Abstract:
Systems and methods are disclosed to process an optical signal using a pre-processor to populate a non-linearity compensation data structure based on a set of predetermined rules in a non-real-time off-line mode; and an amplifier applying said predetermined rules in real-time to one or more channel input data using the data structure to determine a non-linearity compensation output.

Description:
This application claims priority to Provisional Application Ser. Nos. 61/375,327 filed Aug. 20, 2010 and 61/375,329 filed Aug. 20, 2010, the contents of which are incorporated by reference. 
    
    
     BACKGROUND 
     The present invention relates to fiber non-linearity compensation. 
     Fiber-based amplifiers offer the ability to amplify ultrafast pulses to energies comparable with conventional bulk solid-state systems with significant practical advantages such as compactness, reduction of complex components, and freedom from misalignment. However, the smaller beam confinement and larger interaction lengths render them vulnerable to nonlinear effects, for single wavelength transmission (compared with WDM case), the dominant of which is self-phase modulation (SPM). Due to the Kerr effect, high optical intensity in a medium (e.g. an optical fiber) causes a nonlinear phase delay which has the same temporal shape as the optical intensity. This can be described as a nonlinear change in the refractive index:
 
Δ n=n   2   I  
 
with the nonlinear index n 2  and the optical intensity I. In the context of self-phase modulation, the emphasis is on the temporal dependence of the phase shift, whereas the transverse dependence for some beam profile leads to the phenomenon of self-focusing.
 
     Although the refractive index is a very weak function of signal power, the higher power from optical amplifiers and long transmission distances make it no longer negligible in modern optical communication systems. In fact, phase modulation distortion due to intensity dependent refractive index induces various nonlinear effects, namely, self-phase modulation (SPM) and cross-phase modulation (XPM). (Four-wave mixing (FWM) is another non-linearity distortion but not related to refractive index.) 
     One nonlinear phase shift originating from the Kerr effect is cross-phase modulation (XPM). While SPM is the effect of a pulse on it own phase, XPM is a nonlinear phase effect due to optical pulses in other channels. Therefore, XPM occurs only in multi-channel systems. In a multi-channel system, the nonlinear phase shift of the signal at the center wavelength λ is described as, 
     
       
         
           
             
               ϕ 
               NL 
             
             = 
             
               
                 
                   2 
                   ⁢ 
                   π 
                 
                 
                   λ 
                   1 
                 
               
               ⁢ 
               
                 n 
                 2 
               
               ⁢ 
               
                 z 
                 [ 
                 
                   
                     
                       I 
                       i 
                     
                     ⁡ 
                     
                       ( 
                       t 
                       ) 
                     
                   
                   + 
                   
                     2 
                     ⁢ 
                     
                       
                         ∑ 
                         
                           i 
                           ≠ 
                           j 
                         
                       
                       ⁢ 
                       
                         
                           I 
                           j 
                         
                         ⁡ 
                         
                           ( 
                           t 
                           ) 
                         
                       
                     
                   
                 
                 ] 
               
             
           
         
       
     
     The first term is responsible for SPM, and the second term is for XPM. The above equation might lead to a speculation that the effect of XPM could be at least twice as significant as that of SPM. However, XPM is more effective when pulses in the other channels are synchronized with the signal of interest. When pulses in each channel travel at different group velocities due to dispersion, the pulses slide past each other while propagating.  FIG. 1A  illustrates how two isolated pulses in different channels collide with each other. When the faster traveling pulse has completely walked through the slower traveling pulse, the XPM effect becomes weaker. The relative transmission distance for two pulses in different channels to collide with each other is called the walk-off distance. 
               L   w     =         T   o                v   g     -   1       ⁡     (     λ   1     )       -       v   g     -   1       ⁡     (     λ   2     )                ≈       T   o            D   ⁢           ⁢   Δλ                    
where T o  is the pulse width, v g  is the group velocity, and λ 1 , λ 2  are the center wavelength of the two channels. D is the dispersion coefficient, and Δλ=|λ 1 −λ 2 |.
 
     When dispersion is significant, the walk-off distance is relatively short, and the interaction between the pulses will not be significant, which leads to a reduced effect of XPM. However, the spectrum broadened due to XPM will induce more significant distortion of temporal shape of the pulse when large dispersion is present, which makes the effect of dispersion on XPM complicated. 
     The dependence of the refractive index on optical intensity causes a nonlinear phase shift while propagating through an optical fiber. The nonlinear phase shift is given by 
               ϕ   NL     =         2   ⁢   π     λ     ⁢     n   2     ⁢     I   ⁡     (   t   )       ⁢   z           
where λ is the wavelength of the optical wave, and z is the propagation distance.
 
