Abstract:
A method for processing a plurality of sub-blocks in a block of video is disclosed. The method generally includes the steps of (A) intra predicting a first group of the sub-blocks in a first quadrant of the block, (B) intra predicting a second group of the sub-blocks in a second quadrant of the block after starting the intra predicting of the first group and (C) intra predicting a third group of the sub-blocks in the first quadrant after starting the intra predicting of the second group, wherein the first group and the third group together account for all of the sub-blocks in the first quadrant.

Description:
FIELD OF THE INVENTION 
     The present invention relates to video processing generally and, more particularly, to a method and/or architecture for block and mode reordering that may be suitable for H.264. 
     BACKGROUND OF THE INVENTION 
     A latest video compression technique, commonly referred to as an H.264/Advanced Video Coding recommendation (International Telecommunication Union-Telecommunication Standardization Sector, Geneva, Switzerland) and/or an MPEG-4 Part 10 recommendation (document ISO/IEC 14496-10 International Organization for Standardization/International Electrotechnical Commission, Geneva, Switzerland) has a better coding efficiency for intra predictions compared with previous video coding standards. The intra prediction coding efficiency is achieved by an extensive use of spatial context to derive a prediction. Intra-coded macroblocks are predicted either as 16×16 sample blocks, 8×8 sample blocks or 4×4 sample blocks. The 4×4 sample prediction mode is better suited for areas that have many spatial details. 
     Referring to  FIG. 1 , a diagram of an H.264/AVC intra 4×4 luminance order sequence  90  is shown. A luminance component of a macroblock is partitioned in four 8×8 sample blocks and each of the 8×8 sample blocks is further partitioned in four 4×4 sample blocks. The 4×4 sample blocks are coded using the order  90  from a position 0 to a position 15 sequentially. A prediction of each 4×4 sample block is based on the samples in the spatial neighbors. The dependencies between spatial neighbors impose a limit of how far the intra 4×4 encoding and decoding can be parallelized. 
     SUMMARY OF THE INVENTION 
     The present invention concerns a method for processing a plurality of sub-blocks in a block of video. The method generally comprises the steps of (A) intra predicting a first group of the sub-blocks in a first quadrant of the block, (B) intra predicting a second group of the sub-blocks in a second quadrant of the block after starting the intra predicting of the first group and (C) intra predicting a third group of the sub-blocks in the first quadrant after starting the intra predicting of the second group, wherein the first group and the third group together account for all of the sub-blocks in the first quadrant. 
     The objects, features and advantages of the present invention include providing a method and/or architecture for block and mode reordering that may (i) be suitable for H.264, (ii) reorder block order processing, (iii) reorder intra prediction mode directions, (iv) increase a throughput of parallel intra-block predictions and/or (v) increase a throughput of parallel motion vector predictions. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       These and other objects, features and advantages of the present invention will be apparent from the following detailed description and the appended claims and drawings in which: 
         FIG. 1  is a diagram of an H.264/AVC intra 4×4 luminance order sequence; 
         FIG. 2  is a diagram of intra prediction mode directions; 
         FIG. 3  is a block diagram of a block with surrounding context; 
         FIG. 4  is a table for intra 4×4 prediction dependencies on a spatial context; 
         FIG. 5  is a table for intra 4×4 prediction mode dependencies; 
         FIG. 6  is a block diagram of a 4×4 prediction order shown in accordance with a preferred embodiment of the present invention; 
         FIG. 7  is a table for intra 4×4 prediction dependencies using the processing order; 
         FIG. 8  is a flow diagram of an example parallel processing method using the prediction order; 
         FIGS. 9   a - 9   g  are a set of prediction mode sequences; 
         FIG. 10  is a block diagram of an example set of 4×4 blocks and associated motion vectors; 
         FIG. 11  is a block diagram of a 4×8 prediction order; 
         FIG. 12  is a block diagram of an 8×4 prediction order; 
         FIG. 13  is a block diagram of an example prediction order; and 
         FIG. 14  is a block diagram of another example prediction order. 
     
    
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS 
     The present invention discloses a new processing order for 4×4 sample blocks different from the H.264/AVC order that may minimize dependencies for intra predictions and/or predicted motion vectors. The new processing order generally allows a more efficient implementation compared with conventional techniques. Furthermore, intra 4×4 prediction modes may be prioritized in support of parallel operations. 
