Abstract:
Systems and methods of polarization-time coding are disclosed. One method includes encoding information in orthogonal polarizations of light and correlated information in multiple time slots, and transmitting the information using the orthogonal polarizations in the time slots. Another method includes receiving a first input pair which specifies a first polarization state and a second input pair containing which specifies a second polarization state; transforming each input pair according to a matrix specifying a conjugate operation to produce four output pairs. The method further includes transmitting at a first time the first output pair using the first polarization state and the third output pair using the second polarization state. The method further includes transmitting at a second time the second output pair using the first polarization state and the fourth output pair using the second polarization state.

Description:
CROSS REFERENCE TO RELATED APPLICATIONS 
       [0001]    This application claims the benefit of U.S. Provisional Application No. 60/916,900, filed May 9, 2007, which is incorporated by reference herein in its entirety. 
     
    
     FIELD OF THE DISCLOSURE 
       [0002]    The present disclosure relates to optical communications, and more specifically to coding for coherent optical communications. 
       BACKGROUND 
       [0003]    Communication using multiple transmitters and multiple receivers can be used to provide redundancy and thus to achieve reliability. Such systems also sometimes referred to as multiple input multiple output (MIMO) systems. Multiple spatially-diverse antennas have been used in wireless MIMO systems, and polarization can be used in optical MIMO systems to provide diversity and thus redundancy. Polarization diversity can address impairments in optical fiber such as cross-phase modulation (XPM) induced by polarization scattering, and also polarization-mode dispersion. Polarization diversity can also be used to address impairments in optical free-space communication, such as scattering and scintillatio. Polarization diversity uses multiple transmitters, each of which transmits using a different polarization state, thus transmitting redundant forms of the data to a receiver. The receiver can exploit the differences in the various received versions of the data to improve recovery of received data. However, conventional techniques employ multiple receivers as well as multiple transmitters, thus adding to the cost. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0004]    Many aspects of the disclosure can be better understood with reference to the following drawings. The components in the drawings are not necessarily to scale, emphasis instead being placed upon clearly illustrating the principles of the present disclosure. 
           [0005]      FIG. 1  is a block diagram of a communication system including an embodiment of a system and method of polarization time coding for optical communications. 
           [0006]      FIG. 2  is a flowchart describing operation of one embodiment of the optical transmitter from  FIG. 1 . 
           [0007]      FIG. 3  is a block diagram of the optical transmitter of  FIG. 1 , showing further details of the operation of the polarization time encoder from  FIG. 1 . 
           [0008]      FIG. 4  is a block diagram of the optical receiver of  FIG. 1 , showing further details of the operation of the polarization time decoder from  FIG. 1 . 
           [0009]      FIG. 5  is a block diagram of selected components of the transmitter and receiver from  FIG. 1 , showing further details of the optical components. 
           [0010]      FIG. 6  is a hardware block diagram of a computing device which can be used to implement various embodiments systems and methods of polarization time coding for optical communications 
       
    
    
