Abstract:
A method of manufacturing an optical cable including plural waveguides each including plural optical channels and each of the waveguides and the optical channels having a first end and a second end. A central portion of each of the waveguides is displaced along a central longitudinal axis of the waveguides which traverses a central bifurcation line of the first and second connectors. A first optical channel connection pattern is formed on the first connector by the first ends of the optical channels of the waveguides connected thereto; and a second optical channel connection pattern formed on the second connector by the second ends of the optical channels of the waveguides connect to the second connector. The first optical channel connection pattern is a different pattern than the second optical channel connection pattern in relation to a connection hole pattern which is the same for both the first and second connectors.

Description:
CROSS REFERENCE TO RELATED APPLICATION 
       [0001]    This application is a divisional application of U.S. patent application Ser. No. 13/277,767 filed on Oct. 20, 2011 which application claims the benefit under 35 U.S.C. §119(e) of the filing date of U.S. Provisional Patent Application No. 61/525,390, filed Aug. 19, 2011, the disclosure of which is incorporated herein by reference in its entirety. 
     
    
     FIELD OF THE INVENTION 
       [0002]    The present invention generally relates to optical cables and a method of manufacture thereof, and more particularly, includes an optical cable having waveguide layer. 
       BACKGROUND 
       [0003]    Optical data communications technology has a number of advantages over wire technology, such as increased bandwidth, data rate and response characteristics superior to those of conventional wire technology. Also, optical technology is essentially immune to radio frequency interference (RFI) and electromagnetic interference (EMI) issues associated with wire technology. Optical data communication is therefore desirable in a variety of applications such as multi-chip modules (MCMs), printed circuit board (PCB) technologies, and integrated backplanes. 
         [0004]    In conventional optical connectors, electronic circuitry, optical source and optical detectors are typically mounted on PCBs which are received in card guides mounted to an equipment frame. A backplane mounted to the rear of the frame includes board edge connectors aligned with the card guides and electrical conductors interconnecting the board edge connectors. The circuit boards are provided with board edge electrical contacts which are received in the board edge connectors when the circuit boards are inserted in the card guides to electrically connect the circuitry to the electrical conductors on the back plane. The electrical conductors provide the required electrical connections between circuit boards. 
         [0005]    The circuit boards also include optical connector parts which are optically coupled to the optical sources and to the optical detectors of the receivers and transmitters. The board mounted optical connector parts must be mated with frame mounted optical connector parts to optically connect the optical sources and the optical detectors to optical fibers terminating on the frame mounted optical connectors. The optical fibers are typically a glass fiber manufactured from glass. 
         [0006]    In the current board edge optical connector arrangements the circuit board mounted optical connector parts are mounted at leading edges of the circuit boards. One disadvantage of this arrangement is that the leading edges are already congested with board edge electrical contacts. In addition, in the board edge optical connector arrangements the frame mounted optical connector parts are mounted at the back plane, which is already congested with electrical board edge connectors and electrical conductors. In current systems, optical fibers may be left to hang loose between packs or bundles of fibers which tend to create a messy (“rat&#39;s nest”) entanglement of fibers. Further, what is needed is a method to reorder the layers within an optical cable without increasing its thickness (or bulkiness), without twisting or bending the waveguide layers, and without using optical vias. 
         [0007]    Another approach is to use polymer waveguide optical backplanes, which can contain thousands of optical channels. A polymer waveguide may be composed of two different polymer materials, for instance, a lower index cladding material and a higher index core material. Light is guided in a core (optical channels) due to the index contrast between the core and clad regions. The optical backplane may interconnect multiple server drawers, distributing and reordering the optical channels between the drawers as necessary. To facilitate the reordering within a multi-layer optical cable, it is necessary to reorder the individual waveguide layers from the input connector to the output connector. The waveguide layer reordering may be achieved by twisting and bending individual waveguide layers. This approach can result in excessive cable bulk. Further, current waveguides are difficult to bend to achieve cable reordering of the optical fibers between two connection points. Another approach is to introduce optical vias between waveguide layers to facilitate the layer redistribution, however, optical vias introduce additional loss and are costly to fabricate. Another difficult and undesirable approach is to bend (or twist) layers to realize layer reordering 
         [0008]    In view of the shortcoming in the prior art, there is a need to provide an apparatus and method to connect large numbers of optical fibers to an optical backplane and avoid the entanglement of wires associated with multiple fiber-to-fiber connections and/or routing systems. Additionally, there is a need for a device and/or method of reordering the layers within an optical cable without increasing its thickness (or bulkiness), without twisting or bending the waveguide layers, and without using optical vias. 