     Since the nonlinear phase shift is dependent on its own pulse shape, it is called self-phase modulation (SPM). When the optical signal is time varying, such as an intensity modulated signal, the time-varying nonlinear phase shift results in a broadened spectrum of the optical signal. If the spectrum broadening is significant, it may cause cross talk between neighboring channels in a dense wavelength division multiplexing (DWDM) system. Even in a single channel system, the broadened spectrum could cause a significant temporal broadening of optical pulses in the presence of chromatic dispersion. 
     Back-propagation method has been proposed to compensate the fiber non-linearity. The NLSE is an invertible equation. In the absence of noise, the transmitted signal can be exactly recovered by “back-propagating” the received signal through the inverse NLSE given by: 
                 ∂   E       ∂   z       =       (       -     D   ^       -     N   ^       )     ⁢   E           
This operation is equivalent to passing the received signal through a fictitious fiber having opposite-signed parameters, such as through a receiver side back propagation  10  ( FIG. 1A ). It is also possible to perform back-propagation at the transmitter side by pre-distorting the signal to invert the channel, and then transmitting the pre-distorted waveform through a transmitter side back propagation  12  ( FIG. 1B ). In the absence of noise, both schemes are equivalent.
 
     Back-propagation operates directly on the complex-valued field E(z,t). Hence, the technique is universal, as the transmitted signal can have any modulation format or pulse shape, including multicarrier transmission using OFDM. 
     Some differences between optical system simulation and impairment compensation may occur. In the former, knowing the input to a fiber enables the output be computed to arbitrary precision; whereas in back-propagation, noise prevents exact recovery of the transmitted signal. It has been demonstrated that in the presence of noise, a modified back-propagation equation is effective in compensating nonlinearity:
 
 E   BP ( z,t )=exp(− h ( {circumflex over (D)}+ξ{circumflex over (N)} )) E   BP ( z+h,t ),
 
where 0≦ξ≦1 is the fraction of the nonlinearity compensated. For every set of system parameters, there exists an optimum ξ that minimizes the mean square error (MSE) between the transmitted signal E(0,t) and the back-propagation solution E BP (0, t). In zero-dispersion fiber, for example, where back-propagation is equivalent to nonlinear phase rotation, it was shown that ξ=0.5 is optimal.
 