     DETAILED DESCRIPTION 
       [0011]    Various embodiments described herein use polarization multiple input, multiple output (MIMO) techniques in the optical domain. The techniques described herein can be applied to mitigate various impairments in optical fiber, such as polarization-mode dispersion and cross-phase modulation (XPM) induced by polarization scattering. These techniques can also be applied to mitigate impairments in free-space optical communication, such as scattering and scintillation. 
         [0012]      FIG. 1  is a block diagram of a communication system including an embodiment of a system and method of polarization time coding for optical communications. System  100  includes an optical transmitter  110  and an optical receiver  120  communicatively coupled through an optical network  130 . Optical transmitter  110  is coupled to optical network  130  through optical fiber  140 . Optical receiver  120  is coupled to optical network  130  through optical fiber  150 . Optical network  130  may include various components such as amplifiers, repeaters, multiplexers, etc., as understood by a person of ordinary skill in the art. 
         [0013]    Optical transmitter  110  includes a polarization-time encoder  160 . Optical receiver  120  includes a polarization-time decoder  170  which performs the inverse function of polarization-time encoder  160 . As described in further detail in connection with  FIGS. 3-5 , the use of encoder  160  and decoder  170  allows optical transmitter  110  to transmit data using multiple polarization states while also allowing optical receiver  120  to include a single detector and to be insensitive to polarization. System  100  can thus be viewed as a polarization multiple-input, multiple output (PMIMO) system of the form 2×1: two (logical) transmitters and a single receiver. The redundancy provided by multiple polarization states allows the receiver to exploit the various received versions of the data, thus improving the reliability of communication. In particular, the encoding/decoding described herein reduces random polarization scattering, and the cross-phase modulation induced by the scattering. The encoding/decoding described herein can be used in transmission over optical fiber using single or multiple carriers. The multiple carriers can be generated optically, electrically, or a combination thereof. The encoding/decoding described herein can also be used to transmit in free space. 
         [0014]      FIG. 2  is a flowchart describing operation of one embodiment of optical transmitter  110 . The process begins at block  210 , where data is encoded in two dimensions: in multiple orthogonal polarizations and in correlated time slots. At block  220 , the encoded data is transmitted using respective ones of the orthogonal polarizations and in respective ones of the time slots. In some embodiments, the time slots are successive. The process is then complete. 
         [0015]    The details of one embodiment of polarization-time encoder  160  will now be discussed in connection with  FIG. 3 .  FIG. 3  is a block diagram of optical transmitter  110  from  FIG. 1 , showing further details of one embodiment of polarization-time encoder  160 . A data stream  310  including {d 1 , d 2 }, {d 3 , d 4 } is supplied to polarization-time encoder  160 . Each pair in the stream is a complex number associated with a polarization state. In some embodiments, the input pairs are uncoded symbols provided to polarization-time encoder  160  by a mapper (not shown), which maps a bit stream to an uncoded symbol stream. 
         [0016]    Polarization-time encoder  160  generates a linear block code which encodes in one dimension by encoding data in orthogonal polarizations, and in another dimension by encoding correlated data in multiple time slots. A linear block code of length=2 will be discussed in connection with  FIG. 3 , but other linear block codes using the polarity and time dimensions are also contemplated. 
         [0017]    In this example, each pair of inputs {z 0 , z 1 } in stream  310  is transformed into the matrix M 
         [0000]    
       
         
           
             
               [ 
               
                 
                   
                     
                       z 
                       0 
                     
                   
                   
                     
                       - 
                       
                         z 
                         1 
                         * 
                       
                     
                   
                 
                 
                   
                     
                       z 
                       1 
                     
                   
                   
                     
                       z 
                       0 
                       * 
                     
                   
                 
               
               ] 
             
             , 
           
         
       
     
         [0000]    where * represents the complex conjugate and each row represents a time slot (earliest time at the left). Polarization-time encoder  160  thus produces two streams of coded symbols, each associated with a respective polarization state. Symbols earliest in time are shown on the right. In the example of  FIG. 3 , coded symbol stream  320  corresponds to a parallel polarization state and is provided to modulator  330 , while coded symbol stream  340  corresponds to a perpendicular polarization state and is provided to modulator  350 . However, other polarization states are also contemplated. 
         [0018]    In this example, polarization-time encoder  160  applies matrix operations to the first pair {d 1 ,d 2 }, producing a first coded symbol {d 1 , −d 2 *} and a second symbol {d 2 , d 1 *}. At time T 1 , the first symbol {d 1 , −d 2 *} produced from the first pair is provided to modulator  330 , for transmission using a first polarization state. At time T 2 , the second symbol {d 2 , d 1 *} produced from the first pair is provided to modulator  330 , for transmission using the first polarization state. 
         [0019]    The second input pair {d 3 ,d 4 } is also coded using the matrix M to produce a first coded symbol {d 3 , −d 4 *} and a second coded symbol {d 4 , d 3 *}. At time T 1 , the first symbol {d 3 , −d 4 *} produced by coding the second pair is provided to modulator  350 , for transmission with a second polarization state (different than the first). At time T 2 , the second symbol {d 4 , d 3 *} produced by coding the second pair is provided to modulator  350 , for transmission with the second polarization state. 
         [0020]      FIG. 4  is a block diagram of optical receiver  120  from  FIG. 1 , showing further details of the operation of polarization-time decoder  170 . Although transmitter  110  transmits using two different polarization states, optical receiver  120  includes a single coherent detector and is polarization insensitive. This example embodiment includes a coherent receiver at x-polarization, but receivers using other polarization states are also contemplated. A coherent detector  410  detects in-phase and quadrature components, which are represented as a stream of coded symbols  420 . Polarization-time decoder  170  performs the inverse of the coding procedure used by encoder  160  to produce a stream of decoded symbols  430 . The decoded symbols  430  are then mapped to a bit stream (corresponding to the original bit stream received by optical transmitter  110 ). 
         [0021]    The detection and decoding process will now be described in further detail. The relationship between the transmitted optical fields E x  and E y  (produced by optical transmitter  110 ) and the optical fields E′ x  and E′ y  (received by optical receiver  120 ) is described by: 
         [0000]    
       