         [0009]    Referring to  FIGS. 1-2 , a prior art optical cable  10  includes four waveguides  14 . Each of the waveguides  14  includes a plurality of optical fibers  22  (shown in  FIG. 3 ) encased in a polymer such that the waveguide  14  is planar and has a defined width. Each of the waveguides  14  and optical fibers  22  have a first and a second end connected to respective first and second connectors  30 ,  32 . Each of the first and second connectors  30 ,  32  include connector holes in columns and rows, or connection points, i.e., for receiving optical fibers, which may also include, for example, electrically conductive sleeves, pins, or other connection points. Each of the ends of the waveguides, i.e., the optical fiber  22  ends, correspond to waveguide connection points, collectively designated as connection points  31 ,  33 , respectively, on the first and second connectors  30 ,  32 . Each of the first ends of the optical fibers  22  of the waveguides  14  are connecting to columns and rows of the first connector, and each of the second ends of the optical fibers  22  of the waveguides are connected to corresponding columns and rows of the second connector. Each of the ends of the optical fibers  22  of each of the waveguides  14  are connected to specified waveguide connection points  31 ,  33  on each of the first and second connectors  30 ,  32  resulting in a connection pattern (alternatively called a pin pattern) on the first and second connectors  30 ,  32 . The connection pattern is a geometric pattern, for example, as shown in the connectors  30 ,  32  of  FIG. 2 , which depicts a rectangular grid of connection points  31 ,  33  arranged in waveguide fiber columns  1 - 4  and rows  5   a - 5   l,  as shown in greater detail in the generic connector  75  in  FIG. 5 . Waveguide fiber connection points in column  1  are the outermost column on both connectors  30 ,  31 . Rows  5   a - 5   l,  which are grouped as rows  5 , form the rectangular grid of connection points  31 ,  33  with the columns on each of the connectors  30 ,  32 . Each of the first and second connectors  30 ,  32 , include four connector columns  8   a,    8   b,    8   c,    8   d,  as shown in generic connector  75  in  FIG. 5 , from outside to inside, as shown in a generic connector  75  having connectors holes  78 , shown in  FIG. 5 . The connection holes  78  form a connection hole pattern in one or more connectors which is identical, and is generally a grid pattern as shown in  FIGS. 5 and 7 . 
         [0010]    The connector  75  of  FIG. 5  is equivalent to, in the orientation of the related figures, the left side connector, for example, connectors  30 ,  60 ,  130 , and its mirror image applies to the right side connectors  32 ,  64 ,  140  of the figures. However, the optical fiber column, i.e., the optical fibers at one end of each of the waveguides which correspond to the optical fibers at the other end of each of the waveguides, may be positioned in a different connector column in the opposite connector. Thus, as shown in  FIG. 3 , and discussed more extensively below, fiber column  1  on the first connector, corresponding to fiber column  1  on the second connector, may be physically located at a different connector column on each of the connectors  30 ,  31 . 
         [0011]    As shown in  FIG. 2 , the connection point pattern of the first connector  30  geometrically corresponds to the connection point pattern of the second connector  32 . Further, the optical fiber connection pattern, i.e., the waveguide connection points  31 ,  33 , geometrically correspond between the first and second connectors. Specifically, the first end of the same optical fiber of the same waveguide is connected to a connection point of the first connector  30  located at connector column  1 , row  5   a  of the first connector, and the second end of the same optical fiber is connected to a connection point of the second connector  32  located at connector column  1 , row  5   a  of the second connector, wherein the connectors have the same geometric connector pattern (or pin pattern). Thus, each optical fiber at one end of the wave guide  14  is connected to a corresponding row on the opposite connector, which also is the same physical location on the connector for each of the connectors  30 ,  32 . Any reordering of the waveguide optical fibers is difficult due to the semi0rigid nature of the waveguides, and individual reordering of each of the optical fibers is difficult and tedious. 
         [0012]    Referring to  FIGS. 3 and 4 , an alternative prior art optical cable  50  includes a wave guide  54  having optical fibers  22  connected from a first connector  60  to a second connector  64 , as shown in  FIG. 3 . As shown in  FIG. 4 , first connector  60  has a different fibber connection point geometry than the second connector  64 . Specifically, the second connector  64  has a fiber connection point  66  fiber column sequence of  2 ,  1 ,  4 ,  3 , from outside to inside, opposed to the first connector  60  having a fiber connection point  62  fiber column sequence of  1 ,  2 ,  3 ,  4 . Thus, the second connector  64  does not have the same waveguide fiber connection column geometry as the first connector  60 . In the optical cable  50  shown in  FIG. 3 , an optical fiber  22  is shown individually connected at one end to connector column  1  on the first connector  60 , and to connector column  1  on the second connector  64 . As can be seen, the optical fiber in fiber row  1  of the first connector  60 , corresponds to connector hole row  8   a,  and fiber row  1  is shifted to connector hole row  8   b  in the second connector  64 . As shown in  FIG. 4 , on the second connector  64 , fiber column  1 , at physical location connector column  8   b,  corresponds to fiber column  1  on the first connector  60 , at physical location connector column  8   a.  This is because, for example, one end of the optical fibers  22  (thereby one end of a waveguide) are connected to connection points at connector column  8   a  of the first connector  60 , thereby being designated as fiber column  1 , and the other end of the same optical fibers  22  (thereby the opposite end of the waveguide) are connected to connection points at column  8   b  on the second connector  64 , which is designated as fiber column  1  for the second connector  64 , which is physically shifted over one column, that is connector column  8   b,  from outside to inside of the second connector  64 . Therefore, the fiber  22  connected at column  1  on the first connector  60 , is connected to column  1  on the second connector  64 , however, column  1  on the second connector  64  is physically located where column  2  is on the first connector  60 . 
       BRIEF SUMMARY OF THE INVENTION 
       [0013]    An optical cable including connectors includes a plurality of waveguides each including a plurality of optical channels encased in a polymer, and each of the waveguides and optical channels have a first end and a second end. First and second connectors each include a plurality of electrically conductive pins, and each of the plurality of optical channels of each of the waveguides, at their first and second ends, are connected to a specified pin on each of the first and second connectors, respectively. A first optical channel connection pattern on the first connector is formed by the first ends of the optical channels of the plurality of waveguides which are connected to the first connector. A second optical channel connection pattern on the second connector is formed by the second ends of the optical channels of the plurality of waveguide layers which is connected to the second connector. The first optical channel connection pattern on the first connector is a different pattern than the second optical channel connection pattern on the second connector in relation to a connection hole pattern which is the same for both the first and second connectors. 
     
