       
                         e 
                         
                           
                             - 
                             j 
                           
                           ⁢ 
                           θ 
                         
                       
                     
                   
                   
                     
                       cos 
                       ⁡ 
                       ( 
                       α 
                       ) 
                     
                   
                 
               
               ) 
             
           
         
       
     
     Applying the polarization matrix to ET allows the polarized rotated signal to be represented as:
 
 Ê   R ( t )=cos(α)[ I ( t )+ jQ ( t )]{circumflex over ( x )}−sin(α) e   −jθ [ I ( t )+ jQ ( t )]{circumflex over ( y )}  (2)
 
where:
         ŷ: The ‘Y’ component or ‘Y’ polarization of the outputted signal.   α: The angle between the actual signal oscillation direction (the signal vector direction in the X- and Y-polarization space) and the reference direction. α can take values between 0 to 90 degrees.   Θ: The phase difference between the X-polarized component and the Y-polarized component. Θ can take values between 0 to 90 degrees.       

     This equation represents the received polarization-rotated 2D vector optical signal at the input to receiver  230  at folding unit  240 . 
     With reference to equation 2, the portion preceding the {circumflex over (x)} can be considered to be the “X” signal and the portion preceding the ŷ can be considered to be the “Y” signal. As the {circumflex over (x)} or ŷ polarizations may be rotated, the component of each polarization can be referred to as the signal from each component after transmission from the transmitter and at the input of a receiver. With reference to other Figures used in this disclosure, the “X” and the “Y” signal can have similar meaning. 
     PBS  232  separates the X and Y received polarization components, as well as rotates the Y-polarization component into the X-polarization component. As the Y component is delayed by a time of ‘T’, the signal leaving polarization-folding unit  240  can be represented as: 
                         E   ˆ       R   ⁢   x       (   t   )     =           √   2     2     ⁢       cos   ⁡   (   α   )     [       I   ⁡   (   t   )     +     j   ⁢     Q   ⁡   (   t   )         ]     ⁢     x   ˆ       -         √   2     2     ⁢     sin   ⁡   (   α   )     ⁢       e       -   j     ⁢   θ       [       I   ⁡   (     t   -   T     )         +     j   ⁢     Q   ⁡   (     t   -   T     )         ]     ⁢     x   ˆ                 (   3   )               
Ê Rx (t) is 2D vector optical signal, which can be detected by a phase-diversity 2D coherent receiver as shown in  FIG.  2    and can be viewed as the result of folding the Y-polarization component into the X-polarization component. This approach may be considered as polarization folding coherent technology. Introduction of the delay T, or multiple T, before folding the Y-polarization component into the X-polarization space mitigates against destructive interference between X-polarization component and Y-polarization component under certain link polarization conditions. One skilled in the art should appreciate from Ê Rx (t) that it includes both the originally received X-polarization optical signal component, cos(α)[I(t)+jQ(t)], and that the originally received, but delayed, Y-polarization optical signal component, sin(α)e −jθ [I(t−T)+jQ(t−T)].
 