     Referring to  FIG. 2 , a diagram of intra prediction mode directions is shown. Depending on an availability of neighboring partitions, each 4×4 block (or sub-block) and/or 8×8 block (or sub-block) within a 16×16 macroblock may be predicted in up to 9 different directions. A prediction mode 2 (not shown in  FIG. 2 ) is a DC prediction mode that is non-directional, but may depend on the samples above and the samples to the left of a current block. The predictions modes may be referred to as a vertical mode (e.g., mode 0), a horizontal mode (e.g., mode 1), a DC mode (e.g., mode 2), a diagonal down left mode (e.g., mode 3), a diagonal down right mode (e.g., mode 4), a vertical right mode (e.g., mode 5), a horizontal down mode (e.g., mode 6), a vertical left mode (e.g., mode 7) and a horizontal up mode (e.g., mode 8). Each 16×16 block may be predicted in up to 4 different directions (e.g., the vertical mode 0, the horizontal mode 1, the DC mode 2 and a plane mode 3). 
     Referring to  FIG. 3 , a block diagram of a block  100  with surrounding context is shown. The block  100  may be referred to as a current block (or sub-block). The current block  100  may represent any one of the block positions (or indices) 0-15 at a time as shown in  FIG. 1 . The current block  100  generally comprises 16 luminance samples (e.g., a-p) arranged in a 4×4 matrix. The surrounding context generally comprises a block  102 , a block  104 , a block  106  and a block  108 . A bottom row of samples (e.g., A-D) in the block  102  directly above the current block  100  generally provide a portion of the upper context. A bottom row of samples (e.g., E-H) in the block  104  above and to the right (above-right) of the current block  100  generally provide a second portion of the upper context. The samples (e.g., I-L) in a right column of the block  106  may provide a left context. A lower-right corner sample (e.g., M) of the block  108  may provide an above and to the left (above-left) context for the current block  100 . Rules for intra predicting samples (both luminance and chrominance) are generally disclosed in section 8.3 and the associated subsections of the ITU-T H.264 (E) recommendation ISO/IEC 14496-10 (E) recommendation, which are hereby incorporated by reference in its entirety. 
     Referring to  FIG. 4 , a table for intra 4×4 prediction dependencies on a spatial context is shown. An intra prediction for each of the block positions/indices shown in  FIG. 1  (e.g., numbers 0-15) is generally dependent on the availability of the surrounding context shown in  FIG. 3 . For block position 3, 7, 11, 13 and 15, the prediction modes 3 and 7 do not use the above-right context in the block  104 . Except for the DC prediction mode 2, each of the other prediction modes may be applied only when the appropriate context is available. Exceptions generally exist at (i) picture boundaries where the context is generally considered not available and (ii) slice boundaries where the context may or may not be available depending on a flag (e.g., constrained_intra_pred_flag) that may change for every picture. Hence, all 9 prediction modes shown in  FIG. 2  may be used most of the time to find a best match between the predicted block and the original block being encoded. 
     Each “X” in the table generally indicates that a dependency exists between the intra prediction mode and a corresponding context (e.g., blocks  102 - 108 ). Consider the mode 4 column as an example. An intra prediction for the current block  100  may use the context from the left block  106 , the above-left block  108  and the above block  102 . If any one or more of the context samples in the blocks  102 ,  106  and/or  108  are unavailable, the mode 4 intra prediction may not be performed. As such, the prediction mode 4 is dependent on the left context, the above-left context and the above context. Blank boxes in the table generally indicate that no dependency may exist between the prediction mode and the corresponding context. For example, no dependency exists between the mode 4 direction and the above-right context block  104 . As such, the mode 4 intra prediction may be performed regardless of the availability/non-availability of the samples E-H in the above-right block  104 . 
     Referring to  FIG. 5 , a table for intra 4×4 prediction mode dependencies is shown. When the 4×4 blocks are processed in the coding order  90  (e.g., position 0 through position 15 as shown in  FIG. 1 ), the processing may advance to a next 4×4 block only after a previous 4×4 block has been processed. Each number in the table cells in  FIG. 5  generally indicates the number of prediction modes that may wait for a previous 4×4 block to be completed, where the previous block is to the left, above-left, above or above-right. 