    
     
       BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWINGS 
         [0014]    Objects, features and advantages of the present invention will become apparent from the following detailed description of illustrative embodiments thereof, which is to be read in connection with the accompanying drawings. The various features of the drawings are not to scale as the illustrations are for clarity in facilitating one skilled in the art in understanding the invention in conjunction with the detailed description. In the drawings: 
           [0015]      FIG. 1  is a side elevational view of a prior art optical cable including waveguides being connected to connectors at each of their ends; 
           [0016]      FIG. 2  is a plan view of the prior art optical cable and connectors shown in  FIG. 1 ; 
           [0017]      FIG. 3  is a side elevational view of another prior art optical cable wherein connection points on the connectors are different from each other; 
           [0018]      FIG. 4  is a plan view of the prior art optical cable and connectors shown in  FIG. 3 ; 
           [0019]      FIG. 5  is a plan view of a generic connector showing in detail, depicting the connector hole pattern and optical channel connection points therein; 
           [0020]      FIG. 6  is a side elevational view of an optical cable according to an embodiment of the invention which includes waveguides connected to connectors at each of their ends; 
           [0021]      FIG. 7  is a plan view of the optical cable shown in  FIG. 6 ; 
           [0022]      FIG. 8  is a plan view of the separated waveguides shown in  FIGS. 6 and 7 ; 
           [0023]      FIG. 9  is an isometric view of the optical cable shown in  FIGS. 6-7 ; 
           [0024]      FIG. 10  is a plan view of two waveguides according to an embodiment of the invention; 
           [0025]      FIG. 11  is a bottom view of an optical cable according to an embodiment of the invention using the waveguides shown in  FIG. 10 ; 
           [0026]      FIG. 12  is a side elevational view of the optical cable shown in  FIG. 11 ; 
           [0027]      FIG. 13  is a plan view of the optical cable shown in  FIGS. 11-12 ; 
           [0028]      FIG. 14  is a plan view of a generic connector showing in detail, depicting the connector hole pattern and optical channel connection points therein; 
           [0029]      FIG. 15  is a plan view of an opposing generic connector for a waveguide in relation to the connector shown in  FIG. 14 , depicting the connector hole pattern and optical channel connection points therein; and 
           [0030]      FIG. 16  is an isometric view of an optical backplane for use with the optical cables of the present disclosure. 
       