     As a delay of ‘T’ was introduced on the Y polarization component before it was folded back into the X component, the polarization-folded optical signal shown in equation (3) above can be understood to be a 2D 1-tap partial response signal. This signal can be demodulated using one or more algorithms. Non-limiting examples of applicable algorithms include partial-response signal recovery algorithms such as for example, maximum-likelihood sequence estimation (MSLE) algorithms. 
       FIG.  3    depicts an example system  300  illustrating coherent optical technology in accordance with one or more aspects of the disclosed technology. System  300  may include a transmitter  310  and a receiver  330 . Transmitter  310  can comprise a light source, such as laser  312 . Laser  312  can be similar to laser  212 . Laser  312  can be optically coupled to modulator  314 . Modulator  314  can be a modulator configured to modulate a “1D” format of light, e.g. SP-PAM. The output of transmitter  310  can be transmitted to receiver  330 . During transmission from transmitter  310  to receiver  330 , the orientation of the light which was generated at transmitter  310  can change in orientation, as explained above with reference to  FIG.  2    through the representation of matrix U. Transmitter  310  will thus transmit light with only a quadrature or in-phase component of light in one direction of polarization. As transmitter  310  is a “1D” transmitter, it can modulate only one the in phase or quadrature component of light, eliminating the need for two MZMs. 
     At receiver  330 , similar to  FIG.  2   , a transmitted signal first encounters PBS  332 . PBS  332  may be similar to PBS  102  or  232 . PBS  232  can separate the “X” and “Y” polarization components of the received optical signal and output those signals as an X signal and a Y signal. In some examples, PBS  232  can rotate one of the components rotates the Y-component so that it is also output as X-polarized signals. However, the rotation can occur at other components of receiver  330 , such as before optical coupler  336  or at time delay element  334  as explained herein. 
     While light modulated from transmitter  310  was modulated only with X-polarization, the signals outputted from PBS  332  can comprise X-polarized and Y-polarized signals as a result of the rotation light during transmission. The “Y” component signal (which has now been rotated into a X-polarization state) is fed to a time delay element  334 , which delays the signal it receives by a symbol period T. Time delay element  234  is capable of receiving and then delaying the transmission of a received signal by a period of time period of “T.” In some examples, the time period ‘T’ can be related to a period of a frequency of the light which has been encoded and is being transmitted to avoid destructive interference between a delayed portion of an optical signal and a portion which has not been delayed, such as for example, the X-polarization and Y-polarization components. 
     The signals outputted from the PBS (X signal) and the time delay module  234  (Y signal) are coupled to an optical coupler (OC)  336 , which then combines them into an output signal. This output signal can be sent to a 90 degree hybrid  342 . 90 degree hybrid  342  can be similar to 90 degree hybrid  242 . 90 degree hybrid can also receive a signal from a local oscillator  338  which can be similar to local oscillator  238 . Similar to the function described in receiver  230 , local oscillator  338  can provide a reference signal to assist with signal extraction. 
     Similar to the process described with respect to  FIG.  2   , 90 degree hybrid  342  outputs the X polarized light which contains both the information in the X and the Y signal and can contain both the I and Q component of the light. The signal outputted from the 90 degree hybrid  342  can be transmitted to PD/TIA  343  and PD/TIA  344 . PD/TIAs  343 - 344  can be similar to PD/TIAs  110 - 116 . PD/TIAs  343 - 344  output analog electrical signals of the I and Q signals to respective ADCs  245  and  246  as shown. The output of ADCs  345  and  346  are then coupled to DSP  350 . DSP  350  can recover the transmitted 1D format signal. 
       FIG.  4    depicts an example system  400  illustrating coherent optical technology in accordance with one or more aspects of the disclosed technology. System  400  may include a transmitter  410  and a receiver  430 . Transmitter  410  can comprise a light source, such as laser  412 . Laser  412  can be similar to laser  212  or laser  312 . Laser  412  can be optically coupled to modulator  414 . Modulator  414  can be similar to modulator  314 . 
     System  400  includes a transmitter which delays one output of an I/Q modulator relative to the other by a symbol period and combines the delayed and un-delayed I/Q signals in a polarization beam combiner (PBC) for transmission through an optical fiber. In some examples, the transmitter can be configured to modulate two-dimensional QAM modulation formats. 
     As shown in  FIG.  4   , modulator  414  may include a Mach-Zehnder modulator (MZM)  315  which receives the inphase component of an optical signal generated by laser  412  and a Mach-Zehnder modulator  416  which receives a quadrature component of light generated by laser  412 . Modulator  416  can be optically coupled with an element  418 . Element  418  is capable of shifting or changing the phase of the angle of light. Although  FIG.  4    illustrates element  418  to be the angle of light by 90 degrees or π/2 radians, element  418  can shift the angle of light by configurable degree. The signal transmitted from the phase shifter  418  can be represented as I(t)+jQ(t). 
     Modulator  416  can be optically connected to a time delay module  419 . Time delay module can be similar to time delay module  214  and can delay the optical signal by a time period of ‘T,’ corresponding to one or more symbol time periods. In general, T may be chosen or determined so that the X and Y components of light do not destructively interfere with one another. The signal which is emitted from time delay module  419  can be represented as jI(t−T)+Q(t−T). The optical signals from element  418  and from time delay module  419  can arrive at PBC  420 , which can combine both components of the transmitted optical signal. 
     The output of transmitter  410  can be represented as:
 
 Ê   R ( t )=cos(α)[ I ( t )+ jQ ( t )]{circumflex over ( x )}−[ jI ( t−T )+ Q ( t−T )]{circumflex over ( y )}  (4)
 
     As a person of skill in the art will appreciate from the equation above, as the X component and Y component are functions shifted by ‘T’ in time, it is possible to extract identical information from only the x or the y component. In some examples, it is possible or may be desirable to discard the x or y component of the signal above and only analyze the remaining portion. 
     The signal can be received by the receiver  430 . Receiver  430  can be similar to receiver  330  and contain a PBS  432 , which can be similar to PBS  332 . PBS  432  can split the received optical signals into an X signal corresponding to the {circumflex over (x)} component and a Y signal corresponding to the ŷ component. As will be appreciated from the equations described herein, the Y component is a redundant copy or otherwise generally contains the same information encoded within the X component signal, and can thus be discarded. In some examples, no analysis or monitoring the Y component will take place. In other examples, a y component of the optical signal can optionally be monitored for analysis or quality of service requirements. 
     Upon transmission, the {circumflex over (x)} component of the optical signal received at receiver  430  and transmitted through optical fiber can be represented as:
 
 Ê   Rx ( t )=cos(α)[ I ( t )+ jQ ( t )] {circumflex over (x)} −sin(α) e   −jθ [ I ( t−T )+ jQ ( t−T )] {circumflex over (x)}   (5)
 