     The odd-numbered blocks (e.g., block positions 1, 3, 5, 7, 9, 11, 13 and 15) may have to wait for the previous block to be fully processed in 6 out of the 9 prediction modes. For some of the block numbers (e.g., block positions 2, 6, 10, and 14), 2 out of the 9 prediction modes may have to wait for the previous block to be fully processed. For example, the block 9 may have to wait for the left context (e.g., block 8) to be available in order to predict using the six prediction modes 8, 1, 6, 4, 5 and 2. No dependencies are shown for block 9 regarding the above-left context (e.g., block 2), above context (e.g., block 3) and the above-right context (e.g., block 6), as the earlier blocks 2, 3 and 6 are generally considered available (e.g., completed processing) before the block 9 processing is initiated. 
     A macroblock may have sixteen 4×4 blocks (or sub-block), each with 9 prediction modes. Therefore, up to 144 (=16×9) 4×4 prediction modes may be performed for a single macroblock. If the 4×4 blocks are processed in the coding order  90  shown in  FIG. 1 , 56 (=8×6 left context+4×2 above-right context) out of the 144 prediction modes may have to wait for the previous block to be fully processed. 
     Referring to  FIG. 6 , a block diagram of a 4×4 prediction order  120  is shown in accordance with a preferred embodiment of the present invention. The prediction order  120  generally accounts for the dependencies for intra 4×4 prediction and motion vector prediction. Generally, the prediction order  120  differs from the coding order  90  in that (i) the positions 3 and 4 may be swapped, (ii) the positions 7 and 8 may be swapped and (iii) the positions 11 and 12 may be swapped. A transformation from the coding order  90  to the prediction order  120  may be implemented with a 4×4 block buffer to delay the earlier of the swapped blocks. 
     Referring to  FIG. 7 , a table for intra 4×4 prediction dependencies using the processing order  120  is shown. The dependencies for most of the odd-numbered blocks have been eliminated, except for the block numbers 1 and 15. Therefore, the number of block dependencies may be reduced from 56 to only 20 (=2×6 left context+4×2 above-right context) out of 144. The dependency reduction generally increases a codec throughput since more blocks may be processed in parallel. 
     Referring to  FIG. 8 , a flow diagram of an example parallel processing method  140  using the prediction order  120  is shown. The method (or process)  140  may be referred to as a parallel processing method. The parallel processing method  140  generally comprises a step (or block)  142 , a step (or block)  144 , a step (or block)  146 , a step (or block)  148 , a step (or block)  150 , a step (or block)  152 , a step (or block)  154 , a step (or block)  156 , a step (or block)  158 , a step (or block)  160 , a step (or block)  162 , a step (or block)  164 , a step (or block)  166 , a step (or block)  168 , a step (or block)  170 , a step (or block)  172 , a step (or block)  174 , a step (or block)  176  and a step (or block)  178 . The parallel processing method  140  is generally illustrated as two parallel processes. Other numbers of parallel processes may be implemented to meet the criteria of a particular application. 
     In the step  142 , a left parallel process may begin by intra predicting a block at index number (or position) 0. Since the left context block  106 , the above-left context block  108 , the above context block  102  and the above-right context block  104  may already be known, the intra prediction of the block 0 may have no dependencies for any of the 9 prediction modes. An intra prediction of the block at index umber 1 may begin in a right parallel process with the step  144  substantially simultaneously with the intra prediction of the block 0 in the step  142 . However, the block 0 generally forms the left context for the block 1. Therefore, prediction modes 0, 3 and/or 7 may be performed first in the step  144  since the prediction modes 0, 3 and 7 do not depend on the left context. The remaining prediction modes 1, 2, 4, 5, 6 and 8 may be used in the step  144  after the block 0 context becomes settled (e.g., step  142  ends). 
     Referring to  FIGS. 9   a - 9   g , a set of prediction mode sequences is shown. For the step  142  where the appropriate surrounding context is known, a first prediction mode sequence may be used as shown in  FIG. 9   a . For the step  144  where the left context may be absent at the start of the intra prediction, a second prediction sequence may be used as shown in  FIG. 9   b . The second prediction sequence generally schedules the prediction modes that depend on the missing left context toward an end of the sequence. 
     Referring again to  FIG. 8 , in the step  146 , the block index number 2 may begin processing after completion of the block 0. Since the block 2 uses the block 1 as the above-right context, the intra prediction of the block 2 may (i) begin with the prediction modes 0, 1, 2, 4, 5, 6 and/or 8 and (ii) end with the prediction modes 3 and/or 7. For the step  146  where the above-right context may be absent at the start of the intra prediction, a third prediction sequence may be used, as shown in  FIG. 9   c . If the above context were absent at the start of the step  146  (e.g., block 2 is processed in parallel to block 0), a fourth sequence of the prediction modes may be used starting with the modes 1 and/or 8, as shown in  FIG. 9   d . Furthermore, if the blocks are received in the coding order  90 , the block index number 4 (coding order block 3) may be temporarily buffered in the step  148 . 
     The block index number 3 (coding order block 4) may begin processing in the step  150  after completion of the block 1. Block 3 generally uses the block 1 as the left context, the block  102  for the above context and the block  104  and the above-right context. As such, the intra prediction of the block 3 may have no processing dependencies. The block 0, the block 1 and the block 2 reside in an upper-left quadrant of the 16×16 block and thus may be considered as a first group of the sub-blocks. The block 3 resides in an upper-right quadrant of the 16×16 block and thus may be considered as a second group of the sub-blocks. 
     In the step  152 , the previously buffered block 4 may begin intra prediction in the left process upon completion of the block 2. Since the block 4 uses the block 3 as the above-right context, the block 4 may begin the intra prediction using the third sequence shown in  FIG. 9   c . The block 5 may begin intra prediction in the right process in the step  154  upon completion of the processing for the block 3. Since the block 5 uses the block 3, the block  102  and the block  104  for context, no intra prediction dependencies may exist for the block 5. 
     Intra prediction for the block 6 may begin in step  156  upon completion of the intra prediction for the block 4. The block 6 generally uses the block 4, the block 1, the block 3 and the block 5 as the surrounding context. Since the prediction of the block 5 in step  154  may not be complete when the prediction of the block 6 begins in the step  156 , the step  156  may use the third prediction mode sequence shown in  FIG. 9   c . If the blocks are received in the coding order  90 , the block index number 8 (coding order block 7) may be temporarily buffered in the step  158 . The block 4 may reside in the upper-left quadrant along with the block 0, the block 1 and the block 2. As such, the block 4 may be considered as part of a third group of the sub-blocks. The block 5 and the block 6 may reside in the upper-right quadrant along with the block 3 (and the block 8). Therefore, the block 5 and the block 6 may be considered as part of a fourth group of the sub-blocks. 
     The block index number 7 (coding order block 8) may begin processing in the step  160  after completion of the block 4. The block 7 generally uses the block  106 , the block  108 , the block 2 and the block 4 as the context. As such, the intra prediction of the block 7 may have no processing dependencies. The block 7 may reside in a lower-left quadrant of the 16×16 block and may be considered a fifth group of the sub-blocks. 
     The intra predictions for the block 8 through the block 13 and the buffering of the block 12 may follow in the steps  162 - 174 , similar to the intra prediction for the block 4 through the block 7. In the step  176 , an intra prediction for the block 14 may begin. Since the block 14 uses the block 13 as the above-right context, the prediction of block 14 may depend on the completion of the block 13 in the step  174 . Therefore, the step  176  may use the third sequence of prediction modes shown in  FIG. 9   c . In the step  178 , an intra prediction for the block 15 may begin. Since the block 15 uses the block 14 as the left context, the step  178  may use the second sequence of prediction modes as shown in  FIG. 9   b.    
     The H.264/AVC recommendation generally defines the same 9 prediction modes for intra 8×8 predictions as the intra 4×4 predictions shown in  FIG. 2 . Therefore, the same four prediction mode sequences may be used for the intra 8×8 predictions, similar to the four prediction modes sequences used for the intra 4×4 predictions. For example, when a left context is absent at the start of an intra 8×8 prediction, the second sequence shown in  FIG. 9   b  may be applied. When an above-right context is absent at the start of an intra 8×8 prediction, the third sequence shown in  FIG. 9   c  may be applied. The fourth prediction mode sequence shown in  FIG. 9   d  may be used where the above context is not initially available. 
     Calculations for each of the predictions modes 0-8 generally create some intermediate results. Furthermore, some of the prediction modes may share the same intermediate results. A number of computations performed during the predictions may be reduced if the sequences are ordered to maximize a sharing of the intermediate results. Therefore, calculations of the prediction mode 8 may immediately follow the calculations of the prediction mode 1. The calculations of the predictions mode 3 may immediately follow the calculations the prediction mode 7. Furthermore, the prediction modes 2, 6, 4 and 5 may be calculated in order. As such, the third prediction mode sequence ( FIG. 9   c ) and the fourth prediction mode sequence ( FIG. 9   d ) may be the same sequence. Other prediction mode sequences may be implemented to meet the criteria of a particular application. 