     The existence of an optimum ξ can be appreciated by considering that in a typical fiber, the magnitude of the dispersion operator is much greater than the nonlinear operator. Thus, nonlinearity can be viewed as a perturbation to a mostly dispersive channel. The optimum phase to de-rotate at each back-propagation step depends on the accuracy of E BP (z, t) as an estimate of E(z,t). The more accurately the receiver estimates E(z,t), the closer ξ can be set to one, since the nonlinear phase rotation will lead to an output closer to the original signal. Conversely, if E(z,t) is not known accurately, error in amplitude will be converted to random phase rotations by the nonlinear operator hξ{umlaut over (N)}, yielding an output that is even further away from the desired signal in Euclidean distance. Hence, the optimum ξ depends on the received SNR as well as any uncompensated distortions that are present during back-propagation. 
     The receiver shown in  FIG. 2  has been proposed for single-carrier transmission system with a coherent optical to electrical conversion system  20 . System  20  includes a polarizing beam splitter (PBS)  22  and two 90-degree hybrids coupled to one or more analog to digital converters  24 . In system  20 , a linear equalizer (FSE)  28  follows a back-propagation module  26 . In the absence of nonlinearity, back-propagation function inverts the fiber CD, so PMD is mitigated by the linear equalizer. At realistic transmission distances and symbol rates, PMD has only short duration, so we expect the signal amplitude profile will not be significantly distorted by PMD. Hence, back-propagation with the linear operator can still compensate most of the interactions between CD and nonlinearity. The linear equalizer compensates PMD and any residual linear effects not already compensated by back-propagation. If back-propagation includes PMD, the linear equalizer is reduced to a fixed down-sampler. 
     The ability of back-propagation to undo nonlinear effects depends on how accurately it can estimate the signal amplitude profile at every point in the fiber. Noise, PMD, and other distortions not estimated by the receiver, but which change the signal intensity profile, thus degrading performance. Since these effects accumulate with distance, the further a signal is back-propagated, the higher the relative error. In receiver-side back-propagation, the signal intensity profile is known accurately at the receiver, but becomes progressively less accurate as it is traced back to the transmitter. 
       FIG. 3A  shows an exemplary arrangement where back-propagation can be done either at the transmitter or receiver side, or can also been split between the transmitter and receiver: transmit-side back-propagation inverts the first half of the channel, while receive-side back-propagation inverts the second half. In  FIG. 3A , input data is provided to a back-propagation non-linearity compensation module  40 , whose output is provided to an array of digital to analog converters  42 . The analog data is provided to an array of electrical-to-optical upconverters  44  and sent to an arrayed waveguide grating (AWG)  46  for transmission to another AWG  48 . At AWG  48 , the information is converted using optical-to-electrical converters  50  and provided to an array of analog to digital converters  52  whose outputs are provided to a back-propagation non-linearity compensation module  54 . Module  54  in turn is connected to an array of linear equalizers  56  driving an array of carrier recovery circuits  58  that generate output data. Since the XPM happens between different channels, multiple channel inputs and outputs need to be processed jointly with the non-linearity compensation module or processor  54  to remove the dispersion caused by XPM during the transmission. 
       FIG. 3B  shows another exemplary arrangement with back-propagation at a transmitter  70  and a receiver  90 . At the transmitter  70 , data input is provided to an OFDM modulator  72  driving a back-propagation module  74 , whose output is applied to a digital to analog converter  76  and provided to an E-O up-converter  78  and transmitted over an optical cable  80  to the receiver  90 . At the receiver  90 , an O-E down converter  92  receives the data which is provided to an analog to digital converter  94 . The digital data is provided to a back-propagation module  96  and optionally to an OFDM demodulator  98 . The data is provided to a linear equalizer  100  and then presented to a carrier recovery circuit  102  to generate output data. In  FIG. 3B , the back-propagation is split evenly between the transmitter and receiver: transmit-side back-propagation inverts the first half of the channel, while receive-side back-propagation inverts the second half. To account for the change in relative error with distance, the parameter ξ should also vary with distance; a larger ξ is used for the spans closer to the transmitter (and receiver), while a smaller ξ is used for spans further away, where the estimated signal intensity is less reliable. 
     One challenge for commercial implementation of the non-linearity compensation process is the high computing complexity. If the transmitter or receiver side non-linearity compensation is used, the (back-propagation) non-linearity compensation function has to run in a real-time mode with multiple steps to compensate the linear and non-linear dispersion span by span. Even with the recent efforts in process simplification, the computing complexity of non-linearity compensation is still two orders of magnitude (greater 50 times) greater than the computing complexity of the linear dispersion compensation (1-tap frequency domain equalization) of the same transmission range. 
     SUMMARY 
     Systems and methods are disclosed to process an optical signal with a pre-processing module to populate a non-linearity compensation look-up table based on a set of predetermined rules in a non-real-time off-line mode; and a transmitter applying said predetermined rules in real-time to multiple channel input data to generate a real-time symbol pattern, searching the look-up table with the real-time symbol pattern to determine a non-linearity compensation output, and modulating the optical signal with the compensation output. 
     Implementations of the above aspect can include one or more of the following. The transmitter can be a single polarization transmitter or a PolMux transmitter. An array of digital to analog converters (DACs) can be connected to the transmitter. An array of in-phase/quadrature (I/Q) modulators can be connected to the DACs. A laser and a PM coupler can provide CW light source to the I/Q modulators. The look-up table is generated by determining a plurality of combination of the input symbol sequences from multiple channels and performing non-linearity processing on the symbol pattern and storing the pattern in the look-up table. The non-linearity compensation can be back-propagation techniques or other suitable techniques that are selectable. The input symbol patterns relate to a modulation format and a transmitter architecture and can be geared to single polarization or polarization multiplexing (PolMux) patterns. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIGS. 1A-1B  show transmitter-side and receiver-side systems with back-propagation. 
         FIG. 2  shows a back-propagation receiver with output linear equalizer to mitigate residual linear distortion for a single-carrier. 
         FIG. 3A  shows back-propagation implementation for XPM at a transmitter and a receiver. 
         FIG. 3B  shows another back-propagation implementation at the transmitter and the receiver. 
         FIG. 4  shows an exemplary process to generate a look-up table for non-linearity compensation output. 
         FIG. 5  shows an exemplary Polarization multiplexing (PolMux) digital transmitter (PDM) with look-up table based non-linearity compensation. 
         FIG. 6  shows an exemplary single polarization digital transmitter with look-up table based non-linearity compensation. 
         FIG. 7  shows another exemplary PolMux (PDM) digital transmitter with look-up table based non-linearity compensation 
         FIG. 8  shows an exemplary single polarization digital transmitter with look-up table based non-linearity compensation. 
         FIG. 9  shows an exemplary system to perform non-linearity compensation with the look-up table. 
     