     The X signal above received at PBS  432 , separated into an X only optical path, and thereafter be transmitted to a 90 degree hybrid  442 . 90 degree hybrid  442  can also receive a signal from local oscillator  438 . Local oscillator  438  can be similar to local oscillator  238  and be used as a reference signal to recover the in-phase and quadrature signals. 
     In a manner similar to that described with respect to the figures above, an optical signal transmitted from 90 degree hybrid  442  can be received at PD/TIAs  443  and  444 . PD/TIAs  444  and  446  can be similar to PD/TIAs  243  and  244 . Similar to system  200  and system  300 , PD/TIA  443  and  444  can be connected to ADCs  445  and  446 , which are in turn connected to a DSP  450 . DSP  450  can be similar to the DSP described with reference to  FIG.  6   . 
     As will be appreciated by a person of skill in the art, as compared to system  200  and system  300 , system  400  does not require an optical coupler. In this manner, a signal loss due to the optical coupler is avoided. As the signal is contained within the X component, an additional receiver side polarization-folding is not required. The transmission link plus the receiver PBS equivalently performs the polarization folding function, for example, a 2D receiver can be used to recover a 2D modulated signal. 
       FIG.  5    illustrates additional aspects of the disclosed technology.  FIG.  5    illustrates system  500 . In some examples, system  500  can be used for “1D” modulation formats, such as for example, 1D PAMs. As will be appreciated from the description below and  FIG.  5   , system  500  enables the transmission of 1D modulation formats without the need for an optical rotator. 
     System  500  can contain a transmitter  510  and a receiver  530 . Transmitter  510  can contain a laser  512 , which can be similar to the lasers described above, such as laser  212 . Transmitter  510  can contain an MZM  815  which can be similar to MZMs  215  or MZM  216 , a time delay module  519  which can be similar to time delay module  419 , and a PBC  520  which can be similar to PBC  320 . Light emitted from laser  512  can be transmitted to MZM  515 , and in turn to the time delay module  519  and the PBC  520 . The light signal received at time delay module  519  can be sent to PBC  820  after adding a time delay of “T” to the signal. The light emitted from PBC  520  can be carried over an optical fiber or other medium to receiver  530 . 
     Receiver  530  can be similar to receiver  430 , and contain a PBS  532 , similar to PBS  432 , which receives a signal from PBC  520 . Similar to the description given above with reference to  FIG.  4   , the “x” or “y” component of the signal can be utilized while the other portion of the signal discarded or optionally used as a monitor port. PBS  532  can split the received optical signals into an X signal corresponding to the {circumflex over (x)} component and a Y signal corresponding to the ŷ component. In some examples, no analysis or monitoring the Y component will take place. In other examples, a y component of the optical signal can optionally be monitored for analysis or quality of service requirements. 
     The signal transmitted from PBS  532  can be received at a 90 degree hybrid  542 . 90 degree hybrid  542  can be similar to 90 degree hybrid  342 . 90 degree hybrid  842  can also receive a signal from LO  538 , which can be similar to LO  338 . The signal from the 90 degree hybrid  842  can be sent to PD/TTAs  533  and  534 , which can be similar to PD/TTAs  543  and  544 . The signal emitted from PD/TTAs  533  and  534  can be sent to ADCs  545  and  546 . These ADCs can be similar to  345  and  346 . The ADCs can convert the captured signal to a digital signal and transmit the signal to a DSP  550 . DSP  550  can be similar to any of the DSPs described herein, including DSPs  250 ,  350 , and  450 . 
     The X signal above received at PBS  532  is separated into an X only optical path, and thereafter transmitted to a 90 degree hybrid  542 , which can be similar to 90 degree hybrid  442 . 90 degree hybrid  542  can also receive a signal from local oscillator  538 . Local oscillator  538  can be similar to local oscillator  238  and be used as a reference signal to recover the in-phase and quadrature signals. 
     In a manner similar to that described with respect to the figures above, an optical signal transmitted from 90 degree hybrid  542  can be received at PD/TIAs  543  and  544 . PD/TIAs  544  and  546  can be similar to PD/TIAs  243  and  244 . Similar to system  200  and system  300 , PD/TIA  543  and  544  can be connected to ADCs  545  and  546 , which are in turn connected to a DSP  550 . In some examples, DSP  550  can be similar to the DSP described with reference to  FIG.  6   . 
     As will be appreciated by a person of skill in the art, as compared to system  200  and system  300 , system  500  does not require an optical coupler. In this manner, a signal loss due to the optical coupler is avoided. As the signal is contained within the X component, an additional receiver side polarization-folding is not required. 
       FIG.  6    illustrates a schematic representation of a digital signal processor (DSP)  600 . As shown in  FIGS.  2 - 4   , the output of the respective ADCs are coupled to respective DSPs for further processing. The DSPs implement the algorithms necessary to process the digital signals received from the ADCs so as to recover the transmitted information. DSP can be used for symbol or information signal recovery according to aspects of the disclosed technology. As transmission link polarization parameters can change over time, such as for example the polarization angles α and θ, the parameters or angles can be tracked in a dynamic manner. Tracking of polarization parameters (i.e. the α and θ) can occur through sending a polarization training sequence at the transmitter side, and using a lower-speed polarization parameter extraction circuit at a receiver side. Then a “single-memory-tap” 2D MLSE algorithms can used to recover the signal based on the extracted polarization parameters. Aspects of a “single-memory-tap” algorithm are described below with reference to  FIGS.  7  and  8   , such as in method  700  and method  800 . 