    
    
     DETAILED DESCRIPTION 
       [0031]    Referring to  FIGS. 5-7 , an optical cable  100  according to one embodiment of the invention is shown which includes the same reference numerals for like elements as shown in  FIGS. 1-4 . The optical cable  100  comprises four waveguides  112 ,  114 ,  116 ,  118  (shown in  FIGS. 6 and 7 ), and also may be referred to as waveguide flex, or waveguide flex cable, are collectively referred to as waveguides  110 . Each of the waveguides  110  flex, and include a plurality of optical channels  23  (shown in  FIGS. 5 ,  14  and  15 ) encased in a polymer such that the waveguide is planar and has a defined width. A polymer waveguide flex cable may be substantially plastic, and may include multiple optical channels. A waveguide layer of the polymer waveguide flex cable may be composed of two different polymer materials as discussed above, such as a lower index cladding material and a higher index core material, wherein light is guided in the core (optical channels) due to the index contrast between the core and clad regions. The optical channels  23  are shown in  FIGS. 5 ,  14  and  15  for illustrative purposes. 
         [0032]    Each of the waveguides  110  are molded to have a center portion which is off center from a longitudinal axis passing through both ends of the waveguides  110 . This is illustratively shown in  FIG. 8 , for waveguide  112  which has an axis  111  extending longitudinally through the center of both ends of the waveguide  112 , but a center portion of the waveguide  112  is off center in relation to the axis  111 . Waveguide  114  is in mirror image relation to waveguide  112 . Similarly for the remaining waveguides  116 ,  118 , are in minor image relation as waveguides  112 ,  114 . In this way, the route of each waveguide is altered, and the waveguides may be overlaid and interweaved or interwoven to be juxtapositioned as shown in  FIG. 7 , which depicts the longitudinal axis  111  passing through substantially the center of the first and second connectors  130 ,  140 . 
         [0033]    Each of the waveguides  110  and optical channels  23  have a first and a second end, connected to respective first and second connectors  130 ,  140 . Each of the first and second connectors  130 ,  140  include a plurality of connection points  132 ,  142 . Each of the first ends of the optical channels  23  of the waveguides  110  are connecting to columns and rows of the first connector  130 , and each of the second ends of the optical channels  23  of the waveguides  110  are connected to corresponding columns and rows of the second connector  140 . 
         [0034]    More specifically, each of the optical channels  23  of each of the waveguides  110  are connected to a specified waveguide connection points on each of the first and second connectors  130 ,  140  resulting in a connection pattern (or pin pattern) on the first and second connectors  130 ,  140 . The connection pattern is a geometric pattern, for example, as shown in the connectors  30  of  FIG. 2 , and the first connector  130  of  FIG. 7 , which depicts a rectangular grid of connection points arranged in columns and rows. Referring to the first connector  130 , connection columns  1 - 4  are sequentially arranged on the first connector  130 , with column  1  being the outermost column on connector  130 , and column  4  being the innermost column. Rows  5   a - 5   l,  which are grouped as rows  5 , form the rectangular grid of connections with the columns on the connector  130 . 
         [0035]    Referring to  FIG. 7 , the waveguide layers  110  (which include waveguides  112 ,  114 ,  116 ,  118 ) are overlaid and interwoven which results in a route for each waveguide layer with which a detour along its path to the opposite connector as its center portion is off-center from its longitudinal axis, as described above. The rerouting and interweaving of the waveguide layers enable reordering of each layer to provide reordering of the connections of the optical channels at the connectors  130 ,  140 . The resulting waveguide optical cable  100  is advantageously thin, and does not contain twists or strong bends, as can be seen in  FIGS. 7 and 9 . 
         [0036]    The second connector  140  (shown in  FIGS. 6 and 7 ) also depicts a rectangular grid of connectors arranged in columns and rows. The second connector columns  8   a - 8   d  (shown in  FIG. 5 ) correspond to waveguide channel connection point columns  2 ,  1 ,  4 ,  3 , respectively, from outside to inside of the connector  140 . Thus, the waveguide channel connection point columns  1 - 4  are not the same physical order for the second connector  140 , as for the first connector  130 . In other words, the first and second connectors have different respective first and second orders of the waveguide channel connection point columns. As discussed above regarding  FIGS. 2 and 4 , the connector columns and rows correspond to holes in the connectors  130 ,  140 , however, the waveguide channel connection column order corresponds to the ends of the optical channels for each of the waveguides, and thus can be coupled to the connector columns and rows, i.e., the holes in the connectors, in varies configurations. The connection holes form a connection hole pattern in each of the connectors  130 ,  140 , which is the same for both connectors, and is generally a grid pattern as shown in  FIG. 7 . 