     For intra 16×16 luminance (luma) predictions, only four prediction modes are defined by the H.264/AVC recommendation. If all of the appropriate context is available for an intra 16×16 prediction, a fifth sequence of prediction modes may be used, as shown in  FIG. 9   e . The vertical prediction mode 0 for the 16×16 blocks is generally independent of the left context. Therefore, an intra 16×16 prediction may be started using a sixth prediction sequence, as shown in  FIG. 9   f . The horizontal prediction mode 1 for the 16×16 blocks is generally independent of the above context. Therefore, an intra 16×16 prediction may be started using a seventh prediction sequence, as shown in  FIG. 9   g , where the above context is initially unsettled. 
     Intra 16×16 chrominance (chroma) predictions generally use the same four types of prediction modes (e.g., an intra chroma DC mode 0, an intra chroma horizontal mode 1, an intra chroma vertical mode 2 and an intra chroma plane mode 3) and the same three prediction sequences as the intra 16×16 luminance predictions. Both chroma blocks (e.g., a Cb block and a Cr block) of the current macroblock may use the same chrominance prediction mode. Once a particular chrominance prediction mode has been, determined, the particular chrominance prediction mode may be applied to each of the chroma blocks separately. 
     Similar dependencies may be present for inter-coded macroblocks/blocks/sub-blocks as predicted motion vectors are generally context dependent. A similar block reordering may be used for 4×4 sample partitions, 4×8 sample partitions, and 8×4 sample partitions to reduce the inter block dependencies. 
     Referring to  FIG. 10 , a block diagram of an example set of 4×4 blocks and associated motion vectors is shown. A predicted motion vector  180  may be calculated for the current block  100  based on the motion vectors of the surrounding blocks. The blocks  102 ,  104 ,  106  and  108  may have respective motion vectors  182 ,  184 ,  186  and  188 . The predicted motion vector  180  may be defined as a median of the motion vectors  182 ,  184  and  186 . The motion vector  188  (if available) may be used in place of the motion vector  186  where the motion vector  186  is not available. The H.264/AVC recommendation generally describes predicted motion vectors in section 8.4.1 and the associated subsections, which are hereby incorporated by reference in its entirety. The median function is generally defined in equation 1 as follows:
 
Median( x,y,z )= x+y+z −Min( x ,Min( y,z ))−Max( x ,Max( y,z ))  Eq. 1
 
The Min (minimum) function may be defined in equation 2 as follows:
 
Min( x,y )= x  if  x≦y  and  y  if  x&gt;y   Eq. 2
 
The Max (maximum) function may be defined in equation 3 as follows:
 
Max( x,y )= x  if  x≧y  and  y  if  x&lt;y   Eq. 3
 
Therefore, calculation of the prediction motion vector  180  depends on knowing the surrounding motion vectors  182 ,  184  and  186  (or  188 ).
 
     Referring again to  FIG. 8 , processing of the blocks 0-15 to calculate the predicted motion vectors may be performed in parallel. Starting at the step  142 , the predicted motion vector (PMV) for the block 0 may be calculated (predicted). Since the surrounding context motion vectors from the left block  106 , the above block  102  and the above-right block  104  may be already known, the prediction of the PMV 0 for block 0 may have no dependencies. In the step  144 , the PMV 1 for the block 1 may be predicted substantially simultaneously with the prediction of the PMV 0. However, the PMV 1 may consider the block 0 as the left context. Therefore, the prediction of the PMV 1 may not be completed until the PMV 0 is settled. 
     Calculations for the PMV 2 of the block 2 may start upon completion of the step  142  for the block 0. Since the PMV 2 may be calculated from the PMV 1, the step  146  may not complete until after the step  144  has completed. In the step  150 , the PMV 3 of block 3 may begin prediction. Calculation of PMV 3 depends on the context in the left block 1, the above block  102  and the above-right block  104  so the PMV 3 may be predicted without any dependencies on completion of the previous block (e.g., block 2). 
     In the step  152 , prediction of the PMV 4 for the block 4 may begin. The PMV 4 generally depends on the PMV 1, the PMV 2 and the PMV 3. As such, the step  152  may not be completed until the PMV 3 is known in the step  150 . In the step  154 , prediction of the PMV 5 for the block 5 may begin. The PMV 5 may have no dependency on the PMV 4 and thus the prediction may be processed without any dependencies on the other steps. 
     Calculations for the PMV 6 in the step  156  may begin upon the completion of the PMV 4. Likewise, calculations for the PMV 7 for the block 7 may begin in the step  158  upon completion of the PMV 5 prediction in the step  154 . The prediction of the PMV 6 may depend on the completion of the PMV 5 prediction. The prediction of the PMV 7 may be processed independently of the PMV 6 under the prediction order  120 . In the steps  162 - 174 , the PMV 8 through the PMV 13 may be generated similar to the PMV 4 through the PMV 7. The PMV 14 may be calculated in the step  176  with a dependency on the completion of the PMV 13. The PMV 15 may be calculated in the step  178  with a dependency on the completion of the PMV 14. 
     The reordering of the prediction order  120  generally helps the processing throughput for both encoders and decoders. An advantage of the present invention may be more significant in the encoders that in the decoders. For example, when several 4×4 prediction modes are tried for each block position, an encoder may process the several prediction modes faster when fewer dependencies exist between the start of one prediction and the ending of another prediction. For the decoders, an advantage of the prediction order  120  generally works statistically. Depending on which mode is coded, the decoder may wait or not for the previous block to be fully processed. The higher the resolution of the fields/frames and/or the lower the clock frequency of the processing circuitry, the more significant the advantages of the prediction order  120  may become. 
     Referring to  FIG. 11 , a block diagram of a 4×8 prediction order  190  is shown. The prediction order  190  generally accounts for the dependencies for motion vector predictions for 4×8 blocks. The prediction order  190  may rearrange the 4×8 blocks within and between the upper-right quadrant and the lower-left quadrant. As such, the eight sub-blocks in the prediction order  190  may have basically the same order as the eight sub-blocks in the top half of the prediction order  120  ( FIG. 6 ). 
     Referring to  FIG. 12 , a block diagram of an 8×4 prediction order  192  is shown. The prediction order  192  generally accounts for the dependencies for motion vector predictions of 8×4 blocks. The prediction order  192  may arrange the even-numbered blocks in a left half of the block and the odd-numbered blocks in a right half of the 16×16 block. 
     Referring to  FIG. 13 , a block diagram of an example prediction order  194  is shown. The prediction order  194  generally accounts for the dependencies where three of the four 8×8 blocks are divided into 4×4 blocks and a single 8×8 block is further divided into 4×8 blocks. 
     Referring to  FIG. 14 , a block diagram of another example prediction order  196  is shown. The prediction order  196  generally accounts for the dependencies where a single 8×8 block is divided into 4×4 blocks, a single 8×8 block is further divided into 4×8 blocks, a single 8×8 block is further divided into 8×4 blocks and a single 8×8 block is not sub-divided. Other prediction orders may be implemented to meet the criteria of a particular application. 
     A number of the intra prediction modes may be reduced based on statistics calculated for the macroblocks. For example, edge information may be used as statistics to determine areas in the original picture for special coding. The edge information may be used to improve intra and inter mode selection during encoding. In some embodiments, an edge direction of a macroblock may be taken as the sole intra prediction direction. 
     The functions performed by the diagrams of  FIGS. 6 ,  8  and  11 - 13  may be implemented using a conventional general purpose digital computer programmed according to the teachings of the present specification, as will be apparent to those skilled in the relevant art(s). Appropriate software coding can readily be prepared by skilled programmers based on the teachings of the present disclosure, as will also be apparent to those skilled in the relevant art(s). 
     The present invention may also be implemented by the preparation of ASICs, FPGAs, or by interconnecting an appropriate network of conventional component circuits, as is described herein, modifications of which will be readily apparent to those skilled in the art(s). 
     The present invention thus may also include a computer product which may be a storage medium including instructions which can be used to program a computer to perform a process in accordance with the present invention. The storage medium can include, but is not limited to, any type of disk including floppy disk, optical disk, CD-ROM, magneto-optical disks, ROMs, RAMs, EPROMs, EEPROMs, Flash memory, magnetic or optical cards, or any type of media suitable for storing electronic instructions. As used herein, the term “simultaneously” is meant to describe events that share some common time period but the term is not meant to be limited to events that begin at the same point in time, end at the same point in time, or have the same duration. 
     While the invention has been particularly shown and described with reference to the preferred embodiments thereof, it will be understood by those skilled in the art that various changes in form and details may be made without departing from the spirit and scope of the invention.