     DSP  600  can receive in-phase and quadrature components of an optical signal, as described for example in the configurations of  FIGS.  2  and  3   . In some examples, the components received have already been converted to a digital signal through the use of an analog to digital convertor. The received signal can be processed using a lower speed Feed-Forward Equalizer (FFE) coefficient extraction block  610 . A FFE is generally circuitry that acts a filter to compensate for frequency dependent loss of a communication channel. At block  610 , the low speed coefficients for the FFE are extracted from the recovered I and Q signals through, for example, non-streaming block by block (to allow lower-speed operation) training based or blind adaptive equalization algorithm. Block  610  communicates with a lower speed polarization coefficient extraction block  620 , which use the periodically inserted training signal to extract the two polarization coefficients (the α and θ) in a non-streaming block by block manner. High speed FFE block  630  receives the I and Q signals and outputs a signal to frequency and phase recovery block  640 . Block  640  outputs a signal which is split to clock recovery block  670  and, clock recovery block  670  recovers a clock signal  670  and LO AFC block  680  recovers a local oscillator (LO) signal whose signal frequency is automatically adjusted via automatic frequency control (AFC). Another output from block  640  is fed to partial signal recovery block  650 , which is discussed in further detail below in accordance with further aspects of the disclosed technology. The output of block  650  is coupled to symbol and forward error correction (FEC) block  650 , which outputs the recovered symbols or information. 
     Although the above description of block  600  has been given with respect to a particular architecture of blocks and circuitry, a person of skill in the art will appreciate that other configurations, settings, permutations, combinations, and variations of blocks can be used to form DSP  400 . In addition, various permutations, combinations, or reordering of the following steps referenced with respect to  FIG.  4    can be made. 
       FIG.  7    illustrates aspects of method  700 . For instance, method  700  can be considered or be part of a “single-tap” algorithm. Method  700  can be used to reduce the amount of power consumption of a DSP. In some examples, the power consumption of the DSP can be reduced by an order of magnitude. In addition, method  700  can be used to reduce the amount of implementation complexity of aspects of the disclosed technology, methods, and techniques. More specifically, the method  700  may be implemented in DSP  500  as part of partial-response signal recovery block  650 . 
     In accordance with aspects of the disclosed technology  FIG.  7    shows a swim-lane type diagram showing a technique for demodulation of a polarization folded 2D-16QAM signal. However, a person of skill in the art will appreciate that other types of coding schemes can be used in accordance with the technology described herein.  FIG.  7    also illustrates a final survival path between states, and an intermediate path. Other paths shown therein illustrate possible connections between the various states. 
     Method  700  can be used as a method of forward propagation MLSE or forward path MLSE. In some examples, the forward propagation MLSE can be used when the polarization angle is less than 45 degrees. Forward propagation MLSE can be a better choice when the polarization angle α is less than 45 degrees. For instance, the detected signal (see Eq. 5) consists of two components, one from the current symbol, which is proportional to cos(α), while the other one from the previous symbol (i.e. the delayed portion), which is proportional to sin(α). When α is less than 45 degrees, the current symbol contributes more than the previous symbol to the detected signal, this make forward-propagation MLSE works better than backward-propagation MLSE since it allows more accurate intermediate survival path determination: the intermediate survival path is determined by assuming a known pre-symbol, and then find the most likely current symbol from all possible current symbol choices, thus a larger portion in the detected signal will help more accurate symbol determination. One extreme example is if cos(α)=0, then there is no contribution from the current symbol in the detected signal, thus there is no way estimating the current symbol from the detected signal. 
     At block  710 , a set-partition algorithm can be used to reduce the number of MLSE states. For example, in a 16 QAM the number of MLSE states can be reduced from 16 regular states to a set of 4 superstates. For example, 16 regular states may each be a vector or n-tuple, but the 16 states can be combined to a 4 by nor set of n-tuples Step  510  can occur at time to. However, the steps of method  700  can occur in any order. The principle of set-partitioning is to divide the regular states into multiple groups to form superstates, where each superstate consists of multiple regular states and the Euclidean distance for states within each superstate is greater than the normal Euclidean distance for the regular states without set-partitioning. 
     At block  720 , a selection of one state from each set of superstates can occur. For example, from each super state, a single state can be chosen. The chosen state from each superstate can be considered to be a surviving state. Step  720  can occur at time ti. 