         
           
             
               
                 
                   
                     ( 
                     
                       
                         
                           
                             d 
                             1 
                             ′ 
                           
                         
                       
                       
                         
                           
                             d 
                             2 
                             
                               ′ 
                               * 
                             
                           
                         
                       
                     
                     ) 
                   
                   = 
                   
                     
                       L 
                        
                       
                         ( 
                         
                           
                             
                               
                                 J 
                                 11 
                               
                             
                             
                               
                                 J 
                                 12 
                               
                             
                           
                           
                             
                               
                                 J 
                                 12 
                                 * 
                               
                             
                             
                               
                                 - 
                                 
                                   J 
                                   11 
                                   * 
                                 
                               
                             
                           
                         
                         ) 
                       
                     
                      
                     
                       ( 
                       
                         
                           
                             
                               d 
                               1 
                             
                           
                         
                         
                           
                             
                               d 
                               2 
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   ( 
                   
                     Equation 
                      
                     
                         
                     
                      
                     1 
                   
                   ) 
                 
               
             
           
         
       
     
         [0000]    where L is a real scalar describing the linear optical loss and the Jones matrix J describes the polarization change during the fiber transmission. Using Eq. 1, the relationship between the received symbols {(d′ 1 , d′ 2 ), (d′ 3 , d′ 4 ) . . . } and the transmitted symbols {(d 1 , d 2 ), (d 3 , d 4 ) . . . } can be described as 
         [0000]    
       
         
           
             
               d 
               1 
               ′ 
             
             = 
             
               
                 L 
                  
                 
                   ( 
                   
                     
                       J 
                       11 
                     
                      
                     
                         
                     
                      
                     
                       J 
                       12 
                     
                   
                   ) 
                 
               
                
               
                 ( 
                 
                   
                     
                       
                         d 
                         1 
                       
                     
                   
                   
                     
                       
                         d 
                         2 
                       
                     
                   
                 
                 ) 
               
             
           
         
       
       
         
           and 
         
       
       
         
           
             
               
                 d 
                 2 
                 ′ 
               
               = 
               
                 
                   L 
                    
                   
                     ( 
                     
                       
                         J 
                         11 
                       
                        
                       
                           
                       
                        
                       
                         J 
                         12 
                       
                     
                     ) 
                   
                 
                  
                 
                   ( 
                   
                     
                       
                         
                           - 
                           
                             d 
                             2 
                             * 
                           
                         
                       
                     
                     
                       
                         
                           d 
                           1 
                           * 
                         
                       
                     
                   
                   ) 
                 
               
             
             , 
           
         
       
     
         [0000]    where a single coherent receiver at X-polarization is used. 
         [0022]    The two equations are rearranged into a 2×2 matrix: 
         [0000]    
       
         
           
             
               
                 
                   
                     ( 
                     
                       
                         
                           
                             d 
                             1 
                             ′ 
                           
                         
                       
                       
                         