    
    
     DESCRIPTION 
       FIG. 4  shows an exemplary system to generate the look-up table for the non-linearity compensation output. Transmission line information is collected first ( 200 ). Next, the process determines a combination of the input symbol sequences from multiple channels and the non-linearity compensation processor ( 202 ). The input symbol patterns may be different for different modulation format and transmitter architecture, for example, OOK or DQPSK, single polarization or Polarization multiplexing (PolMux), among others. The input symbol patterns are re-organized and re-format to generate a one dimension symbol pattern which can be searched within a look-up table ( 204 ). Then all possible input symbol patterns determined in  204  are processed with the non-linearity processor ( 206 ) and generate multiple different outputs. All these outputs are saved with the look-up table ( 208 ) and shown in Table 1. The operations of  FIG. 4  can be done off-line to create the look-up table, and once created, the look-up table can be applied in real-time with minimal complexity. 
     Table 1 below shows one exemplary table look-up architecture: 
     
       
         
               
               
               
             
           
               
                   
               
               
                 Input symbol 
                 Output symbol pattern 
                   
               
               
                 pattern 
                 (single polarization case) 
                 Output symbol pattern (PolMux case) 
               
               
                   
               
             
             
               
                 (c 1 , c 2 , . . . , c M ) 1   
                 (S 1,I , S 1,Q , S 2,I , S 2,Q , . . . , S N,I , S N,Q ) 1   
                 (S 1,X _I, S 1,X _Q, S 1,Y _I, S 1,Y _Q, S 2,X _I, S 2,X _Q, S 2,Y _I, S 2,Y _Q, . . . , 
               
               
                   
                   
                 S N,X _I, S N,X _Q, S N,Y _I, S N,Y _Q) 1   
               
               
                 (c 1 , c 2 , . . . , c M ) 2   
                 (S 1,I , S 1,Q , S 2,I , S 2,Q , . . . , S N,I , S N,Q ) 2   
                 (S 1,X _I, S 1,X _Q, S 1,Y _I, S 1,Y _Q, S 2,X _I, S 2,X _Q, S 2,Y _I, S 2,Y _Q, . . . , 
               
               
                   
                   
                 S N,X _I, S N,X _Q, S N,Y _I, S N,Y _Q) 2   
               
               
                 . . . 
                 . . . 
                 . . . 
               
               
                 (c 1 , c 2 , . . . , c M ) L   
                 (S 1,I , S 1,Q , S 2,I , S 2,Q , . . . , S N,I , S N,Q ) L   
                 (S 1,X _I, S 1,X _Q, S 1,Y _I, S 1,Y _Q, S 2,X _I, S 2,X _Q, S 2,Y _I, S 2,Y _Q, . . . , 
               
               
                   
                   
                 S N,X _I, S N,X _Q, S N,Y _I, S N,Y _Q) L   
               
               
                   
               
             
          
         
       
     