     At block  730 , a Euclidean distance based branch metric criterion to estimate distance between the states illustrated in  FIG.  7   . In some examples, a distance D used as a criterion for forward selection of the states can be defined as D=Max [Abs (I est −I det ), Abs(Q est −Q det )]. Stated alternatively, D is the maximum value of either the absolute value of (I est −I det ) or (Q est −Q det ). I and Q refer to the inphase and quadrature phases respectively. “EST” as used in the formulas above refer to estimated in-phase and quadrature signals. “DET” as used above denotes the detected in-phase and quadrature signals respectively. 
     At block  740 , a lookup table can be used to calculate the values of I est  and Q est . As can be appreciated from the discussion above, the inphase and quadrature components are related to c(α)[I(t)+jQ(t)] and sin(α)e −jθ [I(t−T)+jQ(t−T)] respectively. The calculation of the “c(α)[I(t)+jQ(t)]” term only require 4 real numbers to compute. The calculation of the “s(α)e −jθ [I(t−T)+jQ(t−T)]” term only requires 16 complex numbers to compute. The use of a lookup table and the distance above removes the need for computationally intensive and power-hungry multiplication operations. 
       FIG.  8    illustrates method  800  related to backward propagation MLSE or backward pass MLSE. For instance, method  800  can be considered or be part of a “single-tap” algorithm. As an example, the backward propagation MLSE method described with respect to method  600  can be used for demodulation of the polarized folded 2D 16 QAM signal described herein. Method  600  can be carried out similar to method  500  in selection of MLSE states but uses backward propagation rather than forward propagation to come to a final result. 
     In some examples, the forward and backward propagation techniques described herein can be selectively applied or be applied in combination. 
       FIG.  9    illustrates aspects of the disclosed technology as they relate to baseline performance.  FIG.  9    illustrates performance for a non-amplified 118 Gbaud 16QAM system using the conventional polarization and phase diversity coherent technology (left most line of  FIG.  9   ), the polarization-folding coherent optical technology with ideal 1-tap MLSE (proposed with ideal MLSE) (middle line of  FIG.  9   ) and with the proposed low-power MLSE (right most line of  FIG.  9   ). As simulated, a single laser is used for both the signal and LO, with a splitting ratio of 3 to 1. The laser power is assumed to be 13 dBm, corresponding to 11.75 dBm signal power and 7 dBm LO power. The MZM is driven with 0.8 Vpi, biasing at the null point. The T x  bandwidth (Driver and MZM) is assumed to be 70 GHz, while the PD/TIA and ADC bandwidth are assumed to be 60 Hz. TIA thermal noise is assumed to be 16 pA/Hz. The E2E link loss is defined as the end to end link loss, including the Tx MZM insertion loss, Tx coupling loss, the transmission link loss, and the Rx coupling loss. Waveguide loss and excess PBS/PBC/OC losses are neglected for the simulation described in  FIG.  9   . 
     As can be appreciated from  FIG.  9    the disclosed 2D coherent receiver technology can achieve a similar performance as the conventional 4D polarization-diverse coherent receiver when BER is below the typical KP4 FEC threshold  2   e - 4 . 
       FIG.  10    is a schematic illustration of an example system  1000 . System  1000  is an example PAM or APSK transceiver which can operate by employing the disclosed polarization-folding coherent optical technology. Any method or combination of methods described herein can be used in conjunction with system  1000 . Components of system  1000  which are interconnected are illustrated in system  100 .  FIG.  10    illustrates the operational principles of both PAM or APSK system. In some examples,  FIG.  10    can be used to implemented into a datacenter or other unit as part of a migration to the polarization-folding technology from current architectures. 
     System  1000  can contain a transmitter side  1010 , which can contain a light source, such as laser  1012 , coupled to MZMs  1015  and  1206 , a phase shifter  1018 , a coarse wavelength division multiplexing (CWDM) multiplexer (MUX) module  1019 , and a PBC  1020 . Laser  1012 , MZMs  1015  and  1016 , phase shifter  1018 , and PBC  1020  can be similar to similar components described above, such as  312 ,  315 - 316 ,  318 , and  320  respectively for example. CWDM MUX module  1019  can multiplex, and send multiple signals on a carrier channel at the same time in the form of a single complex signal. 
     At the transmitter side  1010 , the I/Q modulator can be configured to generate a PAM signal by configuring the modulator biasing conditions. To generate the PAM signal, both MZMs are biased at the quadrature, and the same data signals are used to drive the two MZMs  1015  and  1016 . To generate the optimal PAM signal, the I/Q biasing phase at phase shifter  1018  can be set to be 0. 
     Receiver  1030  can contain a PBS  1032 , a time delay unit  1033 , a CWDM demultiplex (DMUX)  1034 , a 90 degree hybrid  1042 , PD/TIAs  1043  and  1044 , and ADCs  1045  and  1046 , and a DSP  1050 . PBS  1032 , time delay unit  1033 , CWDM demultiplex (DMUX)  1034 , 90 degree hybrid  1042 , PD/TIAs  1043  and  1044 , and ADCs  1045  and  1046 , and DSP  1050  can be similar to PBS  332 , a time delay unit  333 , 90 degree hybrid  342 , PD/TIAs  343  and  344 , and ADCs  345  and  346 , and a DSP  350 . CWDM DMUX  1034  can receive, recover, and separate signals from CWDM MUX  1119 . Receiver  930  can also contain a Mach-Zehnder interferometer (MZI)  1051 . In some examples, MZI  1051  can be replaced with a 3 dB coupler. In other examples, MZI  1051  can be configured to act as a two to one coupler. The signal can then be transmitted to 90 degree hybrid  1042 , and thereafter processed by PD/TAs, ADCs, and DSP  1050  as described in this disclosure. 