         [0037]    For example, the pattern of holes  78  of columns  8   a - 8   d  on the first connector  130  and the pattern of holes of columns  8   a - 8   d  on the second connector  140  are the same, however, the connector columns  1 - 4 , which correspond to where the ends of each of the channel of the waveguides are connected to each column of the first and second connectors, are not the same for each of the first and second connectors  130 ,  140 . In one example, the four connector columns can be re-ordered to result in up to 24 different orders of connector columns, for example, connector columns in the following orders:  1234 ,  2134 ,  2314  . . . etc., for example, N!, wherein N=(number of rows). 
         [0038]    Referring to  FIG. 7 , the connector pattern of the first connector geometrically corresponds to the connection points of the second connector, (similarly shown in  FIG. 2 ). In the embodiment of the invention shown in  FIG. 7 , the optical channel connection pattern geometrically corresponds between the first and second connectors. That is, the first end of the same optical channel of the same waveguide is connected to the connection points located at column  1 , row  1  of the first connector, as the second end of the same optical channel which is connected to the connector located at column  1 , row  1  of the second connector, when the connectors have the same geometric connection pattern. 
         [0039]    Referring to  FIGS. 10-13 , in another embodiment according to the disclosure wherein like elements have the same reference numerals as the previous embodiments, an optical cable  200  is shown in  FIGS. 11-13 . The optical cable  200  includes two waveguides (shown in  FIG. 10 )  210   a,    210   b  which have a predetermined angular displacement in relation to a longitudinal axis along their lengths. The optical cable  200  is shown with two waveguides connecting to one column on each of the connector for illustrative purposes, additional waveguides and connection can be added to use four columns as in the previous embodiment of the disclosure. Each of the waveguides  210   a,    201   b  are connected at their opposite ends to first and second connectors  230 ,  240 , respectively. As shown in  FIG. 11 , the waveguides  201   a,    201   b  cross such that the ends of the waveguides are connected to different connection points on each connector  230 ,  240 . The first connector  230  includes connector column  232   a,  and the second connector  240  includes connecter column  242   a.    
         [0040]    Referring to  FIGS. 14 and 15 , first and second connecters  230 ,  240  includes connector points  9   a - 9   l  (which are labeled partially on each connector for illustrative purposes), and waveguide channel connection points  251 - 262 . As shown in  FIGS. 14 and 15 , waveguide channel connection points  251 - 256  correspond to connection holes  9   a - 9   f  on the first connector  230 . However, waveguide channel connection points  251 - 256 , which are the opposite ends of the optical connections of waveguide  210   b,  correspond to connection holes  9   g - 9   l  on the second connector  240 . Similarly, waveguide channel connection points  257 - 262  (only connection points  257  and  262  are shown for illustrative purposes) correspond to connection holes  9   g - 9   l  on the first connector  230 . However, waveguide channel connection points  257 - 262  (only connection points  257  and  262  are shown for illustrative purposes), which are the opposite ends of the optical channels of waveguide  210   a,  correspond to connection holes  9   a - 9   f  on the second connector  240 . Thereby, the angular displacement of the waveguides  210   a,    210   b  enables the placement of the waveguide channel ends of the waveguides on each of the first and second connectors  230 ,  240  as shown in  FIGS. 13-15 . 
         [0041]    Referring to  FIG. 16 , an optical backplane  300  for a high performance computer is shown which implements the present invention. The optical backplane  300  includes multiple server draws or blades  304  (or computer boards) connected by multiple optical waveguide cables (jumper cables)  308 , which include thousands of optical channels for distributing and reordering the optical channels between the drawers as necessary, in accordance with the present disclosure. 
         [0042]    One advantage of the present disclosure includes using the optical cables as disclosed above on a high performance optical backplane. A high performance optical backplane benefits from the simplified wiring of the present disclosure, by simplifying the wiring and eliminating potentially thousands of individual optical fibers. 
         [0043]    Thereby, a method is provided for reordering any input waveguide channel location within an N×M waveguide array bundle using 2D planar waveguide lengths, connected to any output waveguide channel location, without going to a 3D structure, such as optical vias. Optical vias or pathways that interconnect the layers of a multi-layer optical flex cable are undesirable because of the additional optical loss caused by the turning minors of the optical vias. Further, in another advantage of the invention, the disclosure provided herein preserves any input channel location within a given row of waveguides (planes), but reorders row location (inter-row) while preserving the 2D planarity of each row (without going to a 3D structure, such as optical vias). Additionally, any input channel location within a row (plane) can be re-ordered (intra-row, or waveguide cross-throughs), to any output channel location while preserving the 2D plane of the row. Further, the optical cable and method disclosed herein provides a plurality of reordering options. 
         [0044]    An example of inter-row re-ordering combinations for an optical cable as in the embodiments discussed above, is shown below in Table 1. In Table 1, the number of possible rows is designated by “n”, and the input row ordering is shown in relation to possible output row ordering in the corresponding columns. 
         [0000]    
       