     The system of  FIG. 4  significantly reduces the implementation complexity by using look-up table search instead of the real-time processing of every signal. The non-linearity compensation feature would certainly improve the transmission performance like the longer span length or total transmission distance. As the system can be implemented at the transmitter side, it can be completely compatible with any receiver solutions. Since the non-linearity compensation processing is done in off-line mode and independent from any specific algorithm, although back-propagation method is used in one embodiment, the system can easily use or update to any other algorithms available for the compensation. When other algorithms are desired, only the look-up table needs to be updated to change to the new algorithm without any hardware changes at the transmitter side. 
     The symbol stream to the DAC can be sampled twice the Nyquist rule. In one embodiment, the system up-samples data before the look-up table processing. To up-sample the signal, there are many methods, such as interpolation or filter-based method can be used. By repeating the symbol twice the up-sampled signal would give the same performance compared with other methods when the same digital coherent receiver is used. By repeating the symbol twice, the 2-times sampling signal can still be used for look-up table search. For other up-sampling methods, since the symbol values are not binary data, the look-up table search would be difficult and the up-sampling has to be done after the look-up table searching. Although 2-sampling is used, the present inventors contemplate that 1-time sampling signal can be used for the DAC sampling. 
     Turning now to  FIG. 5 , a PolMux digital transmitter (PDM) is shown with the look-up table based non-linearity compensation. The input binary data of two polarizations (X,Y) from K channels are processed jointly with the symbol pattern generator ( 210 ) with the same re-organize and re-format rule as step ( 204 ) of  FIG. 3  to generate a one dimension symbol pattern which can be read and searched within the look-up table. Then the input symbol pattern is searched in the look-up table and the corresponding output symbol pattern is located ( 212 ). The output symbols are then send to the DAC  214  to generate the analog I/O signals which will be used to drive the I/O modulators and the generate the optical PolMux transmit signals. The optical transmitters are sent to the transmission line through the AWG  220 . 
     The system of  FIG. 5  provides a digital transmitter solution with non-linearity compensation feature based on a look-up table instead of the real-time non-linearity compensation function conventionally done. Operations  210 - 212  need to be done in real-time. The system of  FIG. 5  significantly reduces the implementation complexity by using look-up table searches instead of real-time processing of every signal. The non-linearity compensation feature would also improve the transmission performance to support a longer span length or total transmission distance, among others. 
     The digital transmitter can utilize the original error-free data symbols to do the compensation without the interferences from any noise and other linear dispersion caused by the transmission. In addition, because of the digital transmitter and availability of the original input data symbol patterns, a look-up table search becomes possible. The look-up table can be generated off-line previously for finite combinations which can cover all the possibilities of the input symbols patterns. 
     For a transmission system, the maximum dispersion length is determined first so that the compensation pattern length is fixed. The transmitter side non-linearity compensation is processed in a pattern/packet base and the pattern/packet length needs to be larger than the maximum dispersion length. After the pattern length is known, there would be a number of total different input signal patterns which is eventually the look-up table size. The look-up table needs to be previously calculated for all these input signal patterns and find the optimal output symbols for every single signal pattern. During the transmission, the digital transmitter will read the data inputs from multiple channels and generate a data pattern which can be matched/compared it to the look-up and find the corresponding optimal output symbols after the non-linearity compensation. The optimal symbols would be sent to the DAC, converted to analog signals and used to drive the modulator. The look-up table search processing can be done parallel which can fully utilize the hardware resources in an FPGA or ASIC chip. 
       FIG. 6  shows an exemplary single polarization digital transmitter with look-up table based non-linearity compensation. In  FIG. 6 , the input binary data of two polarizations (X,Y) from K channels are processed jointly with the symbol pattern generator ( 210 ) with the same re-organize and re-format rule as step ( 204 ) of  FIG. 3  to generate a one dimension symbol pattern which can be read and searched within the look-up table. Then the input symbol pattern is searched in the look-up table and the corresponding output symbol pattern is located ( 212 ). The output symbols are then send to the DAC  214  to generate the analog I/Q signals which will be used to drive the I/O modulators and generate single carrier optical transmit signals ( 236 ). The optical transmitters are sent to the transmission line through the AWG  220 . 
     In  FIG. 6 , a digital transmitter can utilize the original error-free data symbols to do the compensation without the interferences from any noise and other linear dispersion caused by the transmission. In addition, because of the digital transmitter and availability of the original input data symbol patterns, a look-up table search becomes possible. The look-up table can be generated off-line previously for finite combinations which can cover all the possibilities of the input symbols patterns. 