                           
                             d 
                             2 
                             
                               ′ 
                               * 
                             
                           
                         
                       
                     
                     ) 
                   
                   = 
                   
                     
                       L 
                        
                       
                         ( 
                         
                           
                             
                               
                                 J 
                                 11 
                               
                             
                             
                               
                                 J 
                                 12 
                               
                             
                           
                           
                             
                               
                                 J 
                                 12 
                                 * 
                               
                             
                             
                               
                                 - 
                                 
                                   J 
                                   11 
                                   * 
                                 
                               
                             
                           
                         
                         ) 
                       
                     
                      
                     
                       ( 
                       
                         
                           
                             
                               d 
                               1 
                             
                           
                         
                         
                           
                             
                               d 
                               2 
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   ( 
                   
                     Equation 
                      
                     
                         
                     
                      
                     2 
                   
                   ) 
                 
               
             
           
         
       
     
         [0023]    In this manner, a virtual 2×2 PMIMO system is derived from the initial 2×1 PMIMO system, where the decoding process is independent of the polarization state of the received signal. Polarization-time decoder  170  operates by performing the matrix operation described by Eq. 2 on the received symbols {(d′ 1 , d′ 2 ), (d′ 3 , d′ 4 ) . . . }. 
         [0024]    The Jones matrix J used in the computations of decoder  170  is obtained by detector  410  using a channel estimation algorithm, such as a least-mean-squares or other algorithm known to a person of ordinary skill in the art. In some embodiments, the Jones matrix J for the entire frame is estimated using a training sequence in the preamble of each frame, which removes polarization crosstalk. 
         [0025]    The polarization of lightwave in fiber generally drifts with the time due to environmental variation, but the rate of this polarization drift is generally much slower than the transmission data rate. One embodiment of polarization-time decoder  170  uses least-mean-squares to estimate J as follows: 
         [0000]    
       
         
           
             
               
                 J 
                 i 
               
               = 
               
                 
                   
                     J 
                     
                       i 
                       - 
                       1 
                     
                   
                   + 
                   
                     μ 
                     × 
                     
                       [ 
                       
                         
                           ( 
                           
                             
                               
                                 
                                   E 
                                   x 
                                   ′ 
                                 
                               
                             
                             
                               
                                 
                                   E 
                                   y 
                                   ′ 
                                 
                               
                             
                           
                           ) 
                         
                          
                         
                           | 
                           i 
                         
                          
                         
                           
                             - 
                             
                               J 
                               
                                 i 
                                 - 
                                 1 
                               
                             
                           
                            
                           
                             L 
                              
                             
                               ( 
                               
                                 
                                   
                                     
                                       E 
                                       x 
                                     
                                   
                                 
                                 
                                   
                                     
                                       
                                           
                                         y 
                                       
                                        
                                       E 
                                     
                                   
                                 
                               
                               ) 
                             
                           
                         
                          
                         
                           | 
                           i 
                         
                       
                       ] 
                     
                     × 
                     
                       L 
                        
                       
                         ( 
                         
                           
                             
                               
                                 E 
                                 x 
                               
                             
                           
                           
                             
                               
                                 E 
                                 y 
                               
                             
                           
                         
                         ) 
                       
                     
                   
                 
                  
                 
                   | 
                   i 
                 
               
             
             , 
             
               
 
             
              
             
               i 
               ≥ 
               0 
             
             , 
             
               
                 J 
                 - 
                 1 
               
               = 
               
                 initial 
                  
                 
                     
                 
                  
                 guess 
               
             
           
         
       
     
         [0000]    where μ refers to a positive step-size, i refers to the label of training sequences, and L can be obtained from the received average power. 
         [0026]      FIG. 5  is a block diagram of selected components of optical transmitter  110  and optical receiver  120  from  FIG. 1 , showing further details of the optical components. Transmission laser  510  produces a beam which is split by a polarization beam splitter (PBS)  520  into a first polarized light beam  530  having one polarization state, and a second polarized light beam  540  having another polarization state. First polarized light beam  530  is modulated by modulator  330 , according to coded symbol stream  320  produced by polarization-time encoder  160 . Second polarized light beam  540  is modulated by modulator  350  according to coded symbol stream  340 , also produced by polarization-time encoder  160 . Modulated polarized beams  530  and  540  are recombined by polarization beam combiner (PBC)  550  and transmitted along fiber  140 . 
         [0027]    The polarization of the signal is modified as it passes through optical network  130 . The modified signal is received by a 90° optical hybrid  560  which operates as a coherent detector. Using laser  570  as a reference signal, hybrid  560  simultaneously measures the in-phase I′ x  and I′ y  and quadrature Q′ x , and Q′ y  components of the received signal. In some embodiments, state of polarization of laser  570  is chosen so that its power is equally split between orthogonal polarizations, and is phase-locked to transmission laser  510 . 
         [0028]    Using the techniques described above in connection with  FIG. 4 , the inverse of estimated Jones matrix J (i.e., the conjugate transpose of J) is applied to measured components I′ x , I′ y , Q′ x , and Q′ y  to recover the transmitted components I x , I y , Q x  and Q y . The recovered components, representing coded symbols, are then decoded into the originally transmitted symbols. In some embodiments, the received signal polarization estimation and tracking is performed by in the electrical domain (e.g., by an algorithm executed on a digital signal processor), so that no optical dynamic polarization control is required at optical receiver  120 . 
         [0029]      FIG. 6  is a hardware block diagram of a computing device  600  which can be used to implement various embodiments of systems and methods of polarization time coding for optical communications. Computing device  600  contains a number of components that are well known in the computer arts, including a processor  610  (e.g., microprocessor, digital signal processor, network processor), an optical transceiver  620 , and memory  630  These components are coupled via a bus  640 . Some embodiments also include a storage device  650 , such as non-volatile memory or a disk drive. In the embodiment of  FIG. 6 , polarization-time encoder  160  and polarization-time decoder  170  reside in memory  630  as instructions which, when executed by processor  610 , implement systems and methods of polarization time coding for optical communications. Omitted from  FIG. 6  are a number of conventional components that are unnecessary to explain the operation of computing device  600 . 
         [0030]    In other embodiments (not shown), polarization-time encoder  160 , polarization-time decoder  170 , or both, are implemented in hardware, including, but not limited to, a programmable logic device (PLD), programmable gate array (PGA), field programmable gate array (FPGA), an application-specific integrated circuit (ASIC), a system on chip (SoC), and a system in package (SiP). 
         [0031]    Polarization-time encoder  160 , polarization-time decoder  170 , or both can be embodied in any computer-readable medium for use by or in connection with an instruction execution system, apparatus, or device. Such instruction execution systems include any computer-based system, processor-containing system, or other system that can fetch and execute the instructions from the instruction execution system. In the context of this disclosure, a “computer-readable medium” can be any means that can contain, store, communicate, propagate, or transport the program for use by, or in connection with, the instruction execution system. The computer readable medium can be, for example but not limited to, a system or that is based on electronic, magnetic, optical, electromagnetic, infrared, or semiconductor technology. 
         [0032]    Specific examples of a computer-readable medium using electronic technology would include (but are not limited to) the following: random access memory (RAM); read-only memory (ROM); and erasable programmable read-only memory (EPROM or Flash memory). A specific example using magnetic technology includes (but is not limited to) a portable computer diskette. Specific examples using optical technology include (but are not limited to) compact disk (CD) and digital video disk (DVD). 
         [0033]    The foregoing description has been presented for purposes of illustration and description. It is not intended to be exhaustive or to limit the disclosure to the precise forms disclosed. Obvious modifications or variations are possible in light of the above teachings. The implementations discussed, however, were chosen and described to illustrate the principles of the disclosure and its practical application to thereby enable one of ordinary skill in the art to utilize the disclosure in various implementations and with various modifications as are suited to the particular use contemplated. All such modifications and variation are within the scope of the disclosure as determined by the appended claims when interpreted in accordance with the breadth to which they are fairly and legally entitled.