         
               
             
               
               
               
             
               
               
               
             
           
               
                 TABLE 1 
               
             
             
               
                   
               
               
                 Inter-Row re-ordering combinations for an example of 4 rows 
               
             
          
           
               
                 Possibilities 
                   
                   
               
               
                 (n! where 
               
               
                 n = # of rows) 
                 Input row ordering 
                 Output row ordering 
               
               
                   
               
             
          
           
               
                 1 
                 1 2 3 4 
                 1 2 3 4 
               
               
                 2 
                 1 2 3 4 
                 1 2 4 3 
               
               
                 3 
                 1 2 3 4 
                 1 3 2 4 
               
               
                 4 
                 1 2 3 4 
                 1 3 4 2 
               
               
                 5 
                 1 2 3 4 
                 1 4 2 3 
               
               
                 6 
                 1 2 3 4 
                 1 4 3 2 
               
               
                 7 
                 1 2 3 4 
                 2 1 3 4 
               
               
                 8 
                 1 2 3 4 
                 2 1 4 3 
               
               
                 9 
                 1 2 3 4 
                 2 3 1 4 
               
               
                 10 
                 1 2 3 4 
                 2 3 4 1 
               
               
                 11 
                 1 2 3 4 
                 2 4 1 3 
               
               
                 12 
                 1 2 3 4 
                 2 4 3 1 
               
               
                 13 
                 1 2 3 4 
                 3 1 2 4 
               
               
                 14 
                 1 2 3 4 
                 3 1 4 2 
               
               
                 15 
                 1 2 3 4 
                 3 2 1 4 
               
               
                 16 
                 1 2 3 4 
                 3 2 4 1 
               
               
                 17 
                 1 2 3 4 
                 3 4 1 2 
               
               
                 18 
                 1 2 3 4 
                 3 4 2 1 
               
               
                 19 
                 1 2 3 4 
                 4 1 2 3 
               
               
                 20 
                 1 2 3 4 
                 4 1 3 2 
               
               
                 21 
                 1 2 3 4 
                 4 2 1 3 
               
               
                 22 
                 1 2 3 4 
                 4 2 3 1 
               
               
                 23 
                 1 2 3 4 
                 4 3 1 2 
               
               
                 24 
                 1 2 3 4 
                 4 3 2 1 
               
               
                   
               
             
          
         
       
     
         [0045]    An example of intra-row re-ordering combinations for an optical cable as in the embodiments discussed above, is shown below in Table 2. In Table 2, the number of possible rows is designated by “n”, and the input row ordering is shown in relation to possible output row ordering in the corresponding columns. 
         [0000]    
       
         
               
             
               
               
               
             
           
               
                 TABLE 2 
               
             
             
               
                   
               
               
                 Intra-Row re-ordering combinations for an example of 12 rows 
               
             
          
           
               
                 Possibilities 
                   
                   
               
               
                 (n! where 
               
               
                 n = # of 
               
               
                 rows) 
                 Input row ordering 
                 Output row ordering 
               
               
                   
               
               
                     1 
                 1-2-3-4-5-6-7-8-9-10-11-12 
                 1-2-3-4-5-6-7-8-9-10-11-12 
               
               
                     2 
                 1-2-3-4-5-6-7-8-9-10-11-12 
                 1-2-3-4-5-6-7-8-9-10-12-11 
               
               
                     3 
                 1-2-3-4-5-6-7-8-9-10-11-12 
                 1-2-3-4-5-6-7-8-9-11-10-12 
               
               
                     4 
                 1-2-3-4-5-6-7-8-9-10-11-12 
                 1-2-3-4-5-6-7-8-9-11-12-10 
               
               
                     5 
                 1-2-3-4-5-6-7-8-9-10-11-12 
                 1-2-3-4-5-6-7-8-9-12-10-11 
               
               
                     6 
                 1-2-3-4-5-6-7-8-9-10-11-12 
                 1-2-3-4-5-6-7-8-9-12-11-10 
               
               
                     7 
                 1-2-3-4-5-6-7-8-9-10-11-12 
                 1-2-3-4-5-6-7-8-10-9-11-12 
               
               
                     8 
                 1-2-3-4-5-6-7-8-9-10-11-12 
                 1-2-3-4-5-6-7-8-10-9-12-11 
               
               
                     9 
                 1-2-3-4-5-6-7-8-9-10-11-12 
                 1-2-3-4-5-6-7-8-10-11-9-12 
               
               
                     10 
                 1-2-3-4-5-6-7-8-9-10-11-12 
                 1-2-3-4-5-6-7-8-10-11-12-9 
               
               
                     11 
                 1-2-3-4-5-6-7-8-9-10-11-12 
                 1-2-3-4-5-6-7-8-10-12-9-11 
               
               
                     12 
                 1-2-3-4-5-6-7-8-9-10-11-12 
                 1-2-3-4-5-6-7-8-10-12-11-9 
               
               
                 . . . 
                   
                 . . . 
               
               
                 239500800 
                 1-2-3-4-5-6-7-8-9-10-11-12 
                 7-8-9-10-11-12-1-2-3-4-5-6 
               
               
                 . . . 
                   
                 . . . 
               
               
                 479001584 
                 1-2-3-4-5-6-7-8-9-10-11-12 
                 12-11-10-9-8-7-6-5-3-4-2-1 
               
               
                 479001585 
                 1-2-3-4-5-6-7-8-9-10-11-12 
                 12-11-10-9-8-7-6-5-4-1-2-3 
               
               
                 479001586 
                 1-2-3-4-5-6-7-8-9-10-11-12 
                 12-11-10-9-8-7-6-5-4-1-3-2 
               
               
                 479001587 
                 1-2-3-4-5-6-7-8-9-10-11-12 
                 12-11-10-9-8-7-6-5-4-2-1-3 
               
               
                 479001598 
                 1-2-3-4-5-6-7-8-9-10-11-12 
                 12-11-10-9-8-7-6-5-4-2-3-1 
               
               
                 479001599 
                 1-2-3-4-5-6-7-8-9-10-11-12 
                 12-11-10-9-8-7-6-5-4-3-1-2 
               
               
                 479001600 
                 1-2-3-4-5-6-7-8-9-10-11-12 
                 12-11-10-9-8-7-6-5-4-3-3-2-1 
               
               
                   
               
             
          
         
       
     
         [0046]    While the present invention has been particularly shown and described with respect to preferred embodiments thereof, it will be understood by those skilled in the art that changes in forms and details may be made without departing from the spirit and scope of the present application. It is therefore intended that the present invention not be limited to the exact forms and details described and illustrated herein, but falls within the scope of the appended claims.