     Similar to the description provided above with reference to  FIG.  3   , light generated at a laser can be modulated at by an MZM to generate an a 1D format signal, such as a PAM signal. This signal can be sent to CWDM MUX  1019 , which can multiplex various signals. Any quadrature signal need not be phase shifted or be phase shifted by 0 degrees at phase shifter  1118 . The CWDM signal can be sent to a PBC  1020 . A signal emerging from PBC  1020  can then be sent to receiver  1030  where it is received by PBS  1032 . A time delay can be introduced into a portion of the signal as split by the PBS  1032 . MZI switch  1051  can receive component signals split by PBS  1032  and act or be configured as a coupler to combine the signals. The signal can be then transmitted to CWDM DMUX  1034 , and after being demultiplexed, send a signal to 90 degree hybrid. Both signals can then be received at CWDM MUX module  1019 . These signals can thereafter be sent to PBC  1120  where they can be combined together. A signal can be transmitted from transmitter  1110  to receiver  1130  through for example, an optical fiber. PBS  1132  can thereafter receive the signal and transmit the signal over the “X signal” component to MZI switch  1151 . MZI switch  1151  can act as a 1 in to 1 out filter and transmit the signal to CWDM DMUX  1134 , which can demultiplex the signal. The signal can then be transmitted to 90 degree hybrid  1142 , and thereafter processed by PD/TAs, ADCs, and DSP  1150  as described in this disclosure. 
       FIG.  11    illustrates a schematic illustration of an example system  1100 . System  1100  is an example PAM transceiver which can operate by employing the proposed polarization-folding coherent optical technology. Components of system  1100  which are interconnected are illustrated in system  110 .  FIG.  11    illustrates the operational principles of both QAM system. In some examples,  FIG.  11    can be used to integrate into a datacenter or other unit. 
     System  110  can contain a transmitter side  911 , which can contain a light source, such as laser  1112 , coupled to MZMs  1115  and  1116 , a phase shifter  1118 , a coarse wavelength division multiplexing (CWDM) multiplexer (MUX) module  1119 , and a PBC  1120 . Laser  1112 , MZMs  1115  and  1116 , phase shifter  1118 , and PBS  1120  can be similar to similar components described above, such as  312 ,  315 - 316 ,  318 , and  320  respectively for example. CWDM MUX module  1119  can multiplex, and send multiple signals on a carrier channel at the same time in the form of a single complex signal. 
     At the transmitter side  1110 , the I/Q modulator can be configured to generate a PAM signal by simply changing the modulator biasing conditions. To generate the QAM signal, both MZMs can be biased at a null point, and two different data signals, I(t) and Q(t), can be used to drive two parallel MZMs  1115  and  1116 . A π/2 phase shift can be introduced to one MZM output signal, which is referred to as I/Q biasing phase herein. To generate the QAM signal, both MZMs can be biased at a null point, and two different data signals, I(t) and Q(t), can be used to drive two parallel MZMs  1115  and  1116 . A π/2 phase shift can be introduced to one MZM output signal, which is referred to as I/Q biasing phase herein. 
     Receiver  1130  can contain a PBS  1132 , a time delay unit  1133 , a CWDM demultiplex (DMUX)  1134 , a 90 degree hybrid  1142 , PD/TIAs  1143  and  1144 , and ADCs  1145  and  1146 , and a DSP  1150 . PBS  1132 , time delay unit  1133 , CWDM demultiplex (DMUX)  1134 , 90 degree hybrid  1142 , PD/TIAs  1143  and  1144 , and ADCs  1145  and  1146 , and DSP  1150  can be similar to PBS  332 , a time delay unit  333 , 90 degree hybrid  342 , PD/TIAs  343  and  344 , and ADCs  345  and  346 , and a DSP  350 . CWDM DMUX  1134  can receive, recover, and separate signals from CWDM MUX  1119 . Receiver  1130  can also contain a Mach-Zehnder interferometer (MZI)  1151 . In some examples, MZI  1151  can be replaced with a 3 dB coupler. In other examples, MZI  1151  can be configured to act as a two to one coupler. 
     Similar to the description provided above with reference to  FIGS.  2  and  4   , light generated at a laser can be modulated at MZMs  1115  and  1116  to generate an inphase and quadrature signal. The quadrature signal can be phase shifted at phase shifter  1118 . With reference to  FIG.  10   , the inphase signal can be sent along one path, and also be time delayed, while the other quadrature signal can be sent along another path. Both signals can then be received at CWDM MUX module  1019 . These signals can thereafter be sent to PBC  1120  where they can be combined together. A signal can be transmitted from transmitter  1110  to receiver  1130  through for example, an optical fiber. PBS  1132  can thereafter receive the signal and transmit the signal over the “X signal” component to MZI switch  1151 . MZI switch  1151  can act as a 1 in to 1 out filter and transmit the signal to CWDM DMUX  1134 , which can demultiplex the signal. The signal can then be transmitted to 90 degree hybrid  1142 , and thereafter processed by PD/TAs, ADCs, and DSP  1150  as described in this disclosure. 
       FIG.  12    illustrates a schematic illustration of an example system  1200 . System  1200  is an example dual QAM/PAM transceiver which can operate by employing the proposed polarization-folding coherent optical technology. Components of system  1200  which are interconnected are illustrated in system  1200 .  FIG.  12    simultaneously illustrates the operational principles of both a QAM and PAM system. 
     System  1200  can contain a transmitter side  1210 , which can contain a light source, such as laser  1212 , coupled to MZMs  1215  and  1216 , a rotator  1218 , a coarse wavelength division multiplexing (CWDM) multiplexer (MUX) module  1219 , and a PBS  1220 . Laser  1212 , MZMs  1215  and  1216 , rotator  1218 , and PBS  1220  can be similar to  312 ,  315 - 316 ,  318 , and  320  respectively. CWDM MUX module  1219  can multiplex, and send multiple signals on a carrier channel at the same time in the form of a single complex signal. In some examples, transmitter side  1210  can also contain a time delay unit, which is unlabeled but represented with a “T” in  FIG.  12   . 
     In some examples, there may be multiple wavelengths carrying multiple baseband signals across system  1200 . In other examples, multiple lasers or multiple DSPs can be used in parallel to transmit additional information across system  1200 . 