     An exemplary implementation is discussed next. For a PDM-QPSK 40G transmission (12.5 GHz baud rate, 80 ps/symbol) with 80 km span and DCF, the maximum Chromatic dispersion is 17 ps/km/nm*0.1 nm*80 km=136 ps which is about two symbols duration. The transmitter side non-linearity compensation will be processed in a packet base and the packet length needs to be larger than the maximum dispersion length which is 2 symbols in this example. Assuming the packet length is 5 symbols, the number of bits for those 5 symbols is 5*2*2 or 20 (considering the 2 bits/symbol QPSK and polarization multiplexing.) For this example, there are approximately 2^20=1048576 different input signal patterns. The look-up table needs to be determined in advance for all 1048576 input signal patterns and optimal output symbols are determined for every single signal pattern. During transmission, the digital transmitter will read the input data pattern, match/compare it to the look-up and find the corresponding optimal output symbols after the non-linearity compensation. The optimal symbols would be sent to the DAC, converted to analog signals and used to drive the modulator. The look-up table search processing can be done parallel which can fully utilize the hardware resources in a FPGA or ASIC chip. 
       FIG. 7  shows another exemplary PolMux (PDM) digital transmitter with look-up table based non-linearity compensation. In  FIG. 7 , a symbol pattern generator module  250  is used to generate the symbol pattern. The pattern is stored as a look-up table  252 . The look-up table  252  is used to provide the appropriate symbol pattern to an array of digital to analog converters  254 , and the DACs  254  drive a corresponding I/Q modulators  260 . A laser  256  drives a PM coupler  258 , which in turn controls the I/O modulator  260   s . The outputs of the IQ modulators  260  are provided to a PBC. 
     During operation, the PolMux digital transmitter applies the look-up table based non-linearity compensation. The input binary data of two polarizations (X,Y) are processed with the symbol pattern generator  250  with the same re-organize and re-format rule as operation  204  ( FIG. 3 ) to generate a one dimension symbol pattern which can be read and searched within the look-up table. Then the input symbol pattern is searched in the look-up table and the corresponding output symbol pattern is located. The output symbols are then send to the DAC to generate the analog I/Q signals which will be used to drive the I/Q modulators and the generate the optical transmit signals. Similar architecture can be found in  FIG. 6  for single polarization transmitters. 
       FIG. 8  shows an exemplary single polarization digital transmitter with look-up table based non-linearity compensation. In  FIG. 8 , the symbol pattern generator module  250  is used to generate the symbol pattern. The pattern is stored in the look-up table  252 . The look-up table  252  is used to provide the appropriate symbol pattern to an array of digital to analog converters  254 , and the DACs  254  drive an I/Q modulator  260 . A laser  256  drives the I/Q modulator  260  whose output is provided to the transmission line. 
       FIG. 9  shows an exemplary process to enhance the optical transmission of data with the look-up table approach. The system of  FIG. 9  moves the computationally intensive processing done by a non-linearity compensation processor  314  to an off-line processing operation so that subsequent computing complexity can be avoided. A look-up table  316  then stores the off-line processing results. For the digital transmitter, the non-linearity compensation is simplified to the look-up table search operations  332 - 334  instead of complicated digital signal processing. The look-up table search is much easier to be implemented and is highly parallelizable. The process of  FIG. 9  has an off-line processing module  300  and a real-time processing module  330  that receives data from hardware and outputs 
     Turning now to  FIG. 9 , transmission channel information such span length, fiber type, and dispersion coefficients, among others, is captured by block  302 . The process generates combinations of multiple-channel input symbol patterns for a single polarization and PolMux coefficients in block  304 . Next, one dimensional symbol patterns are generated using predetermined rules in block  306 . The pattern is provided to a non-linearity compensation processor  314 . The processor has access to programmatic details of the back propagation method in block  310  or other non-linearity compensation methods to select from block  312 . The processed output is saved to a non-linearity compensation look-up table  316 , or is used to update the look-up table  316 . 
     Turning now to the real-time processing module  330 , multiple channel input binary data is applied by block  332  to generate the symbol pattern using the predetermined rule used in block  306 . Next, the process searches the look-up table with the input symbol pattern in block  334 . The result of the table look-up is provided to a DAC. 
     The real-time processing module  330  also receives data from a multiple channel joint non-linearity compensation block  340 . The multiple channel joint non-linearity compensation block  340  receives multiple channel input binary data  342  for single polarization and multiple channel input binary data  344  for PolMux. The output of the non-linearity compensation block  340  is provided to a DAC array  350  that drives a single polarization driver/modulator  352  and a PolMux driver/modulator  354 . The outputs of modulators  352  and  354  are provided to the AWG and the transmission line  356 . 
     In the foregoing embodiments, the non-linearity compensation processing is done in off-line mode and independent from any specific algorithm. Further, although the preferred embodiment uses the back-propagation method, the system can easily use or be updated to any other algorithms available for the compensation. When other algorithms become available in the future, only the look-up table needs to be updated to change to the new algorithm without any hardware changes at the transmitter side. Further, as the preferred embodiment is implemented at the transmitter side, it can completely compatible with any receiver solutions.