     At the transmitter side  1210 , the I/Q modulator can be configured to generate either QAM signal or PAM signal by simply changing the modulator biasing conditions. To generate the QAM signal, both MZMs can be biased at a null point, and two different data signals, I(t) and Q(t), can be used to drive two parallel MZMs  1215  and  1216 . A π/2 phase shift can be introduced to one MZM output signal, which is referred to as I/Q biasing phase herein. To generate the PAM signal, both MZMs are biased at the quadrature, and the same data signals, I(t) and I(t), are used to drive the two MZMs  1215  and  1216 . To generate the optimal PAM signal, the I/Q biasing phase can be set to be 0. 
     Receiver  1230  can contain a PBS  1232 , a time delay unit  1233 , a CWDM demultiplex (DMUX)  1234 , a 90 degree hybrid  1242 , PD/TIAs  1243  and  1244 , and ADCs  1245  and  1246 , and a DSP  1250 . PBS  1232 , time delay unit  1233 , CWDM demultiplex (DMUX)  1234 , 90 degree hybrid  1242 , PD/TIAs  1243  and  1244 , and ADCs  1245  and  1246 , and DSP  1250  can be similar to PBS  332 , a time delay unit  333 , 90 degree hybrid  342 , PD/TIAs  343  and  344 , and ADCs  345  and  346 , and a DSP  350 . CWDM DMUX  1234  can receive, recover, and separate signals from CWDM MUX  919 . Receiver  930  can also contain a Mach-Zehnder interferometer (MZI)  1251 . In some examples, MZI  1251  can be replaced with a 3 dB coupler. 
     At the receiver side  1230 , the polarization-folding coherent-optical technology discussed herein can be used to detect both QAM and PAM signals. To enable dual QAM/PAM operation, a 3 dB coupler can be replaced by a 2×2 or 2×1 Mach-Zehnder interferometer (MZI) based two-mode switch. In reference to the MZI, when a received signal is already polarization-folded from a new transmitter as described in this document, the MZI can configured as a 1 to 1 through filter. In some migration examples, the MZI can be configured as a 3 dB coupler in the case when a received signal from a non-polarization-folded ASK/PAM transmitter. 
       FIG.  13    is a block diagram  1300  illustrating an example computer system  1310  with which aspects of this disclosure, including the machine learning systems and techniques described herein, and any components thereof, can be implemented. In certain aspects, the computer system  1310  may be implemented using hardware or a combination of software and hardware, either in a dedicated server, or integrated into another entity, or distributed across multiple entities. In some examples, example computing system  1310  can be a user computing system or device. 
     In broad overview, the computing system  1310  includes at least one processor  1350  for performing actions in accordance with instructions and one or more memory devices  1370  or  1375  for storing instructions and data. The illustrated example computing system  1310  includes one or more processors  1350  in communication, via a bus  1315 , with at least one network interface driver controller  1320  with one or more network interface cards  1322  connecting to one or more network devices  1324 , memory  1370 , and any other devices  1380 , e.g., an I/O interface. The network interface card  122  may have one or more network interface driver ports to communicate with the connected devices or components. Generally, a processor  1350  executes instructions received from memory. The processor  1350  illustrated incorporates, or is directly connected to, cache memory  1375 . 
     In more detail, the processor  1350  may be any logic circuitry that processes instructions, e.g., instructions fetched from the memory  1370  or cache  1375 . In many embodiments, the processor  1350  is a microprocessor unit or special purpose processor. The computing device  1310  may be based on any processor, or set of processors, capable of operating as described herein. The processor  1350  may be a single core or multi-core processor. The processor  1350  may be multiple processors. In some implementations, the processor  1350  can be configured to run multi-threaded operations. In some implementations, the processor  1350  may host one or more virtual machines or containers, along with a hypervisor or container manager for managing the operation of the virtual machines or containers. In such implementations, the methods shown and described above or the electronics described above can be implemented within the virtualized or containerized environments provided on the processor  1350  or otherwise operate in conjuction with processor  1350 . 
     The memory  1370  may be any device suitable for storing computer readable data. The memory  1370  may be a device with fixed storage or a device for reading removable storage media. Examples include all forms of non-volatile memory, media and memory devices, semiconductor memory devices, such as EPROM, EEPROM, SDRAM, and flash memory devices, magnetic disks, magneto optical disks, and optical discs, such as CD ROM, DVD-ROM, and Blu-ray® discs. A computing system  1310  may have any number of memory devices  1370 . In some implementations, the memory  1370  supports virtualized or containerized memory accessible by virtual machine or container execution environments provided by the computing system  1310 . 
     The cache memory  1375  is generally a form of computer memory placed in close proximity to the processor  1350  for fast read times. In some implementations, the cache memory  175  is part of, or on the same chip as, the processor  150 . In some implementations, there are multiple levels of cache  1375 , e.g., L2 and L3 cache layers. 
     The network interface driver controller  1320  manages data exchanges via the network interface driver  1322  (also referred to as network interface driver ports). The network interface driver controller  1320  handles the physical and data link layers of the OSI model for network communication. In some implementations, some of the network interface driver controller&#39;s tasks are handled by the processor  1350 . In some implementations, the network interface driver controller  1320  is part of the processor  1350 . In some implementations, a computing system  113  has multiple network interface driver controllers  1320 . The network interface driver ports configured in the network interface card  1322  are connection points for physical network links. In some implementations, the network interface controller  1320  supports wireless network connections and an interface port associated with the network interface card  1322  is a wireless receiver/transmitter. Generally, a computing device  1310  exchanges data with other network devices  1324  via physical or wireless links that interface with network interface driver ports configured in the network interface card  1322 . In some implementations, the network interface controller  1320  implements a network protocol such as Ethernet. 
     The other network devices  1324  are connected to the computing device  1310  via a network interface driver port included in the network interface card  1322 . The other network devices  1324  may be peer computing devices, network devices, or any other computing device with network functionality. For example, a first network device  1324  may be a network device such as a hub, a bridge, a switch, or a router, connecting the computing device  1310  to a data network such as the Internet. 
     The other devices  1380  may include an I/O interface, external serial device ports, and any additional co-processors. For example, a computing system  113  may include an interface (e.g., a universal serial bus (USB) interface) for connecting input devices (e.g., a keyboard, microphone, mouse, or other pointing device), output devices (e.g., video display, speaker, or printer), or additional memory devices (e.g., portable flash drive or external media drive). In some implementations, a computing device  1300  includes an additional device  1380  such as a coprocessor, e.g., a math co-processor can assist the processor  1350  with high precision or complex calculations. 
     Instructions on computing system  1310  may control various components and functions of computing system  1310 . For example, the instructions may be executed to perform any of the methods indicated in this disclosure. In some examples, algorithms can be included as a subset of or otherwise as part of instructions included on computing system  1310 . Instructions can include algorithms to execute any of the methods or a subset of the methods described within this disclosure. 
     User interfaces on the computing system  1310  may include a screen which allows a user to interact with computing system  1310 , such as a touch screen or buttons. A display can also be included such as an LCD, LED, mobile phone display, electronic ink, or other display to display information about computing system  1310 . The user interface can allow for both input from a user and output to a user. A communication interface(s) can include hardware and software to enable communication of data over standards such as Wi-Fi, Bluetooth, infrared, radio-wave, and/or other analog and digital communication standards. Communication interface(s) allow for computing system  1310  to be updated and information generated by computing system  1310  to be shared to other devices. In some examples, communication interface(s) can send information stored in memory to another user device for display, storage or further analysis. 
     Although the above examples are given with respect to particular methods of encoding signals and are exemplary, a person of skill in the art will appreciate understand that additional variations and configurations of such methods are possible. In addition, the methods and technology disclosed herein can be combined in various permutations. 
     While this disclosure contains many specific implementation details, these should not be construed as limitations on the scope of what may be claimed, but rather as descriptions of features specific to particular implementations. Certain features that are described in this specification in the context of separate implementations may also be implemented in combination in a single implementation. Conversely, various features that are described in the context of a single implementation may also be implemented in multiple implementations separately or in any suitable sub-combination. Moreover, although features may be described above as acting in certain combinations and even initially claimed as such, one or more features from a claimed combination may in some cases be excised from the combination, and the claimed combination may be directed to a sub-combination or variation of a sub-combination. 
     Similarly, while operations are depicted in the drawings in a particular order, this should not be understood as requiring that such operations be performed in the particular order shown or in sequential order, or that all illustrated operations be performed, to achieve desirable results. In certain circumstances, multitasking and parallel processing may be advantageous. 
     References to “or” may be construed as inclusive so that any terms described using “or” may indicate any of a single, more than one, and all of the described terms. The labels “first,” “second,” “third,” and so forth are not necessarily meant to indicate an ordering and are generally used merely to distinguish between like or similar items or elements. 
     Various modifications to the implementations described in this disclosure may be readily apparent to those skilled in the art, and the generic principles defined herein may be applied to other implementations without departing from the spirit or scope of this disclosure. Thus, the claims are not intended to be limited to the implementations shown herein, but are to be accorded the widest scope consistent with this disclosure, the principles and the novel features disclosed herein. 
     Non-limiting aspects of the disclosed technology can include the following features: