Abstract:
Methods having corresponding apparatus and computer-readable media comprise: receiving an estimated frame index, and an estimated symbol index, for a time-sliced OFDM signal; identifying a plurality of possible frame indexes, and a plurality of possible symbol indexes, based on the estimated frame index and the estimated symbol index; selecting a plurality of possible forward error correction code offsets based on the possible frame indexes and the possible symbol indexes; and selecting one of the possible frame indexes, and one of the possible symbol indexes, based on the possible forward error correction code offsets and a SYNC byte of the time-sliced OFDM signal.

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
       [0001]    This application claims benefit of U.S. Provisional Patent Application Ser. No. 61/078,811 filed Jul. 8, 2008, the disclosure thereof incorporated by reference herein in its entirety. 
     
    
     FIELD 
       [0002]    The present disclosure relates generally to receiver synchronization for receiving wireless signals. More particularly, the present disclosure relates to receiver link re-synchronization for time-sliced orthogonal frequency-division multiplexing communication systems. 
       BACKGROUND 
       [0003]    Wireless mobile communications devices such as mobile telephones are now increasingly used to receive and display digital video. Wireless communication technologies are being used to deliver this high-bandwidth content to the mobile devices. One such technology is orthogonal frequency-division multiplexing (OFDM). To conserve power in mobile receivers, some OFDM signals are time-sliced. These signals transmit data in bursts. A receiver can reduce power between bursts, and power up again to process each burst. To do this efficiently, the receiver needs knowledge of the start time for each burst. Determining these start times is referred to as link re-synchronization. 
       SUMMARY 
       [0004]    In general, in one aspect, an embodiment features a method comprising: receiving an estimated frame index, and an estimated symbol index, for a time-sliced OFDM signal; identifying a plurality of possible frame indexes, and a plurality of possible symbol indexes, based on the estimated frame index and the estimated symbol index; selecting a plurality of possible forward error correction code offsets based on the possible frame indexes and the possible symbol indexes; and selecting one of the possible frame indexes, and one of the possible symbol indexes, based on the possible forward error correction code offsets and a SYNC byte of the time-sliced OFDM signal. 
         [0005]    Embodiments of the method can include one or more of the following features. Some embodiments comprise re-synchronizing a receiver of the OFDM signal based on the one of the possible frame indexes and the one of the possible symbol indexes. Some embodiments comprise displaying content of the OFDM signal based on the re-synchronizing. In some embodiments, the OFDM signal comprises a DVB-H signal. In some embodiments, selecting one of the possible frame indexes, and one of the possible symbol indexes, comprises: correlating the SYNC byte with a plurality of transport stream packets of the OFDM signal according to each of the possible forward error correction code offsets. 
         [0006]    In general, in one aspect, an embodiment features an apparatus comprising: an input module to receive an estimated frame index, and an estimated symbol index, for a time-sliced OFDM signal; an index module to identify a plurality of possible frame indexes, and a plurality of possible symbol indexes, based on the estimated frame index and the estimated symbol index; an offset module to select a plurality of possible forward error correction code offsets based on the possible frame indexes and the possible symbol indexes; and a synchronization module to select one of the possible frame indexes, and one of the possible symbol indexes, based on the possible forward error correction code offsets and a SYNC byte of the time-sliced OFDM signal. 
         [0007]    Embodiments of the apparatus can include one or more of the following features. Some embodiments comprise a timing module to re-synchronize a receiver of the OFDM signal based on the one of the possible frame indexes and the one of the possible symbol indexes. Some embodiments comprise a display to display content of the OFDM signal based on the one of the possible frame indexes and the one of the possible symbol indexes. In some embodiments, the OFDM signal comprises a DVB-H signal. In some embodiments, the synchronization module comprises: a correlator to correlate the SYNC byte with a plurality of transport stream packets of the OFDM signal according to each of the possible forward error correction code offsets. 
         [0008]    In general, in one aspect, an embodiment features computer-readable media embodying instructions executable by a computer to perform a method comprising: receiving an estimated frame index, and an estimated symbol index, for a time-sliced OFDM signal; identifying a plurality of possible frame indexes, and a plurality of possible symbol indexes, based on the estimated frame index and the estimated symbol index; selecting a plurality of possible forward error correction code offsets based on the possible frame indexes and the possible symbol indexes; and selecting one of the possible frame indexes, and one of the possible symbol indexes, based on the possible forward error correction code offsets and a SYNC byte of the time-sliced OFDM signal. 
         [0009]    Embodiments of the computer-readable media can include one or more of the following features. In some embodiments, the method further comprises: re-synchronizing a receiver of the OFDM signal based on the one of the possible frame indexes and the one of the possible symbol indexes. In some embodiments, the method further comprises: displaying content of the OFDM signal based on the re-synchronizing. In some embodiments, the OFDM signal comprises a DVB-H signal. In some embodiments, selecting one of the possible frame indexes, and one of the possible symbol indexes, comprises: correlating the SYNC byte with a plurality of transport stream packets of the OFDM signal according to each of the possible forward error correction code offsets. 
         [0010]    The details of one or more implementations are set forth in the accompanying drawings and the description below. Other features will be apparent from the description and drawings, and from the claims. 
     
    
     
       DESCRIPTION OF DRAWINGS 
         [0011]      FIG. 1  shows elements of a wireless data communication system comprising a wireless communication device receiving wireless OFDM signals from a transmitter according to some embodiments. 
           [0012]      FIG. 2  shows elements of the wireless communication device of  FIG. 1  according to some embodiments. 
           [0013]      FIG. 3  shows a re-synchronization process for the wireless communication device of  FIG. 2  according to some embodiments. 
           [0014]      FIG. 4  shows example code for Reed-Solomon code bit offset estimation. 
       
    
    
       [0015]    The leading digit(s) of each reference numeral used in this specification indicates the number of the drawing in which the reference numeral first appears. 
       DETAILED DESCRIPTION 
       [0016]    Embodiments of the present disclosure provide fast re-synchronization for time-sliced orthogonal frequency-division multiplexing (OFDM) signals. One such signal is DVB-H (Digital Video Broadcasting—Handheld) in time-slice mode. Various embodiments are described with reference to DVB-H signals. However, the disclosed techniques apply to other OFDM signals as well, as will be apparent after reading this disclosure. 
         [0017]      FIG. 1  shows elements of a wireless data communication system  100  comprising a wireless communication device  102  receiving wireless OFDM signals  104  from a transmitter  106  according to some embodiments. Although in the described embodiments, the elements of wireless data communication system  100  are presented in one arrangement, other embodiments may feature other arrangements, as will be apparent to one skilled in the relevant arts based on the disclosure and teachings provided herein. For example, the elements of wireless data communication system  100  can be implemented in hardware, software, or combinations thereof. 
         [0018]      FIG. 2  shows elements of wireless communication device  102  of  FIG. 1  according to some embodiments. Although in the described embodiments, the elements of wireless communication device  102  are presented in one arrangement, other embodiments may feature other arrangements, as will be apparent to one skilled in the relevant arts based on the disclosure and teachings provided herein. For example, the elements of wireless communication device  102  can be implemented in hardware, software, or combinations thereof. For example, wireless communication device  102  can be implemented as a mobile phone, a personal digital assistant (PDA), a personal computer, and the like. 
         [0019]    Referring to  FIG. 2 , wireless communication device  102  includes a receiver  208  to receive wireless OFDM signals  104 , which can include DVB-H signals or the like. Wireless communication device  102  also includes a re-synchronization module  210  to re-synchronize receiver  208  and an output module  212  to output content of OFDM signals  104 . Output module  212  includes a display  214  to display content of OFDM signals  104 . Re-synchronization module  210  includes an input module  216  to receive an estimated frame index  218 , and an estimated symbol index  220 , for OFDM signals  104 ; an index module  222  to select a plurality of possible frame indexes  224 , and a plurality of possible symbol indexes  226 , based on estimated frame index  218  and estimated symbol index  220 ; an offset module  228  to select a plurality of possible forward error correction code offsets  230  based on possible frame indexes  224  and possible symbol indexes  226 ; a synchronization module  232  to select one of possible frame indexes  224 , and one of possible symbol indexes  226 , based on possible forward error correction code offsets  230  and a SYNC byte  234  of OFDM signals  104 , and a timing module  236  to re-synchronize receiver  208  using one or more re-synchronization signals  238  based on selected frame index  224  and selected symbol index  226 . Synchronization module  232  includes a correlator  240  to correlate SYNC byte  234  with a plurality of transport stream packets  242  of OFDM signal  104  according to each of possible forward error correction code offsets  230 . 
         [0020]      FIG. 3  shows a re-synchronization process  300  for wireless communication device  102  of  FIG. 2  according to some embodiments. Although in the described embodiments, the elements of the processes disclosed herein are presented in one arrangement, other embodiments may feature other arrangements, as will be apparent to one skilled in the relevant arts based on the disclosure and teachings provided herein. For example, in various embodiments, some or all of the steps of the disclosed processes can be executed in a different order, concurrently, and the like. 
         [0021]    Referring to  FIG. 3 , receiver  208  receives OFDM signals  104  (step  302 ). In some embodiments, signals  104  include DVB-H signals. Based on signals  104 , receiver  208  generates estimated frame index  218  and estimated symbol index  220 , for example according to conventional techniques. 
         [0022]    Input module  216  of re-synchronization module  210  receives estimated frame index  218  and estimated symbol index  220  (step  304 ). Based on estimated frame index  218  and estimated symbol index  220 , index module  222  of re-synchronization module  210  identifies a plurality of possible frame indexes  224 , and a plurality of possible symbol indexes  226  (step  306 ). Based on possible frame indexes  224  and possible symbol indexes  226 , offset module  228  selects a plurality of possible forward error correction code offsets  230  (step  308 ). 
         [0023]    These identifications and selections can be based on the known patterns of the forward error correction code used in OFDM signal  104 . For example, Tables 1-9 at the end of this disclosure show the known relationships between the Reed-Solomon Code Block Index (#RS block) and Offset (#Offset) for DVB-H signals. Tables 1-3 show the known relationships for 8K mode for Quadrature phase-shift keying (QPSK), 16QAM (Quadrature amplitude modulation), and 64QAM, respectively. Tables 4-6 show the known relationships for 2K mode for QPSK, 16QAM, and 64QAM, respectively. Tables 4-6 show the known relationships for 4K mode for QPSK, 16QAM, and 64QAM, respectively. According to the pattern for the RS code offset within 0-67 symbols (that is, one frame) in Table 1, the minimum repeat period of the RS code is 17 symbols. The possible repeat periods are 17, 34, 68 symbols, etc. Because the scattered pilot pattern is repeated every 4 symbols, the correct RS code offset can be selected if estimated symbol index  220  in the frame (that is, the approximate wake up time) is within +/−34 symbols. 
         [0024]    Synchronization module  232  selects one of possible frame indexes  224 , and one of possible symbol indexes  226 , based on possible forward error correction code offsets  230  and a SYNC byte  234  of OFDM signals  104  (step  310 ). In particular, correlator  240  correlates SYNC byte  234  with a plurality of transport stream packets  242  of OFDM signal  104  according to each of possible forward error correction code offsets  230 . For example, with DVB-H signals, in order to decide to which possible symbol index  226  is correct, SYNC byte  234  is used to verify because different symbol indexes are mapped to different RS code bit offsets, as shown in Tables 1-9. The first byte from the estimated RS code bit offset is SYNC byte  234 . An 8-bit correlation can be applied to all 17 possible RS code offsets, and the absolute correlation value can be accumulated over N times (that is, N transport stream (TS) packets, where each TS packet has one SYNC byte  234  at the head position). Considering time diversity, this N accumulated 8-bit correlation is repeated by M times for verification. An average value is calculated for each RS code offset position among the M accumulated correlation elements. The accumulated correlation elements with values larger than the average value are taken as effective elements for further processing. By doing so, the even/odd de-interleave pattern in 2K mode can be resolved. It should be noted that the N TS packet number is equal to the TS packet number in each OFDM symbol in 2K mode. Furthermore, the average value of the effective elements is calculated for all 17 RS code offset positions. Among the 17 average values of the effective elements, the maximum value is obtained to indicate the correct RS offset with a value larger than a threshold 5/8*8*N (meaning 5 bits correct among the 8 bits of SYNC byte  234 ). Based on this information, synchronization module  232  selects the correct frame index  224  and the correct symbol index  226 .  FIG. 4  shows example code for the RS code bit offset estimation. 
         [0025]    Referring again to  FIG. 3 , timing module  236  re-synchronizes receiver  208  based on selected frame index  224  and selected symbol index  226  (step  312 ). For example, timing module  236  provides the needed information to receiver  208  with re-synchronization signals  238 . Based on selected frame index  224  and selected symbol index  226 , display  214  of output module  212  displays content of OFDM signal  104  (step  314 ). 
         [0000]    
       
         
               
               
               
               
               
             
               
               
               
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 1 
               
             
             
               
                   
               
               
                 1/2 
                 2/3 
                 3/4 
                 5/6 
                 7/8 
               
             
          
           
               
                 #RS block 
                 #Offset 
                 #RS block 
                 #Offset 
                 #RS block 
                 #Offset 
                 #RS block 
                 #Offset 
                 #RS block 
                 #Offset 
               
               
                   
               
             
          
           
               
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 4 
                 480 
                 5 
                 96 
                 6 
                 720 
                 7 
                 1344 
                 7 
                 840 
               
               
                 8 
                 960 
                 10 
                 192 
                 12 
                 1440 
                 13 
                 1056 
                 13 
                 48 
               
               
                 12 
                 1440 
                 15 
                 288 
                 17 
                 528 
                 19 
                 768 
                 20 
                 888 
               
               
                 15 
                 288 
                 20 
                 384 
                 23 
                 1248 
                 25 
                 480 
                 26 
                 96 
               
               
                 19 
                 768 
                 25 
                 480 
                 28 
                 336 
                 31 
                 192 
                 33 
                 936 
               
               
                 23 
                 1248 
                 30 
                 576 
                 34 
                 1056 
                 38 
                 1536 
                 39 
                 144 
               
               
                 26 
                 96 
                 35 
                 672 
                 39 
                 144 
                 44 
                 1248 
                 46 
                 984 
               
               
                 30 
                 576 
                 40 
                 768 
                 45 
                 864 
                 50 
                 960 
                 52 
                 192 
               
               
                 34 
                 1056 
                 45 
                 864 
                 51 
                 1584 
                 56 
                 672 
                 59 
                 1032 
               
               
                 38 
                 1536 
                 50 
                 960 
                 56 
                 672 
                 62 
                 384 
                 65 
                 240 
               
               
                 41 
                 384 
                 55 
                 1056 
                 62 
                 1392 
                 68 
                 96 
                 72 
                 1080 
               
               
                 45 
                 864 
                 60 
                 1152 
                 67 
                 480 
                 75 
                 1440 
                 78 
                 288 
               
               
                 49 
                 1344 
                 65 
                 1248 
                 73 
                 1200 
                 81 
                 1152 
                 85 
                 1128 
               
               
                 52 
                 192 
                 70 
                 1344 
                 78 
                 288 
                 87 
                 864 
                 91 
                 336 
               
               
                 56 
                 672 
                 75 
                 1440 
                 84 
                 1008 
                 93 
                 576 
                 98 
                 1176 
               
               
                 60 
                 1152 
                 80 
                 1536 
                 89 
                 96 
                 99 
                 288 
                 104 
                 384 
               
               
                 64 
                 0 
                 85 
                 0 
                 95 
                 816 
                 106 
                 0 
                 111 
                 1224 
               
               
                 67 
                 480 
                 89 
                 96 
                 101 
                 1536 
                 112 
                 1344 
                 117 
                 432 
               
               
                 71 
                 960 
                 94 
                 192 
                 106 
                 624 
                 118 
                 1056 
                 124 
                 1272 
               
               
                 75 
                 1440 
                 99 
                 288 
                 112 
                 1344 
                 124 
                 768 
                 130 
                 480 
               
               
                 78 
                 288 
                 104 
                 384 
                 117 
                 432 
                 130 
                 480 
                 137 
                 1320 
               
               
                 82 
                 768 
                 109 
                 480 
                 123 
                 1152 
                 136 
                 192 
                 143 
                 528 
               
               
                 86 
                 1248 
                 114 
                 576 
                 128 
                 240 
                 143 
                 1536 
                 150 
                 1368 
               
               
                 89 
                 96 
                 119 
                 672 
                 134 
                 960 
                 149 
                 1248 
                 156 
                 576 
               
               
                 93 
                 576 
                 124 
                 768 
                 139 
                 48 
                 155 
                 960 
                 163 
                 1416 
               
               
                 97 
                 1056 
                 129 
                 864 
                 145 
                 768 
                 161 
                 672 
                 169 
                 624 
               
               
                 101 
                 1536 
                 134 
                 960 
                 151 
                 1488 
                 167 
                 384 
                 176 
                 1464 
               
               
                 104 
                 384 
                 139 
                 1056 
                 156 
                 576 
                 173 
                 96 
                 182 
                 672 
               
               
                 108 
                 864 
                 144 
                 1152 
                 162 
                 1296 
                 180 
                 1440 
                 189 
                 1512 
               
               
                 112 
                 1344 
                 149 
                 1248 
                 167 
                 384 
                 186 
                 1152 
                 195 
                 720 
               
               
                 115 
                 192 
                 154 
                 1344 
                 173 
                 1104 
                 192 
                 864 
                 202 
                 1560 
               
               
                 119 
                 672 
                 159 
                 1440 
                 178 
                 192 
                 198 
                 576 
                 208 
                 768 
               
               
                 123 
                 1152 
                 164 
                 1536 
                 184 
                 912 
                 204 
                 288 
                 215 
                 1608 
               
               
                 127 
                 0 
                 169 
                 0 
                 190 
                 0 
                 211 
                 0 
                 221 
                 816 
               
               
                 130 
                 480 
                 173 
                 96 
                 195 
                 720 
                 217 
                 1344 
                 227 
                 24 
               
               
                 134 
                 960 
                 178 
                 192 
                 201 
                 1440 
                 223 
                 1056 
                 234 
                 864 
               
               
                 138 
                 1440 
                 183 
                 288 
                 206 
                 528 
                 229 
                 768 
                 240 
                 72 
               
               
                 141 
                 288 
                 188 
                 384 
                 212 
                 1248 
                 235 
                 480 
                 247 
                 912 
               
               
                 145 
                 768 
                 193 
                 480 
                 217 
                 336 
                 241 
                 192 
                 253 
                 120 
               
               
                 149 
                 1248 
                 198 
                 576 
                 223  
                 1056 
                 248 
                 1536 
                 260 
                 960 
               
               
                 152 
                 96 
                 203 
                 672 
                 228 
                 144 
                 254 
                 1248 
                 266 
                 168 
               
               
                 156 
                 576 
                 208 
                 768 
                 234 
                 864 
                 260 
                 960 
                 273 
                 1008 
               
               
                 160 
                 1056 
                 213 
                 864 
                 240 
                 1584 
                 266 
                 672 
                 279 
                 216 
               
               
                 164 
                 1536 
                 218 
                 960 
                 245 
                 672 
                 272 
                 384 
                 286 
                 1056 
               
               
                 167 
                 384 
                 223 
                 1056 
                 251 
                 1392 
                 278 
                 96 
                 292 
                 264 
               
               
                 171 
                 864 
                 228 
                 1152 
                 256 
                 480 
                 285 
                 1440 
                 299 
                 1104 
               
               
                 175 
                 1344 
                 233 
                 1248 
                 262 
                 1200 
                 291 
                 1152 
                 305 
                 312 
               
               
                 178 
                 192 
                 238 
                 1344 
                 267 
                 288 
                 297 
                 864 
                 312 
                 1152 
               
               
                 182 
                 672 
                 243 
                 1440 
                 273 
                 1008 
                 303 
                 576 
                 318 
                 360 
               
               
                 186 
                 1152 
                 248 
                 1536 
                 278 
                 96 
                 309 
                 288 
                 325 
                 1200 
               
               
                 190 
                 0 
                 253 
                 0 
                 284 
                 816 
                 316 
                 0 
                 331 
                 408 
               
               
                 193 
                 480 
                 257 
                 96 
                 290 
                 1536 
                 322 
                 1344 
                 338 
                 1248 
               
               
                 197 
                 960 
                 262 
                 192 
                 295 
                 624 
                 328 
                 1056 
                 344 
                 456 
               
               
                 201 
                 1440 
                 267 
                 288 
                 301 
                 1344 
                 334 
                 768 
                 351 
                 1296 
               
               
                 204 
                 288 
                 272 
                 384 
                 306 
                 432 
                 340 
                 480 
                 357 
                 504 
               
               
                 208 
                 768 
                 277 
                 480 
                 312 
                 1152 
                 346 
                 192 
                 364 
                 1344 
               
               
                 212 
                 1248 
                 282 
                 576 
                 317 
                 240 
                 353 
                 1536 
                 370 
                 552 
               
               
                 215 
                 96 
                 287 
                 672 
                 323 
                 960 
                 359 
                 1248 
                 377 
                 1392 
               
               
                 219 
                 576 
                 292 
                 768 
                 328 
                 48 
                 365 
                 960 
                 383 
                 600 
               
               
                 223 
                 1056 
                 297 
                 864 
                 334 
                 768 
                 371 
                 672 
                 390 
                 1440 
               
               
                 227 
                 1536 
                 302 
                 960 
                 340 
                 1488 
                 377 
                 384 
                 396 
                 648 
               
               
                 230 
                 384 
                 307 
                 1056 
                 345 
                 576 
                 383 
                 96 
                 403 
                 1488 
               
               
                 234 
                 864 
                 312 
                 1152 
                 351 
                 1296 
                 390 
                 1440 
                 409 
                 696 
               
               
                 238 
                 1344 
                 317 
                 1248 
                 356 
                 384 
                 396 
                 1152 
                 416 
                 1536 
               
               
                 241 
                 192 
                 322 
                 1344 
                 362 
                 1104 
                 402 
                 864 
                 422 
                 744 
               
               
                 245 
                 672 
                 327 
                 1440 
                 367 
                 192 
                 408 
                 576 
                 429 
                 1584 
               
               
                 249 
                 1152 
                 332 
                 1536 
                 373 
                 912 
                 414 
                 288 
                 435 
                 792 
               
               
                   
               
             
          
         
       
     
         [0000]    
       
         
               
               
               
               
               
             
               
               
               
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 2 
               
             
             
               
                   
               
               
                 1/2 
                 2/3 
                 3/4 
                 5/6 
                 7/8 
               
             
          
           
               
                 #RS block 
                 #Offset 
                 #RS block 
                 #Offset 
                 #RS block 
                 #Offset 
                 #RS block 
                 #Offset 
                 #RS block 
                 #Offset 
               
               
                   
               
             
          
           
               
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 8 
                 960 
                 10 
                 192 
                 12 
                 1440 
                 13 
                 1056 
                 13 
                 48 
               
               
                 15 
                 288 
                 20 
                 384 
                 23 
                 1248 
                 25 
                 480 
                 26 
                 96 
               
               
                 23 
                 1248 
                 30 
                 576 
                 34 
                 1056 
                 38 
                 1536 
                 39 
                 144 
               
               
                 30 
                 576 
                 40 
                 768 
                 45 
                 864 
                 50 
                 960 
                 52 
                 192 
               
               
                 38 
                 1536 
                 50 
                 960 
                 56 
                 672 
                 62 
                 384 
                 65 
                 240 
               
               
                 45 
                 864 
                 60 
                 1152 
                 67 
                 480 
                 75 
                 1440 
                 78 
                 288 
               
               
                 52 
                 192 
                 70 
                 1344 
                 78 
                 288 
                 87 
                 864 
                 91 
                 336 
               
               
                 60 
                 1152 
                 80 
                 1536 
                 89 
                 96 
                 99 
                 288 
                 104 
                 384 
               
               
                 67 
                 480 
                 89 
                 96 
                 101 
                 1536 
                 112 
                 1344 
                 117 
                 432 
               
               
                 75 
                 1440 
                 99 
                 288 
                 112 
                 1344 
                 124 
                 768 
                 130 
                 480 
               
               
                 82 
                 768 
                 109 
                 480 
                 123 
                 1152 
                 136 
                 192 
                 143 
                 528 
               
               
                 89 
                 96 
                 119 
                 672 
                 134 
                 960 
                 149 
                 1248 
                 156 
                 576 
               
               
                 97 
                 1056 
                 129 
                 864 
                 145 
                 768 
                 161 
                 672 
                 169 
                 624 
               
               
                 104 
                 384 
                 139 
                 1056 
                 156 
                 576 
                 173 
                 96 
                 182 
                 672 
               
               
                 112 
                 1344 
                 149 
                 1248 
                 167 
                 384 
                 186 
                 1152 
                 195 
                 720 
               
               
                 119 
                 672 
                 159 
                 1440 
                 178 
                 192 
                 198 
                 576 
                 208 
                 768 
               
               
                 127 
                 0 
                 169 
                 0 
                 190 
                 0 
                 211 
                 0 
                 221 
                 816 
               
               
                 134 
                 960 
                 178 
                 192 
                 201 
                 1440 
                 223  
                 1056 
                 234 
                 864 
               
               
                 141 
                 288 
                 188 
                 384 
                 212 
                 1248 
                 235  
                 480 
                 247 
                 912 
               
               
                 149 
                 1248 
                 198 
                 576 
                 223 
                 1056 
                 248  
                 1536 
                 260 
                 960 
               
               
                 156 
                 576 
                 208 
                 768 
                 234 
                 864 
                 260  
                 960 
                 273 
                 1008 
               
               
                 164 
                 1536 
                 218 
                 960 
                 245 
                 672 
                 272  
                 384 
                 286 
                 1056 
               
               
                 171 
                 864 
                 228 
                 1152 
                 256 
                 480 
                 285  
                 1440 
                 299 
                 1104 
               
               
                 178 
                 192 
                 238 
                 1344 
                 267 
                 288 
                 297  
                 864 
                 312 
                 1152 
               
               
                 186 
                 1152 
                 248 
                 1536 
                 278 
                 96 
                 309 
                 288 
                 325 
                 1200 
               
               
                 193 
                 480 
                 257 
                 96 
                 290 
                 1536 
                 322 
                 1344 
                 338 
                 1248 
               
               
                 201 
                 1440 
                 267 
                 288 
                 301 
                 1344 
                 334 
                 768 
                 351 
                 1296 
               
               
                 208 
                 768 
                 277 
                 480 
                 312 
                 1152 
                 346 
                 192 
                 364 
                 1344 
               
               
                 215 
                 96 
                 287 
                 672 
                 323 
                 960 
                 359 
                 1248 
                 377 
                 1392 
               
               
                 223 
                 1056 
                 297 
                 864 
                 334 
                 768 
                 371 
                 672 
                 390 
                 1440 
               
               
                 230 
                 384 
                 307 
                 1056 
                 345 
                 576 
                 383 
                 96 
                 403 
                 1488 
               
               
                 238 
                 1344 
                 317 
                 1248 
                 356 
                 384 
                 396 
                 1152 
                 416 
                 1536 
               
               
                 245 
                 672 
                 327 
                 1440 
                 367 
                 192 
                 408 
                 576 
                 429 
                 1584 
               
               
                 253 
                 0 
                 337 
                 0 
                 379 
                 0 
                 421 
                 0 
                 442 
                 0 
               
               
                 260 
                 960 
                 346 
                 192 
                 390 
                 1440 
                 433 
                 1056 
                 454 
                 48 
               
               
                 267 
                 288 
                 356 
                 384 
                 401 
                 1248 
                 445 
                 480 
                 467 
                 96 
               
               
                 275 
                 1248 
                 366 
                 576 
                 412 
                 1056 
                 458 
                 1536 
                 480 
                 144 
               
               
                 282 
                 576 
                 376 
                 768 
                 423 
                 864 
                 470 
                 960 
                 493 
                 192 
               
               
                 290 
                 1536 
                 386 
                 960 
                 434 
                 672 
                 482 
                 384 
                 506 
                 240 
               
               
                 297 
                 864 
                 396 
                 1152 
                 445 
                 480 
                 495 
                 1440 
                 519 
                 288 
               
               
                 304 
                 192 
                 406 
                 1344 
                 456 
                 288 
                 507 
                 864 
                 532 
                 336 
               
               
                 312 
                 1152 
                 416 
                 1536 
                 467 
                 96 
                 519 
                 288 
                 545 
                 384 
               
               
                 319 
                 480 
                 425 
                 96 
                 479 
                 1536 
                 532 
                 1344 
                 558 
                 432 
               
               
                 327 
                 1440 
                 435 
                 288 
                 490 
                 1344 
                 544 
                 768 
                 571 
                 480 
               
               
                 334 
                 768 
                 445 
                 480 
                 501 
                 1152 
                 556 
                 192 
                 584 
                 528 
               
               
                 341 
                 96 
                 455 
                 672 
                 512 
                 960 
                 569 
                 1248 
                 597 
                 576 
               
               
                 349 
                 1056 
                 465 
                 864 
                 523 
                 768 
                 581 
                 672 
                 610 
                 624 
               
               
                 356 
                 384 
                 475 
                 1056 
                 534 
                 576 
                 593 
                 96 
                 623 
                 672 
               
               
                 364 
                 1344 
                 485 
                 1248 
                 545 
                 384 
                 606 
                 1152 
                 636 
                 720 
               
               
                 371 
                 672 
                 495 
                 1440 
                 556 
                 192 
                 618 
                 576 
                 649 
                 768 
               
               
                 379 
                 0 
                 505 
                 0 
                 568 
                 0 
                 631 
                 0 
                 662 
                 816 
               
               
                 386 
                 960 
                 514 
                 192 
                 579 
                 1440 
                 643 
                 1056 
                 675 
                 864 
               
               
                 393 
                 288 
                 524 
                 384 
                 590 
                 1248 
                 655 
                 480 
                 688 
                 912 
               
               
                 401 
                 1248 
                 534 
                 576 
                 601 
                 1056 
                 668 
                 1536 
                 701 
                 960 
               
               
                 408 
                 576 
                 544 
                 768 
                 612 
                 864 
                 680 
                 960 
                 714 
                 1008 
               
               
                 416 
                 1536 
                 554 
                 960 
                 623 
                 672 
                 692 
                 384 
                 727 
                 1056 
               
               
                 423 
                 864 
                 564 
                 1152 
                 634 
                 480 
                 705 
                 1440 
                 740 
                 1104 
               
               
                 430 
                 192 
                 574 
                 1344 
                 645 
                 288 
                 717 
                 864 
                 753 
                 1152 
               
               
                 438 
                 1152 
                 584 
                 1536 
                 656 
                 96 
                 729 
                 288 
                 766 
                 1200 
               
               
                 445 
                 480 
                 593 
                 96 
                 668 
                 1536 
                 742 
                 1344 
                 779 
                 1248 
               
               
                 453 
                 1440 
                 603 
                 288 
                 679 
                 1344 
                 754 
                 768 
                 792 
                 1296 
               
               
                 460 
                 768 
                 613 
                 480 
                 690 
                 1152 
                 766 
                 192 
                 805 
                 1344 
               
               
                 467 
                 96 
                 623 
                 672 
                 701 
                 960 
                 779 
                 1248 
                 818 
                 1392 
               
               
                 475 
                 1056 
                 633 
                 864 
                 712 
                 768 
                 791 
                 672 
                 831 
                 1440 
               
               
                 482 
                 384 
                 643 
                 1056 
                 723 
                 576 
                 803 
                 96 
                 844 
                 1488 
               
               
                 490 
                 1344 
                 653 
                 1248 
                 734 
                 384 
                 816 
                 1152 
                 857 
                 1536 
               
               
                 497 
                 672 
                 663 
                 1440 
                 745 
                 192 
                 828 
                 576 
                 870 
                 1584 
               
               
                   
               
             
          
         
       
     
         [0000]    
       
         
               
               
               
               
               
             
               
               
               
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 3 
               
             
             
               
                   
               
               
                 1/2 
                 2/3 
                 3/4 
                 5/6 
                 7/8 
               
             
          
           
               
                 #RS block 
                 #Offset 
                 #RS block 
                 #Offset 
                 #RS block 
                 #Offset 
                 #RS block 
                 #Offset 
                 #RS block 
                 #Offset 
               
               
                   
               
             
          
           
               
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 12 
                 1440 
                 15 
                 288 
                 17 
                 528 
                 19 
                 768 
                 20 
                 888 
               
               
                 23 
                 1248 
                 30 
                 576 
                 34 
                 1056 
                 38 
                 1536 
                 39 
                 144 
               
               
                 34 
                 1056 
                 45 
                 864 
                 51 
                 1584 
                 56 
                 672 
                 59 
                 1032 
               
               
                 45 
                 864 
                 60 
                 1152 
                 67 
                 480 
                 75 
                 1440 
                 78 
                 288 
               
               
                 56 
                 672 
                 75 
                 1440 
                 84 
                 1008 
                 93 
                 576 
                 98 
                 1176 
               
               
                 67 
                 480 
                 89 
                 96 
                 101 
                 1536 
                 112 
                 1344 
                 117 
                 432 
               
               
                 78 
                 288 
                 104 
                 384 
                 117 
                 432 
                 130 
                 480 
                 137 
                 1320 
               
               
                 89 
                 96 
                 119 
                 672 
                 134 
                 960 
                 149 
                 1248 
                 156 
                 576 
               
               
                 101 
                 1536 
                 134 
                 960 
                 151 
                 1488 
                 167 
                 384 
                 176 
                 1464 
               
               
                 112 
                 1344 
                 149 
                 1248 
                 167 
                 384 
                 186 
                 1152 
                 195 
                 720 
               
               
                 123 
                 1152 
                 164 
                 1536 
                 184 
                 912 
                 204 
                 288 
                 215 
                 1608 
               
               
                 134 
                 960 
                 178 
                 192 
                 201 
                 1440 
                 223 
                 1056 
                 234 
                 864 
               
               
                 145 
                 768 
                 193 
                 480 
                 217 
                 336 
                 241 
                 192 
                 253 
                 120 
               
               
                 156 
                 576 
                 208 
                 768 
                 234 
                 864 
                 260 
                 960 
                 273 
                 1008 
               
               
                 167 
                 384 
                 223 
                 1056 
                 251 
                 1392 
                 278 
                 96 
                 292 
                 264 
               
               
                 178 
                 192 
                 238 
                 1344 
                 267 
                 288 
                 297 
                 864 
                 312 
                 1152 
               
               
                 190 
                 0 
                 253 
                 0 
                 284 
                 816 
                 316 
                 0 
                 331 
                 408 
               
               
                 201 
                 1440 
                 267 
                 288 
                 301 
                 1344 
                 334 
                 768 
                 351 
                 1296 
               
               
                 212 
                 1248 
                 282 
                 576 
                 317 
                 240 
                 353 
                 1536 
                 370 
                 552 
               
               
                 223 
                 1056 
                 297 
                 864 
                 334 
                 768 
                 371 
                 672 
                 390 
                 1440 
               
               
                 234 
                 864 
                 312 
                 1152 
                 351 
                 1296 
                 390 
                 1440 
                 409 
                 696 
               
               
                 245 
                 672 
                 327 
                 1440 
                 367 
                 192 
                 408 
                 576 
                 429 
                 1584 
               
               
                 256 
                 480 
                 341 
                 96 
                 384 
                 720 
                 427 
                 1344 
                 448 
                 840 
               
               
                 267 
                 288 
                 356 
                 384 
                 401 
                 1248 
                 445 
                 480 
                 467 
                 96 
               
               
                 278 
                 96 
                 371 
                 672 
                 417 
                 144 
                 464 
                 1248 
                 487 
                 984 
               
               
                 290 
                 1536 
                 386 
                 960 
                 434 
                 672 
                 482 
                 384 
                 506 
                 240 
               
               
                 301 
                 1344 
                 401 
                 1248 
                 451 
                 1200 
                 501 
                 1152 
                 526 
                 1128 
               
               
                 312 
                 1152 
                 416 
                 1536 
                 467 
                 96 
                 519 
                 288 
                 545 
                 384 
               
               
                 323 
                 960 
                 430 
                 192 
                 484 
                 624 
                 538 
                 1056 
                 565 
                 1272 
               
               
                 334 
                 768 
                 445 
                 480 
                 501 
                 1152 
                 556 
                 192 
                 584 
                 528 
               
               
                 345 
                 576 
                 460 
                 768 
                 517 
                 48 
                 575 
                 960 
                 604 
                 1416 
               
               
                 356 
                 384 
                 475 
                 1056 
                 534 
                 576 
                 593 
                 96 
                 623 
                 672 
               
               
                 367 
                 192 
                 490 
                 1344 
                 551 
                 1104 
                 612 
                 864 
                 643 
                 1560 
               
               
                 379 
                 0 
                 505 
                 0 
                 568 
                 0 
                 631 
                 0 
                 662 
                 816 
               
               
                 390 
                 1440 
                 519 
                 288 
                 584 
                 528 
                 649 
                 768 
                 681 
                 72 
               
               
                 401 
                 1248 
                 534 
                 576 
                 601 
                 1056 
                 668 
                 1536 
                 701 
                 960 
               
               
                 412 
                 1056 
                 549 
                 864 
                 618 
                 1584 
                 686 
                 672 
                 720 
                 216 
               
               
                 423 
                 864 
                 564 
                 1152 
                 634 
                 480 
                 705 
                 1440 
                 740 
                 1104 
               
               
                 434 
                 672 
                 579 
                 1440 
                 651 
                 1008 
                 723 
                 576 
                 759 
                 360 
               
               
                 445 
                 480 
                 593 
                 96 
                 668 
                 1536 
                 742 
                 1344 
                 779 
                 1248 
               
               
                 456 
                 288 
                 608 
                 384 
                 684 
                 432 
                 760 
                 480 
                 798 
                 504 
               
               
                 467 
                 96 
                 623 
                 672 
                 701 
                 960 
                 779 
                 1248 
                 818 
                 1392 
               
               
                 479 
                 1536 
                 638 
                 960 
                 718 
                 1488 
                 797 
                 384 
                 837 
                 648 
               
               
                 490 
                 1344 
                 653 
                 1248 
                 734 
                 384 
                 816 
                 1152 
                 857 
                 1536 
               
               
                 501 
                 1152 
                 668 
                 1536 
                 751 
                 912 
                 834 
                 288 
                 876 
                 792 
               
               
                 512 
                 960 
                 682 
                 192 
                 768 
                 1440 
                 853 
                 1056 
                 895 
                 48 
               
               
                 523 
                 768 
                 697 
                 480 
                 784 
                 336 
                 871 
                 192 
                 915 
                 936 
               
               
                 534 
                 576 
                 712 
                 768 
                 801 
                 864 
                 890 
                 960 
                 934 
                 192 
               
               
                 545 
                 384 
                 727 
                 1056 
                 818 
                 1392 
                 908 
                 96 
                 954 
                 1080 
               
               
                 556 
                 192 
                 742 
                 1344 
                 834 
                 288 
                 927 
                 864 
                 973 
                 336 
               
               
                 568 
                 0 
                 757 
                 0 
                 851 
                 816 
                 946 
                 0 
                 993 
                 1224 
               
               
                 579 
                 1440 
                 771 
                 288 
                 868 
                 1344 
                 964 
                 768 
                 1012 
                 480 
               
               
                 590 
                 1248 
                 786 
                 576 
                 884 
                 240 
                 983 
                 1536 
                 1032 
                 1368 
               
               
                 601 
                 1056 
                 801 
                 864 
                 901 
                 768 
                 1001 
                 672 
                 1051 
                 624 
               
               
                 612 
                 864 
                 816 
                 1152 
                 918 
                 1296 
                 1020 
                 1440 
                 1071 
                 1512 
               
               
                 623 
                 672 
                 831 
                 1440 
                 934 
                 192 
                 1038 
                 576 
                 1090 
                 768 
               
               
                 634 
                 480 
                 845 
                 96 
                 951 
                 720 
                 1057 
                 1344 
                 1109 
                 24 
               
               
                 645 
                 288 
                 860 
                 384 
                 968 
                 1248 
                 1075 
                 480 
                 1129 
                 912 
               
               
                 656 
                 96 
                 875 
                 672 
                 984 
                 144 
                 1094 
                 1248 
                 1148 
                 168 
               
               
                 668 
                 1536 
                 890 
                 960 
                 1001 
                 672 
                 1112 
                 384 
                 1168 
                 1056 
               
               
                 679 
                 1344 
                 905 
                 1248 
                 1018 
                 1200 
                 1131 
                 1152 
                 1187 
                 312 
               
               
                 690 
                 1152 
                 920 
                 1536 
                 1034 
                 96 
                 1149 
                 288 
                 1207 
                 1200 
               
               
                 701 
                 960 
                 934 
                 192 
                 1051 
                 624 
                 1168 
                 1056 
                 1226 
                 456 
               
               
                 712 
                 768 
                 949 
                 480 
                 1068 
                 1152 
                 1186 
                 192 
                 1246 
                 1344 
               
               
                 723 
                 576 
                 964 
                 768 
                 1084 
                 48 
                 1205 
                 960 
                 1265 
                 600 
               
               
                 734 
                 384 
                 979 
                 1056 
                 1101 
                 576 
                 1223 
                 96 
                 1285 
                 1488 
               
               
                 745 
                 192 
                 994 
                 1344 
                 1118 
                 1104 
                 1242 
                 864 
                 1304 
                 744 
               
               
                   
               
             
          
         
       
     
         [0000]    
       
         
               
               
               
               
               
             
               
               
               
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 4 
               
             
             
               
                   
               
               
                 1/2 
                 2/3 
                 3/4 
                 5/6 
                 7/8 
               
             
          
           
               
                 #RS block 
                 #Offset 
                 #RS block 
                 #Offset 
                 #RS block 
                 #Offset 
                 #RS block 
                 #Offset 
                 #RS block 
                 #Offset 
               
               
                   
               
             
          
           
               
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 1 
                 120 
                 2 
                 1248 
                 2 
                 996 
                 2 
                 744 
                 2 
                 618 
               
               
                 2 
                 240 
                 3 
                 864 
                 3 
                 360 
                 4 
                 1488 
                 4 
                 1236 
               
               
                 3 
                 360 
                 4 
                 480 
                 5 
                 1356 
                 5 
                 600 
                 5 
                 222 
               
               
                 4 
                 480 
                 5 
                 96 
                 6 
                 720 
                 7 
                 1344 
                 7 
                 840 
               
               
                 5 
                 600 
                 7 
                 1344 
                 7 
                 84 
                 8 
                 456 
                 9 
                 1458 
               
               
                 6 
                 720 
                 8 
                 960 
                 9 
                 1080 
                 10 
                 1200 
                 10 
                 444 
               
               
                 7 
                 840 
                 9 
                 576 
                 10 
                 444 
                 11 
                 312 
                 12 
                 1062 
               
               
                 8 
                 960 
                 10 
                 192 
                 12 
                 1440 
                 13 
                 1056 
                 13 
                 48 
               
               
                 9 
                 1080 
                 12 
                 1440 
                 13 
                 804 
                 14 
                 168 
                 15 
                 666 
               
               
                 10 
                 1200 
                 13 
                 1056 
                 14 
                 168 
                 16 
                 912 
                 17 
                 1284 
               
               
                 11 
                 1320 
                 14 
                 672 
                 16 
                 1164 
                 17 
                 24 
                 18 
                 270 
               
               
                 12 
                 1440 
                 15 
                 288 
                 17 
                 528 
                 19 
                 768 
                 20 
                 888 
               
               
                 13 
                   
                 17 
                 1536 
                 19 
                 1524 
                 21 
                 1512 
                 22 
                 1506 
               
               
                 1560 
                 (NULL) 
                 18 
                 1152 
                 20 
                 888 
                 22 
                 624 
                 23 
                 492 
               
               
                 13 
                 48 
                 19 
                 768 
                 21 
                 252 
                 24 
                 1368 
                 25 
                 1110 
               
               
                 14 
                 168 
                 20 
                 384 
                 23 
                 1248 
                 25 
                 480 
                 26 
                 96 
               
               
                 15 
                 288 
                 22 
                 0 
                 24 
                 612 
                 27 
                 1224 
                 28 
                 714 
               
               
                 16 
                 408 
                 23 
                 1248 
                 26 
                 1608 
                 28 
                 336 
                 30 
                 1332 
               
               
                 17 
                 528 
                 24 
                 864 
                 27 
                 972 
                 30 
                 1080 
                 31 
                 318 
               
               
                 18 
                 648 
                 25 
                 480 
                 28 
                 336 
                 31 
                 192 
                 33 
                 936 
               
               
                 19 
                 768 
                 26 
                 96 
                 30 
                 1332 
                 33 
                 936 
                 35 
                 1554 
               
               
                 20 
                 888 
                 28 
                 1344 
                 31 
                 696 
                 34 
                 48 
                 36 
                 540 
               
               
                 21 
                 1008 
                 29 
                 960 
                 32 
                 60 
                 36 
                 792 
                 38 
                 1158 
               
               
                 22 
                 1128 
                 30 
                 576 
                 34 
                 1056 
                 38 
                 1536 
                 39 
                 144 
               
               
                 23 
                 1248 
                 31 
                 192 
                 35 
                 420 
                 39 
                 648 
                 41 
                 762 
               
               
                 24 
                 1368 
                 33 
                 1440 
                 37 
                 1416 
                 41 
                 1392 
                 43 
                 1380 
               
               
                 25 
                 1488 
                 34 
                 1056 
                 38 
                 780 
                 42 
                 504 
                 44 
                 366 
               
               
                 26 
                   
                 35 
                 672 
                 39 
                 144 
                 44 
                 1248 
                 46 
                 984 
               
               
                 1608 
                 (NULL) 
                 36 
                 288 
                 41 
                 1140 
                 45 
                 360 
                 48 
                 1602 
               
               
                 26 
                 96 
                 38 
                 1536 
                 42 
                 504 
                 47 
                 1104 
                 49 
                 588 
               
               
                 27 
                 216 
                 39 
                 1152 
                 44 
                 1500 
                 48 
                 216 
                 51 
                 1206 
               
               
                 28 
                 336 
                 40 
                 768 
                 45 
                 864 
                 50 
                 960 
                 52 
                 192 
               
               
                 29 
                 456 
                 41 
                 384 
                 46 
                 228 
                 51 
                 72 
                 54 
                 810 
               
               
                 30 
                 576 
                 43 
                 0 
                 48 
                 1224 
                 53 
                 816 
                 56 
                 1428 
               
               
                 31 
                 696 
                 44 
                 1248 
                 49 
                 588 
                 55 
                 1560 
                 57 
                 414 
               
               
                 32 
                 816 
                 45 
                 864 
                 51 
                 1584 
                 56 
                 672 
                 59 
                 1032 
               
               
                 33 
                 936 
                 46 
                 480 
                 52 
                 948 
                 58 
                 1416 
                 60 
                 18 
               
               
                 34 
                 1056 
                 47 
                 96 
                 53 
                 312 
                 59 
                 528 
                 62 
                 636 
               
               
                 35 
                 1176 
                 49 
                 1344 
                 55 
                 1308 
                 61 
                 1272 
                 64 
                 1254 
               
               
                 36 
                 1296 
                 50 
                 960 
                 56 
                 672 
                 62 
                 384 
                 65 
                 240 
               
               
                 37 
                 1416 
                 51 
                 576 
                 57 
                 36 
                 64 
                 1128 
                 67 
                 858 
               
               
                 38 
                   
                 52 
                 192 
                 59 
                 1032 
                 65 
                 240 
                 69 
                 1476 
               
               
                 1536 
                 (NULL) 
                 54 
                 1440 
                 60 
                 396 
                 67 
                 984 
                 70 
                 462 
               
               
                 38 
                 24 
                 55 
                 1056 
                 62 
                 1392 
                 68 
                 96 
                 72 
                 1080 
               
               
                 39 
                 144 
                 56 
                 672 
                 63 
                 756 
                 70 
                 840 
                 73 
                 66 
               
               
                 40 
                 264 
                 57 
                 288 
                 64 
                 120 
                 72 
                 1584 
                 75 
                 684 
               
               
                 41 
                 384 
                 59 
                 1536 
                 66 
                 1116 
                 73 
                 696 
                 77 
                 1302 
               
               
                 42 
                 504 
                 60 
                 1152 
                 67 
                 480 
                 75 
                 1440 
                 78 
                 288 
               
               
                 43 
                 624 
                 61 
                 768 
                 69 
                 1476 
                 76 
                 552 
                 80 
                 906 
               
               
                 44 
                 744 
                 62 
                 384 
                 70 
                 840 
                 78 
                 1296 
                 82 
                 1524 
               
               
                 45 
                 864 
                 64 
                 0 
                 71 
                 204 
                 79 
                 408 
                 83 
                 510 
               
               
                 46 
                 984 
                 65 
                 1248 
                 73 
                 1200 
                 81 
                 1152 
                 85 
                 1128 
               
               
                 47 
                 1104 
                 66 
                 864 
                 74 
                 564 
                 82 
                 264 
                 86 
                 114 
               
               
                 48 
                 1224 
                 67 
                 480 
                 76 
                 1560 
                 84 
                 1008 
                 88 
                 732 
               
               
                 49 
                 1344 
                 68 
                 96 
                 77 
                 924 
                 85 
                 120 
                 90 
                 1350 
               
               
                 50 
                 1464 
                 70 
                 1344 
                 78 
                 288 
                 87 
                 864 
                 91 
                 336 
               
               
                 51 
                   
                 71 
                 960 
                 80 
                 1284 
                 89 
                 1608 
                 93 
                 954 
               
               
                 1584 
                 (NULL) 
                 72 
                 576 
                 81 
                 648 
                 90 
                 720 
                 95 
                 1572 
               
               
                 51 
                 72 (same 
                 73 
                 192 
                 82 
                 12 
                 92 
                 1464 
                 96 
                 558 
               
               
                 *P 
                   
                 75 
                 1440 
                 84 
                 1008 
                 93 
                 576 
                 98 
                 1176 
               
               
                 52 
                 192 
                 76 
                 1056 
                 85 
                 372 
                 95 
                 1320 
                 99 
                 162 
               
               
                 53 
                 312 
                 77 
                 672 
                 87 
                 1368 
                 96 
                 432 
                 101 
                 780 
               
               
                 54 
                 432 
                 78 
                 288 
                 88 
                 732 
                 98 
                 1176 
                 103 
                 1398 
               
               
                 55 
                 552 
                 80 
                 1536 
                 89 
                 96 
                 99 
                 288 
                 104 
                 384 
               
               
                 56 
                 672 
                 81 
                 1152 
                 91 
                 1092 
                 101 
                 1032 
                 106 
                 1002 
               
               
                 57 
                 792 
                 82 
                 768 
                 92 
                 456 
                 102 
                 144 
                 108 
                 1620 
               
               
                 58 
                 912 
                 83 
                 384 
                 94 
                 1452 
                 104 
                 888 
                 109 
                 606 
               
               
                 59 
                 1032 
               
               
                 60 
                 1152 
               
               
                 61 
                 1272 
               
               
                 62 
                 1392 
               
               
                 63 
                 1512 
               
               
                   
               
             
          
         
       
     
         [0000]    
       
         
               
               
               
               
               
             
               
               
               
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 5 
               
             
             
               
                   
               
               
                 1/2 
                 2/3 
                 3/4 
                 5/6 
                 7/8 
               
             
          
           
               
                 #RS block 
                 #Offset 
                 #RS block 
                 #Offset 
                 #RS block 
                 #Offset 
                 #RS block 
                 #Offset 
                 #RS block 
                 #Offset 
               
               
                   
               
             
          
           
               
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 2 
                 240 
                 3 
                 864 
                 3 
                 360 
                 4 
                 1488 
                 4 
                 1236 
               
               
                 4 
                 480 
                 5 
                 96 
                 6 
                 720 
                 7 
                 1344 
                 7 
                 840 
               
               
                 6 
                 720 
                 8 
                 960 
                 9 
                 1080 
                 10 
                 1200 
                 10 
                 444 
               
               
                 8 
                 960 
                 10 
                 192 
                 12 
                 1440 
                 13 
                 1056 
                 13 
                 48 
               
               
                 10 
                 1200 
                 13 
                 1056 
                 14 
                 168 
                 16 
                 912 
                 17 
                 1284 
               
               
                 12 
                 1440 
                 15 
                 288 
                 17 
                 528 
                 19 
                 768 
                 20 
                 888 
               
               
                 13 
                 48 
                 18 
                 1152 
                 20 
                 888 
                 22 
                 624 
                 23 
                 492 
               
               
                 15 
                 288 
                 20 
                 384 
                 23 
                 1248 
                 25 
                 480 
                 26 
                 96 
               
               
                 17 
                 528 
                 23 
                 1248 
                 26 
                 1608 
                 28 
                 336 
                 30 
                 1332 
               
               
                 19 
                 768 
                 25 
                 480 
                 28 
                 336 
                 31 
                 192 
                 33 
                 936 
               
               
                 21 
                 1008 
                 28 
                 1344 
                 31 
                 696 
                 34 
                 48 
                 36 
                 540 
               
               
                 23 
                 1248 
                 30 
                 576 
                 34 
                 1056 
                 38 
                 1536 
                 39 
                 144 
               
               
                 25 
                 1488 
                 33 
                 1440 
                 37 
                 1416 
                 41 
                 1392 
                 43 
                 1380 
               
               
                 26 
                 96 
                 35 
                 672 
                 39 
                 144 
                 44 
                 1248 
                 46 
                 984 
               
               
                 28 
                 336 
                 38 
                 1536 
                 42 
                 504 
                 47 
                 1104 
                 49 
                 588 
               
               
                 30 
                 576 
                 40 
                 768 
                 45 
                 864 
                 50 
                 960 
                 52 
                 192 
               
               
                 32 
                 816 
                 43 
                 0 
                 48 
                 1224 
                 53 
                 816 
                 56 
                 1428 
               
               
                 34 
                 1056 
                 45 
                 864 
                 51 
                 1584 
                 56 
                 672 
                 59 
                 1032 
               
               
                 36 
                 1296 
                 47 
                 96 
                 53 
                 312 
                 59 
                 528 
                 62 
                 636 
               
               
                 38 
                 1536 
                 50 
                 960 
                 56 
                 672 
                 62 
                 384 
                 65 
                 240 
               
               
                 39 
                 144 
                 52 
                 192 
                 59 
                 1032 
                 65 
                 240 
                 69 
                 1476 
               
               
                 41 
                 384 
                 55 
                 1056 
                 62 
                 1392 
                 68 
                 96 
                 72 
                 1080 
               
               
                 43 
                 624 
                 57 
                 288 
                 64 
                 120 
                 72 
                 1584 
                 75 
                 684 
               
               
                 45 
                 864 
                 60 
                 1152 
                 67 
                 480 
                 75 
                 1440 
                 78 
                 288 
               
               
                 47 
                 1104 
                 62 
                 384 
                 70 
                 840 
                 78 
                 1296 
                 82 
                 1524 
               
               
                 49 
                 1344 
                 65 
                 1248 
                 73 
                 1200 
                 81 
                 1152 
                 85 
                 1128 
               
               
                 51 
                 1584 
                 67 
                 480 
                 76 
                 1560 
                 84 
                 1008 
                 88 
                 732 
               
               
                 52 
                 192 
                 70 
                 1344 
                 78 
                 288 
                 87 
                 864 
                 91 
                 336 
               
               
                 54 
                 432 
                 72 
                 576 
                 81 
                 648 
                 90 
                 720 
                 95 
                 1572 
               
               
                 56 
                 672 
                 75 
                 1440 
                 84 
                 1008 
                 93 
                 576 
                 98 
                 1176 
               
               
                 58 
                 912 
                 77 
                 672 
                 87 
                 1368 
                 96 
                 432 
                 101 
                 780 
               
               
                 60 
                 1152 
                 80 
                 1536 
                 89 
                 96 
                 99 
                 288 
                 104 
                 384 
               
               
                 62 
                 1392 
                 82 
                 768 
                 92 
                 456 
                 102 
                 144 
                 108 
                 1620 
               
               
                 64 
                 0 
                 85 
                 0 
                 95 
                 816 
                 106 
                 0 
                 111 
                 1224 
               
               
                 65 
                 240 
                 87 
                 864 
                 98 
                 1176 
                 109 
                 1488 
                 114 
                 828 
               
               
                 67 
                 480 
                 89 
                 96 
                 101 
                 1536 
                 112 
                 1344 
                 117 
                 432 
               
               
                 69 
                 720 
                 92 
                 960 
                 103 
                 264 
                 115 
                 1200 
                 120 
                 36 
               
               
                 71 
                 960 
                 94 
                 192 
                 106 
                 624 
                 118 
                 1056 
                 124 
                 1272 
               
               
                 73 
                 1200 
                 97 
                 1056 
                 109 
                 984 
                 121 
                 912 
                 127 
                 876 
               
               
                 75 
                 1440 
                 99 
                 288 
                 112 
                 1344 
                 124 
                 768 
                 130 
                 480 
               
               
                 76 
                 48 
                 102 
                 1152 
                 114 
                 72 
                 127 
                 624 
                 133 
                 84 
               
               
                 78 
                 288 
                 104 
                 384 
                 117 
                 432 
                 130 
                 480 
                 137 
                 1320 
               
               
                 80 
                 528 
                 107 
                 1248 
                 120 
                 792 
                 133 
                 336 
                 140 
                 924 
               
               
                 82 
                 768 
                 109 
                 480 
                 123 
                 1152 
                 136 
                 192 
                 143 
                 528 
               
               
                 84 
                 1008 
                 112 
                 1344 
                 126 
                 1512 
                 139 
                 48 
                 146 
                 132 
               
               
                 86 
                 1248 
                 114 
                 576 
                 128 
                 240 
                 143 
                 1536 
                 150 
                 1368 
               
               
                 88 
                 1488 
                 117 
                 1440 
                 131 
                 600 
                 146 
                 1392 
                 153 
                 972 
               
               
                 89 
                 96 
                 119 
                 672 
                 134 
                 960 
                 149 
                 1248 
                 156 
                 576 
               
               
                 91 
                 336 
                 122 
                 1536 
                 137 
                 1320 
                 152 
                 1104 
                 159 
                 180 
               
               
                 93 
                 576 
                 124 
                 768 
                 139 
                 48 
                 155 
                 960 
                 163 
                 1416 
               
               
                 95 
                 816 
                 127 
                 0 
                 142 
                 408 
                 158 
                 816 
                 166 
                 1020 
               
               
                 97 
                 1056 
                 129 
                 864 
                 145 
                 768 
                 161 
                 672 
                 169 
                 624 
               
               
                 99 
                 1296 
                 131 
                 96 
                 148 
                 1128 
                 164 
                 528 
                 172 
                 228 
               
               
                 101 
                 1536 
                 134 
                 960 
                 151 
                 1488 
                 167 
                 384 
                 176 
                 1464 
               
               
                 102 
                 144 
                 136 
                 192 
                 153 
                 216 
                 170 
                 240 
                 179 
                 1068 
               
               
                 104 
                 384 
                 139 
                 1056 
                 156 
                 576 
                 173 
                 96 
                 182 
                 672 
               
               
                 106 
                 624 
                 141 
                 288 
                 159 
                 936 
                 177 
                 1584 
                 185 
                 276 
               
               
                 108 
                 864 
                 144 
                 1152 
                 162 
                 1296 
                 180 
                 1440 
                 189 
                 1512 
               
               
                 110 
                 1104 
                 146 
                 384 
                 164 
                 24 
                 183 
                 1296 
                 192 
                 1116 
               
               
                 112 
                 1344 
                 149 
                 1248 
                 167 
                 384 
                 186 
                 1152 
                 195 
                 720 
               
               
                 114 
                 1584 
                 151 
                 480 
                 170 
                 744 
                 189 
                 1008 
                 198 
                 324 
               
               
                 115 
                 192 
                 154 
                 1344 
                 173 
                 1104 
                 192 
                 864 
                 202 
                 1560 
               
               
                 117 
                 432 
                 156 
                 576 
                 176 
                 1464 
                 195 
                 720 
                 205 
                 1164 
               
               
                 119 
                 672 
                 159 
                 1440 
                 178 
                 192 
                 198 
                 576 
                 208 
                 768 
               
               
                 121 
                 912 
                 161 
                 672 
                 181 
                 552 
                 201 
                 432 
                 211 
                 372 
               
               
                 123 
                 1152 
                 164 
                 1536 
                 184 
                 912 
                 204 
                 288 
                 215 
                 1608 
               
               
                 125 
                 1392 
                 166 
                 768 
                 187 
                 1272 
                 207 
                 144 
                 218 
                 1212 
               
               
                   
               
             
          
         
       
     
         [0000]    
       
         
               
               
               
               
               
             
               
               
               
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 6 
               
             
             
               
                   
               
               
                 1/2 
                 2/3 
                 3/4 
                 5/6 
                 7/8 
               
             
          
           
               
                 #RS block 
                 #Offset 
                 #RS block 
                 #Offset 
                 #RS block 
                 #Offset 
                 #RS block 
                 #Offset 
                 #RS block 
                 #Offset 
               
               
                   
               
             
          
           
               
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 3 
                 360 
                 4 
                 480 
                 5 
                 1356 
                 5 
                 600 
                 5 
                 222 
               
               
                 6 
                 720 
                 8 
                 960 
                 9 
                 1080 
                 10 
                 1200 
                 10 
                 444 
               
               
                 9 
                 1080 
                 12 
                 1440 
                 13 
                 804 
                 14 
                 168 
                 15 
                 666 
               
               
                 12 
                 1440 
                 15 
                 288 
                 17 
                 528 
                 19 
                 768 
                 20 
                 888 
               
               
                 14 
                 168 
                 19 
                 768 
                 21 
                 252 
                 24 
                 1368 
                 25 
                 1110 
               
               
                 17 
                 528 
                 23 
                 1248 
                 26 
                 1608 
                 28 
                 336 
                 30 
                 1332 
               
               
                 20 
                 888 
                 26 
                 96 
                 30 
                 1332 
                 33 
                 936 
                 35 
                 1554 
               
               
                 23 
                 1248 
                 30 
                 576 
                 34 
                 1056 
                 38 
                 1536 
                 39 
                 144 
               
               
                 26 
                 1608 
                 34 
                 1056 
                 38 
                 780 
                 42 
                 504 
                 44 
                 366 
               
               
                 28 
                 336 
                 38 
                 1536 
                 42 
                 504 
                 47 
                 1104 
                 49 
                 588 
               
               
                 31 
                 696 
                 41 
                 384 
                 46 
                 228 
                 51 
                 72 
                 54 
                 810 
               
               
                 34 
                 1056 
                 45 
                 864 
                 51 
                 1584 
                 56 
                 672 
                 59 
                 1032 
               
               
                 37 
                 1416 
                 49 
                 1344 
                 55 
                 1308 
                 61 
                 1272 
                 64 
                 1254 
               
               
                 39 
                 144 
                 52 
                 192 
                 59 
                 1032 
                 65 
                 240 
                 69 
                 1476 
               
               
                 42 
                 504 
                 56 
                 672 
                 63 
                 756 
                 70 
                 840 
                 73 
                 66 
               
               
                 45 
                 864 
                 60 
                 1152 
                 67 
                 480 
                 75 
                 1440 
                 78 
                 288 
               
               
                 48 
                 1224 
                 64 
                 0 
                 71 
                 204 
                 79 
                 408 
                 83 
                 510 
               
               
                 51 
                 1584 
                 67 
                 480 
                 76 
                 1560 
                 84 
                 1008 
                 88 
                 732 
               
               
                 53 
                 312 
                 71 
                 960 
                 80 
                 1284 
                 89 
                 1608 
                 93 
                 954 
               
               
                 56 
                 672 
                 75 
                 1440 
                 84 
                 1008 
                 93 
                 576 
                 98 
                 1176 
               
               
                 59 
                 1032 
                 78 
                 288 
                 88 
                 732 
                 98 
                 1176 
                 103 
                 1398 
               
               
                 62 
                 1392 
                 82 
                 768 
                 92 
                 456 
                 102 
                 144 
                 108 
                 1620 
               
               
                 64 
                 120 
                 86 
                 1248 
                 96 
                 180 
                 107 
                 744 
                 112 
                 210 
               
               
                 67 
                 480 
                 89 
                 96 
                 101 
                 1536 
                 112 
                 1344 
                 117 
                 432 
               
               
                 70 
                 840 
                 93 
                 576 
                 105 
                 1260 
                 116 
                 312 
                 122 
                 654 
               
               
                 73 
                 1200 
                 97 
                 1056 
                 109 
                 984 
                 121 
                 912 
                 127 
                 876 
               
               
                 76 
                 1560 
                 101 
                 1536 
                 113 
                 708 
                 126 
                 1512 
                 132 
                 1098 
               
               
                 78 
                 288 
                 104 
                 384 
                 117 
                 432 
                 130 
                 480 
                 137 
                 1320 
               
               
                 81 
                 648 
                 108 
                 864 
                 121 
                 156 
                 135 
                 1080 
                 142 
                 1542 
               
               
                 84 
                 1008 
                 112 
                 1344 
                 126 
                 1512 
                 139 
                 48 
                 146 
                 132 
               
               
                 87 
                 1368 
                 115 
                 192 
                 130 
                 1236 
                 144 
                 648 
                 151 
                 354 
               
               
                 89 
                 96 
                 119 
                 672 
                 134 
                 960 
                 149 
                 1248 
                 156 
                 576 
               
               
                 92 
                 456 
                 123 
                 1152 
                 138 
                 684 
                 153 
                 216 
                 161 
                 798 
               
               
                 95 
                 816 
                 127 
                 0 
                 142 
                 408 
                 158 
                 816 
                 166 
                 1020 
               
               
                 98 
                 1176 
                 130 
                 480 
                 146 
                 132 
                 163 
                 1416 
                 171 
                 1242 
               
               
                 101 
                 1536 
                 134 
                 960 
                 151 
                 1488 
                 167 
                 384 
                 176 
                 1464 
               
               
                 103 
                 264 
                 138 
                 1440 
                 155 
                 1212 
                 172 
                 984 
                 180 
                 54 
               
               
                 106 
                 624 
                 141 
                 288 
                 159 
                 936 
                 177 
                 1584 
                 185 
                 276 
               
               
                 109 
                 984 
                 145 
                 768 
                 163 
                 660 
                 181 
                 552 
                 190 
                 498 
               
               
                 112 
                 1344 
                 149 
                 1248 
                 167 
                 384 
                 186 
                 1152 
                 195 
                 720 
               
               
                 114 
                 72 
                 152 
                 96 
                 171 
                 108 
                 190 
                 120 
                 200 
                 942 
               
               
                 117 
                 432 
                 156 
                 576 
                 176 
                 1464 
                 195 
                 720 
                 205 
                 1164 
               
               
                 120 
                 792 
                 160 
                 1056 
                 180 
                 1188 
                 200 
                 1320 
                 210 
                 1386 
               
               
                 123 
                 1152 
                 164 
                 1536 
                 184 
                 912 
                 204 
                 288 
                 215 
                 1608 
               
               
                 126 
                 1512 
                 167 
                 384 
                 188 
                 636 
                 209 
                 888 
                 219 
                 198 
               
               
                 128 
                 240 
                 171 
                 864 
                 192 
                 360 
                 214 
                 1488 
                 224 
                 420 
               
               
                 131 
                 600 
                 175 
                 1344 
                 196 
                 84 
                 218 
                 456 
                 229 
                 642 
               
               
                 134 
                 960 
                 178 
                 192 
                 201 
                 1440 
                 223 
                 1056 
                 234 
                 864 
               
               
                 137 
                 1320 
                 182 
                 672 
                 205 
                 1164 
                 227 
                 24 
                 239 
                 1086 
               
               
                 139 
                 48 
                 186 
                 1152 
                 209 
                 888 
                 232 
                 624 
                 244 
                 1308 
               
               
                 142 
                 408 
                 190 
                 0 
                 213 
                 612 
                 237 
                 1224 
                 249 
                 1530 
               
               
                 145 
                 768 
                 193 
                 480 
                 217 
                 336 
                 241 
                 192 
                 253 
                 120 
               
               
                 148 
                 1128 
                 197 
                 960 
                 221 
                 60 
                 246 
                 792 
                 258 
                 342 
               
               
                 151 
                 1488 
                 201 
                 1440 
                 226 
                 1416 
                 251 
                 1392 
                 263 
                 564 
               
               
                 153 
                 216 
                 204 
                 288 
                 230 
                 1140 
                 255 
                 360 
                 268 
                 786 
               
               
                 156 
                 576 
                 208 
                 768 
                 234 
                 864 
                 260 
                 960 
                 273 
                 1008 
               
               
                 159 
                 936 
                 212 
                 1248 
                 238 
                 588 
                 265 
                 1560 
                 278 
                 1230 
               
               
                 162 
                 1296 
                 215 
                 96 
                 242 
                 312 
                 269 
                 528 
                 283 
                 1452 
               
               
                 164 
                 24 
                 219 
                 576 
                 246 
                 36 
                 274 
                 1128 
                 287 
                 42 
               
               
                 167 
                 384 
                 223 
                 1056 
                 251 
                 1392 
                 278 
                 96 
                 292 
                 264 
               
               
                 170 
                 744 
                 227 
                 1536 
                 255 
                 1116 
                 283 
                 696 
                 297 
                 486 
               
               
                 173 
                 1104 
                 230 
                 384 
                 259 
                 840 
                 288 
                 1296 
                 302 
                 708 
               
               
                 176 
                 1464 
                 234 
                 864 
                 263 
                 564 
                 292 
                 264 
                 307 
                 930 
               
               
                 178 
                 192 
                 238 
                 1344 
                 267 
                 288 
                 297 
                 864 
                 312 
                 1152 
               
               
                 181 
                 552 
                 241 
                 192 
                 271 
                 12 
                 302 
                 1464 
                 317 
                 1374 
               
               
                 184 
                 912 
                 245 
                 672 
                 276 
                 1368 
                 306 
                 432 
                 322 
                 1596 
               
               
                 187 
                 1272 
                 249 
                 1152 
                 280 
                 1092 
                 311 
                 1032 
                 326 
                 186 
               
               
                   
               
             
          
         
       
     
         [0000]    
       
         
               
               
               
               
               
             
               
               
               
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 7 
               
             
             
               
                   
               
               
                 1/2 
                 2/3 
                 3/4 
                 5/6 
                 7/8 
               
             
          
           
               
                 #RS block 
                 #Offset 
                 #RS block 
                 #Offset 
                 #RS block 
                 #Offset 
                 #RS block 
                 #Offset 
                 #RS block 
                 #Offset 
               
               
                   
               
             
          
           
               
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 2 
                 240 
                 3 
                 864 
                 3 
                 360 
                 4 
                 1488 
                 4 
                 1236 
               
               
                 4 
                 480 
                 5 
                 96 
                 6 
                 720 
                 7 
                 1344 
                 7 
                 840 
               
               
                 6 
                 720 
                 8 
                 960 
                 9 
                 1080 
                 10 
                 1200 
                 10 
                 444 
               
               
                 8 
                 960 
                 10 
                 192 
                 12 
                 1440 
                 13 
                 1056 
                 13 
                 48 
               
               
                 10 
                 1200 
                 13 
                 1056 
                 14 
                 168 
                 16 
                 912 
                 17 
                 1284 
               
               
                 12 
                 1440 
                 15 
                 288 
                 17 
                 528 
                 19 
                 768 
                 20 
                 888 
               
               
                 13 
                 48 
                 18 
                 1152 
                 20 
                 888 
                 22 
                 624 
                 23 
                 492 
               
               
                 15 
                 288 
                 20 
                 384 
                 23 
                 1248 
                 25 
                 480 
                 26 
                 96 
               
               
                 17 
                 528 
                 23 
                 1248 
                 26 
                 1608 
                 28 
                 336 
                 30 
                 1332 
               
               
                 19 
                 768 
                 25 
                 480 
                 28 
                 336 
                 31 
                 192 
                 33 
                 936 
               
               
                 21 
                 1008 
                 28 
                 1344 
                 31 
                 696 
                 34 
                 48 
                 36 
                 540 
               
               
                 23 
                 1248 
                 30 
                 576 
                 34 
                 1056 
                 38 
                 1536 
                 39 
                 144 
               
               
                 25 
                 1488 
                 33 
                 1440 
                 37 
                 1416 
                 41 
                 1392 
                 43 
                 1380 
               
               
                 26 
                 96 
                 35 
                 672 
                 39 
                 144 
                 44 
                 1248 
                 46 
                 984 
               
               
                 28 
                 336 
                 38 
                 1536 
                 42 
                 504 
                 47 
                 1104 
                 49 
                 588 
               
               
                 30 
                 576 
                 40 
                 768 
                 45 
                 864 
                 50 
                 960 
                 52 
                 192 
               
               
                 32 
                 816 
                 43 
                 0 
                 48 
                 1224 
                 53 
                 816 
                 56 
                 1428 
               
               
                 34 
                 1056 
                 45 
                 864 
                 51 
                 1584 
                 56 
                 672 
                 59 
                 1032 
               
               
                 36 
                 1296 
                 47 
                 96 
                 53 
                 312 
                 59 
                 528 
                 62 
                 636 
               
               
                 38 
                 1536 
                 50 
                 960 
                 56 
                 672 
                 62 
                 384 
                 65 
                 240 
               
               
                 39 
                 144 
                 52 
                 192 
                 59 
                 1032 
                 65 
                 240 
                 69 
                 1476 
               
               
                 41 
                 384 
                 55 
                 1056 
                 62 
                 1392 
                 68 
                 96 
                 72 
                 1080 
               
               
                 43 
                 624 
                 57 
                 288 
                 64 
                 120 
                 72 
                 1584 
                 75 
                 684 
               
               
                 45 
                 864 
                 60 
                 1152 
                 67 
                 480 
                 75 
                 1440 
                 78 
                 288 
               
               
                 47 
                 1104 
                 62 
                 384 
                 70 
                 840 
                 78 
                 1296 
                 82 
                 1524 
               
               
                 49 
                 1344 
                 65 
                 1248 
                 73 
                 1200 
                 81 
                 1152 
                 85 
                 1128 
               
               
                 51 
                 1584 
                 67 
                 480 
                 76 
                 1560 
                 84 
                 1008 
                 88 
                 732 
               
               
                 52 
                 192 
                 70 
                 1344 
                 78 
                 288 
                 87 
                 864 
                 91 
                 336 
               
               
                 54 
                 432 
                 72 
                 576 
                 81 
                 648 
                 90 
                 720 
                 95 
                 1572 
               
               
                 56 
                 672 
                 75 
                 1440 
                 84 
                 1008 
                 93 
                 576 
                 98 
                 1176 
               
               
                 58 
                 912 
                 77 
                 672 
                 87 
                 1368 
                 96 
                 432 
                 101 
                 780 
               
               
                 60 
                 1152 
                 80 
                 1536 
                 89 
                 96 
                 99 
                 288 
                 104 
                 384 
               
               
                 62 
                 1392 
                 82 
                 768 
                 92 
                 456 
                 102 
                 144 
                 108 
                 1620 
               
               
                 64 
                 0 
                 85 
                 0 
                 95 
                 816 
                 106 
                 0 
                 111 
                 1224 
               
               
                 65 
                 240 
                 87 
                 864 
                 98 
                 1176 
                 109 
                 1488 
                 114 
                 828 
               
               
                 67 
                 480 
                 89 
                 96 
                 101 
                 1536 
                 112 
                 1344 
                 117 
                 432 
               
               
                 69 
                 720 
                 92 
                 960 
                 103 
                 264 
                 115 
                 1200 
                 120 
                 36 
               
               
                 71 
                 960 
                 94 
                 192 
                 106 
                 624 
                 118 
                 1056 
                 124 
                 1272 
               
               
                 73 
                 1200 
                 97 
                 1056 
                 109 
                 984 
                 121 
                 912 
                 127 
                 876 
               
               
                 75 
                 1440 
                 99 
                 288 
                 112 
                 1344 
                 124 
                 768 
                 130 
                 480 
               
               
                 76 
                 48 
                 102 
                 1152 
                 114 
                 72 
                 127 
                 624 
                 133 
                 84 
               
               
                 78 
                 288 
                 104 
                 384 
                 117 
                 432 
                 130 
                 480 
                 137 
                 1320 
               
               
                 80 
                 528 
                 107 
                 1248 
                 120 
                 792 
                 133 
                 336 
                 140 
                 924 
               
               
                 82 
                 768 
                 109 
                 480 
                 123 
                 1152 
                 136 
                 192 
                 143 
                 528 
               
               
                 84 
                 1008 
                 112 
                 1344 
                 126 
                 1512 
                 139 
                 48 
                 146 
                 132 
               
               
                 86 
                 1248 
                 114 
                 576 
                 128 
                 240 
                 143 
                 1536 
                 150 
                 1368 
               
               
                 88 
                 1488 
                 117 
                 1440 
                 131 
                 600 
                 146 
                 1392 
                 153 
                 972 
               
               
                 89 
                 96 
                 119 
                 672 
                 134 
                 960 
                 149 
                 1248 
                 156 
                 576 
               
               
                 91 
                 336 
                 122 
                 1536 
                 137 
                 1320 
                 152 
                 1104 
                 159 
                 180 
               
               
                 93 
                 576 
                 124 
                 768 
                 139 
                 48 
                 155 
                 960 
                 163 
                 1416 
               
               
                 95 
                 816 
                 127 
                 0 
                 142 
                 408 
                 158 
                 816 
                 166 
                 1020 
               
               
                 97 
                 1056 
                 129 
                 864 
                 145 
                 768 
                 161 
                 672 
                 169 
                 624 
               
               
                 99 
                 1296 
                 131 
                 96 
                 148 
                 1128 
                 164 
                 528 
                 172 
                 228 
               
               
                 101 
                 1536 
                 134 
                 960 
                 151 
                 1488 
                 167 
                 384 
                 176 
                 1464 
               
               
                 102 
                 144 
                 136 
                 192 
                 153 
                 216 
                 170 
                 240 
                 179 
                 1068 
               
               
                 104 
                 384 
                 139 
                 1056 
                 156 
                 576 
                 173 
                 96 
                 182 
                 672 
               
               
                 106 
                 624 
                 141 
                 288 
                 159 
                 936 
                 177 
                 1584 
                 185 
                 276 
               
               
                 108 
                 864 
                 144 
                 1152 
                 162 
                 1296 
                 180 
                 1440 
                 189 
                 1512 
               
               
                 110 
                 1104 
                 146 
                 384 
                 164 
                 24 
                 183 
                 1296 
                 192 
                 1116 
               
               
                 112 
                 1344 
                 149 
                 1248 
                 167 
                 384 
                 186 
                 1152 
                 195 
                 720 
               
               
                 114 
                 1584 
                 151 
                 480 
                 170 
                 744 
                 189 
                 1008 
                 198 
                 324 
               
               
                 115 
                 192 
                 154 
                 1344 
                 173 
                 1104 
                 192 
                 864 
                 202 
                 1560 
               
               
                 117 
                 432 
                 156 
                 576 
                 176 
                 1464 
                 195 
                 720 
                 205 
                 1164 
               
               
                 119 
                 672 
                 159 
                 1440 
                 178 
                 192 
                 198 
                 576 
                 208 
                 768 
               
               
                 121 
                 912 
                 161 
                 672 
                 181 
                 552 
                 201 
                 432 
                 211 
                 372 
               
               
                 123 
                 1152 
                 164 
                 1536 
                 184 
                 912 
                 204 
                 288 
                 215 
                 1608 
               
               
                 125 
                 1392 
                 166 
                 768 
                 187 
                 1272 
                 207 
                 144 
                 218 
                 1212 
               
               
                   
               
             
          
         
       
     
         [0000]    
       
         
               
               
               
               
               
             
               
               
               
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 8 
               
             
             
               
                   
               
               
                 1/2 
                 2/3 
                 3/4 
                 5/6 
                 7/8 
               
             
          
           
               
                 #RS block 
                 #Offset 
                 #RS block 
                 #Offset 
                 #RS block 
                 #Offset 
                 #RS block 
                 #Offset 
                 #RS block 
                 #Offset 
               
               
                   
               
             
          
           
               
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 4 
                 480 
                 5 
                 96 
                 6 
                 720 
                 7 
                 1344 
                 7 
                 840 
               
               
                 8 
                 960 
                 10 
                 192 
                 12 
                 1440 
                 13 
                 1056 
                 13 
                 48 
               
               
                 12 
                 1440 
                 15 
                 288 
                 17 
                 528 
                 19 
                 768 
                 20 
                 888 
               
               
                 15 
                 288 
                 20 
                 384 
                 23 
                 1248 
                 25 
                 480 
                 26 
                 96 
               
               
                 19 
                 768 
                 25 
                 480 
                 28 
                 336 
                 31 
                 192 
                 33 
                 936 
               
               
                 23 
                 1248 
                 30 
                 576 
                 34 
                 1056 
                 38 
                 1536 
                 39 
                 144 
               
               
                 26 
                 96 
                 35 
                 672 
                 39 
                 144 
                 44 
                 1248 
                 46 
                 984 
               
               
                 30 
                 576 
                 40 
                 768 
                 45 
                 864 
                 50 
                 960 
                 52 
                 192 
               
               
                 34 
                 1056 
                 45 
                 864 
                 51 
                 1584 
                 56 
                 672 
                 59 
                 1032 
               
               
                 38 
                 1536 
                 50 
                 960 
                 56 
                 672 
                 62 
                 384 
                 65 
                 240 
               
               
                 41 
                 384 
                 55 
                 1056 
                 62 
                 1392 
                 68 
                 96 
                 72 
                 1080 
               
               
                 45 
                 864 
                 60 
                 1152 
                 67 
                 480 
                 75 
                 1440 
                 78 
                 288 
               
               
                 49 
                 1344 
                 65 
                 1248 
                 73 
                 1200 
                 81 
                 1152 
                 85 
                 1128 
               
               
                 52 
                 192 
                 70 
                 1344 
                 78 
                 288 
                 87 
                 864 
                 91 
                 336 
               
               
                 56 
                 672 
                 75 
                 1440 
                 84 
                 1008 
                 93 
                 576 
                 98 
                 1176 
               
               
                 60 
                 1152 
                 80 
                 1536 
                 89 
                 96 
                 99 
                 288 
                 104 
                 384 
               
               
                 64 
                 0 
                 85 
                 0 
                 95 
                 816 
                 106 
                 0 
                 111 
                 1224 
               
               
                 67 
                 480 
                 89 
                 96 
                 101 
                 1536 
                 112 
                 1344 
                 117 
                 432 
               
               
                 71 
                 960 
                 94 
                 192 
                 103 
                 624 
                 118 
                 1056 
                 124 
                 1272 
               
               
                 75 
                 1440 
                 99 
                 288 
                 112 
                 1344 
                 124 
                 768 
                 130 
                 480 
               
               
                 78 
                 288 
                 104 
                 384 
                 117 
                 432 
                 130 
                 480 
                 137 
                 1320 
               
               
                 82 
                 768 
                 109 
                 480 
                 123 
                 1152 
                 136 
                 192 
                 143 
                 528 
               
               
                 86 
                 1248 
                 114 
                 576 
                 128 
                 240 
                 143 
                 1536 
                 150 
                 1368 
               
               
                 89 
                 96 
                 119 
                 672 
                 134 
                 960 
                 149 
                 1248 
                 156 
                 576 
               
               
                 93 
                 576 
                 124 
                 768 
                 139 
                 48 
                 155 
                 960 
                 163 
                 1416 
               
               
                 97 
                 1056 
                 129 
                 864 
                 145 
                 768 
                 161 
                 672 
                 169 
                 624 
               
               
                 101 
                 1536 
                 134 
                 960 
                 151 
                 1488 
                 167 
                 384 
                 176 
                 1464 
               
               
                 104 
                 384 
                 139 
                 1056 
                 156 
                 576 
                 173 
                 96 
                 182 
                 672 
               
               
                 108 
                 864 
                 144 
                 1152 
                 162 
                 1296 
                 180 
                 1440 
                 189 
                 1512 
               
               
                 112 
                 1344 
                 149 
                 1248 
                 167 
                 384 
                 186 
                 1152 
                 195 
                 720 
               
               
                 115 
                 192 
                 154 
                 1344 
                 173 
                 1104 
                 192 
                 864 
                 202 
                 1560 
               
               
                 119 
                 672 
                 159 
                 1440 
                 178 
                 192 
                 198 
                 576 
                 208 
                 768 
               
               
                 123 
                 1152 
                 164 
                 1536 
                 184 
                 912 
                 204 
                 288 
                 215 
                 1608 
               
               
                 127 
                 0 
                 169 
                 0 
                 190 
                 0 
                 211 
                 0 
                 221 
                 816 
               
               
                 130 
                 480 
                 173 
                 96 
                 195 
                 720 
                 217 
                 1344 
                 227 
                 24 
               
               
                 134 
                 960 
                 178 
                 192 
                 201 
                 1440 
                 223 
                 1056 
                 234 
                 864 
               
               
                 138 
                 1440 
                 183 
                 288 
                 206 
                 528 
                 229 
                 768 
                 240 
                 72 
               
               
                 141 
                 288 
                 188 
                 384 
                 212 
                 1248 
                 235 
                 480 
                 247 
                 912 
               
               
                 145 
                 768 
                 193 
                 480 
                 217 
                 336 
                 241 
                 192 
                 253 
                 120 
               
               
                 149 
                 1248 
                 198 
                 576 
                 223 
                 1056 
                 248 
                 1536 
                 260 
                 960 
               
               
                 152 
                 96 
                 203 
                 672 
                 228 
                 144 
                 254 
                 1248 
                 266 
                 168 
               
               
                 156 
                 576 
                 208 
                 768 
                 234 
                 864 
                 260 
                 960 
                 273 
                 1008 
               
               
                 160 
                 1056 
                 213 
                 864 
                 240 
                 1584 
                 266 
                 672 
                 279 
                 216 
               
               
                 164 
                 1536 
                 218 
                 960 
                 245 
                 672 
                 272 
                 384 
                 286 
                 1056 
               
               
                 167 
                 384 
                 223 
                 1056 
                 251 
                 1392 
                 278 
                 96 
                 292 
                 264 
               
               
                 171 
                 864 
                 228 
                 1152 
                 256 
                 480 
                 285 
                 1440 
                 299 
                 1104 
               
               
                 175 
                 1344 
                 233 
                 1248 
                 262 
                 1200 
                 291 
                 1152 
                 305 
                 312 
               
               
                 178 
                 192 
                 238 
                 1344 
                 267 
                 288 
                 297 
                 864 
                 312 
                 1152 
               
               
                 182 
                 672 
                 243 
                 1440 
                 273 
                 1008 
                 303 
                 576 
                 318 
                 360 
               
               
                 186 
                 1152 
                 248 
                 1536 
                 278 
                 96 
                 309 
                 288 
                 325 
                 1200 
               
               
                 190 
                 0 
                 253 
                 0 
                 284 
                 816 
                 316 
                 0 
                 331 
                 408 
               
               
                 193 
                 480 
                 257 
                 96 
                 290 
                 1536 
                 322 
                 1344 
                 338 
                 1248 
               
               
                 197 
                 960 
                 262 
                 192 
                 295 
                 624 
                 328 
                 1056 
                 344 
                 456 
               
               
                 201 
                 1440 
                 267 
                 288 
                 301 
                 1344 
                 334 
                 768 
                 351 
                 1296 
               
               
                 204 
                 288 
                 272 
                 384 
                 306 
                 432 
                 340 
                 480 
                 357 
                 504 
               
               
                 208 
                 768 
                 277 
                 480 
                 312 
                 1152 
                 346 
                 192 
                 364 
                 1344 
               
               
                 212 
                 1248 
                 282 
                 576 
                 317 
                 240 
                 353 
                 1536 
                 370 
                 552 
               
               
                 215 
                 96 
                 287 
                 672 
                 323 
                 960 
                 359 
                 1248 
                 377 
                 1392 
               
               
                 219 
                 576 
                 292 
                 768 
                 328 
                 48 
                 365 
                 960 
                 383 
                 600 
               
               
                 223 
                 1056 
                 297 
                 864 
                 334 
                 768 
                 371 
                 672 
                 390 
                 1440 
               
               
                 227 
                 1536 
                 302 
                 960 
                 340 
                 1488 
                 377 
                 384 
                 396 
                 648 
               
               
                 230 
                 384 
                 307 
                 1056 
                 345 
                 576 
                 383 
                 96 
                 403 
                 1488 
               
               
                 234 
                 864 
                 312 
                 1152 
                 351 
                 1296 
                 390 
                 1440 
                 409 
                 696 
               
               
                 238 
                 1344 
                 317 
                 1248 
                 356 
                 384 
                 396 
                 1152 
                 416 
                 1536 
               
               
                 241 
                 192 
                 322 
                 1344 
                 362 
                 1104 
                 402 
                 864 
                 422 
                 744 
               
               
                 245 
                 672 
                 327 
                 1440 
                 367 
                 192 
                 408 
                 576 
                 429 
                 1584 
               
               
                 249 
                 1152 
                 332 
                 1536 
                 373 
                 912 
                 414 
                 288 
                 435 
                 792 
               
               
                   
               
             
          
         
       
     
         [0000]    
       
         
               
               
               
               
               
             
               
               
               
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 9 
               
             
             
               
                   
               
               
                 1/2 
                 2/3 
                 3/4 
                 5/6 
                 7/8 
               
             
          
           
               
                 #RS block 
                 #Offset 
                 #RS block 
                 #Offset 
                 #RS block 
                 #Offset 
                 #RS block 
                 #Offset 
                 #RS block 
                 #Offset 
               
               
                   
               
             
          
           
               
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 6 
                 720 
                 8 
                 960 
                 9 
                 1080 
                 10 
                 1200 
                 10 
                 444 
               
               
                 12 
                 1440 
                 15 
                 288 
                 17 
                 528 
                 19 
                 768 
                 20 
                 888 
               
               
                 17 
                 528 
                 23 
                 1248 
                 26 
                 1608 
                 28 
                 336 
                 30 
                 1332 
               
               
                 23 
                 1248 
                 30 
                 576 
                 34 
                 1056 
                 38 
                 1536 
                 39 
                 144 
               
               
                 28 
                 336 
                 38 
                 1536 
                 42 
                 504 
                 47 
                 1104 
                 49 
                 588 
               
               
                 34 
                 1056 
                 45 
                 864 
                 51 
                 1584 
                 56 
                 672 
                 59 
                 1032 
               
               
                 39 
                 144 
                 52 
                 192 
                 59 
                 1032 
                 65 
                 240 
                 69 
                 1476 
               
               
                 45 
                 864 
                 60 
                 1152 
                 67 
                 480 
                 75 
                 1440 
                 78 
                 288 
               
               
                 51 
                 1584 
                 67 
                 480 
                 76 
                 1560 
                 84 
                 1008 
                 88 
                 732 
               
               
                 56 
                 672 
                 75 
                 1440 
                 84 
                 1008 
                 93 
                 576 
                 98 
                 1176 
               
               
                 62 
                 1392 
                 82 
                 768 
                 92 
                 456 
                 102 
                 144 
                 108 
                 1620 
               
               
                 67 
                 480 
                 89 
                 96 
                 101 
                 1536 
                 112 
                 1344 
                 117 
                 432 
               
               
                 73 
                 1200 
                 97 
                 1056 
                 109 
                 984 
                 121 
                 912 
                 127 
                 876 
               
               
                 78 
                 288 
                 104 
                 384 
                 117 
                 432 
                 130 
                 480 
                 137 
                 1320 
               
               
                 84 
                 1008 
                 112 
                 1344 
                 126 
                 1512 
                 139 
                 48 
                 146 
                 132 
               
               
                 89 
                 96 
                 119 
                 672 
                 134 
                 960 
                 149 
                 1248 
                 156 
                 576 
               
               
                 95 
                 816 
                 127 
                 0 
                 142 
                 408 
                 158 
                 816 
                 166 
                 1020 
               
               
                 101 
                 1536 
                 134 
                 960 
                 151 
                 1488 
                 167 
                 384 
                 176 
                 1464 
               
               
                 106 
                 624 
                 141 
                 288 
                 159 
                 936 
                 177 
                 1584 
                 185 
                 276 
               
               
                 112 
                 1344 
                 149 
                 1248 
                 167 
                 384 
                 186 
                 1152 
                 195 
                 720 
               
               
                 117 
                 432 
                 156 
                 576 
                 176 
                 1464 
                 195 
                 720 
                 205 
                 1164 
               
               
                 123 
                 1152 
                 164 
                 1536 
                 184 
                 912 
                 204 
                 288 
                 215 
                 1608 
               
               
                 128 
                 240 
                 171 
                 864 
                 192 
                 360 
                 214 
                 1488 
                 224 
                 420 
               
               
                 134 
                 960 
                 178 
                 192 
                 201 
                 1440 
                 223 
                 1056 
                 234 
                 864 
               
               
                 139 
                 48 
                 186 
                 1152 
                 209 
                 888 
                 232 
                 624 
                 244 
                 1308 
               
               
                 145 
                 768 
                 193 
                 480 
                 217 
                 336 
                 241 
                 192 
                 253 
                 120 
               
               
                 151 
                 1488 
                 201 
                 1440 
                 226 
                 1416 
                 251 
                 1392 
                 263 
                 564 
               
               
                 156 
                 576 
                 208 
                 768 
                 234 
                 864 
                 260 
                 960 
                 273 
                 1008 
               
               
                 162 
                 1296 
                 215 
                 96 
                 242 
                 312 
                 269 
                 528 
                 283 
                 1452 
               
               
                 167 
                 384 
                 223 
                 1056 
                 251 
                 1392 
                 278 
                 96 
                 292 
                 264 
               
               
                 173 
                 1104 
                 230 
                 384 
                 259 
                 840 
                 288 
                 1296 
                 302 
                 708 
               
               
                 178 
                 192 
                 238 
                 1344 
                 267 
                 288 
                 297 
                 864 
                 312 
                 1152 
               
               
                 184 
                 912 
                 245 
                 672 
                 276 
                 1368 
                 306 
                 432 
                 322 
                 1596 
               
               
                 190 
                 0 
                 253 
                 0 
                 284 
                 816 
                 316 
                 0 
                 331 
                 408 
               
               
                 195 
                 720 
                 260 
                 960 
                 292 
                 264 
                 325 
                 1200 
                 341 
                 852 
               
               
                 201 
                 1440 
                 267 
                 288 
                 301 
                 1344 
                 334 
                 768 
                 351 
                 1296 
               
               
                 206 
                 528 
                 275 
                 1248 
                 309 
                 792 
                 343 
                 336 
                 360 
                 108 
               
               
                 212 
                 1248 
                 282 
                 576 
                 317 
                 240 
                 353 
                 1536 
                 370 
                 552 
               
               
                 217 
                 336 
                 290 
                 1536 
                 326 
                 1320 
                 362 
                 1104 
                 380 
                 996 
               
               
                 223 
                 1056 
                 297 
                 864 
                 334 
                 768 
                 371 
                 672 
                 390 
                 1440 
               
               
                 228 
                 144 
                 304 
                 192 
                 342 
                 216 
                 380 
                 240 
                 399 
                 252 
               
               
                 234 
                 864 
                 312 
                 1152 
                 351 
                 1296 
                 390 
                 1440 
                 409 
                 696 
               
               
                 240 
                 1584 
                 319 
                 480 
                 359 
                 744 
                 399 
                 1008 
                 419 
                 1140 
               
               
                 245 
                 672 
                 327 
                 1440 
                 367 
                 192 
                 408 
                 576 
                 429 
                 1584 
               
               
                 251 
                 1392 
                 334 
                 768 
                 376 
                 1272 
                 417 
                 144 
                 438 
                 396 
               
               
                 256 
                 480 
                 341 
                 96 
                 384 
                 720 
                 427 
                 1344 
                 448 
                 840 
               
               
                 262 
                 1200 
                 349 
                 1056 
                 392 
                 168 
                 436 
                 912 
                 458 
                 1284 
               
               
                 267 
                 288 
                 356 
                 384 
                 401 
                 1248 
                 445 
                 480 
                 467 
                 96 
               
               
                 273 
                 1008 
                 364 
                 1344 
                 409 
                 696 
                 454 
                 48 
                 477 
                 540 
               
               
                 278 
                 96 
                 371 
                 672 
                 417 
                 144 
                 464 
                 1248 
                 487 
                 984 
               
               
                 284 
                 816 
                 379 
                 0 
                 426 
                 1224 
                 473 
                 816 
                 497 
                 1428 
               
               
                 290 
                 1536 
                 386 
                 960 
                 434 
                 672 
                 482 
                 384 
                 506 
                 240 
               
               
                 295 
                 624 
                 393 
                 288 
                 442 
                 120 
                 492 
                 1584 
                 516 
                 684 
               
               
                 301 
                 1344 
                 401 
                 1248 
                 451 
                 1200 
                 501 
                 1152 
                 526 
                 1128 
               
               
                 306 
                 432 
                 408 
                 576 
                 459 
                 648 
                 510 
                 720 
                 536 
                 1572 
               
               
                 312 
                 1152 
                 416 
                 1536 
                 467 
                 96 
                 519 
                 288 
                 545 
                 384 
               
               
                 317 
                 240 
                 423 
                 864 
                 476 
                 1176 
                 529 
                 1488 
                 555 
                 828 
               
               
                 323 
                 960 
                 430 
                 192 
                 484 
                 624 
                 538 
                 1056 
                 565 
                 1272 
               
               
                 328 
                 48 
                 438 
                 1152 
                 492 
                 72 
                 547 
                 624 
                 574 
                 84 
               
               
                 334 
                 768 
                 445 
                 480 
                 501 
                 1152 
                 556 
                 192 
                 584 
                 528 
               
               
                 340 
                 1488 
                 453 
                 1440 
                 509 
                 600 
                 566 
                 1392 
                 594 
                 972 
               
               
                 345 
                 576 
                 460 
                 768 
                 517 
                 48 
                 575 
                 960 
                 604 
                 1416 
               
               
                 351 
                 1296 
                 467 
                 96 
                 526 
                 1128 
                 584 
                 528 
                 613 
                 228 
               
               
                 356 
                 384 
                 475 
                 1056 
                 534 
                 576 
                 593 
                 96 
                 623 
                 672 
               
               
                 362 
                 1104 
                 482 
                 384 
                 542 
                 24 
                 603 
                 1296 
                 633 
                 1116 
               
               
                 367 
                 192 
                 490 
                 1344 
                 551 
                 1104 
                 612 
                 864 
                 643 
                 1560 
               
               
                 373 
                 912 
                 497 
                 672 
                 559 
                 552 
                 621 
                 432 
                 652 
                 372 
               
               
                   
               
             
          
         
       
     
         [0026]    Embodiments of the disclosure can be implemented in digital electronic circuitry, or in computer hardware, firmware, software, or in combinations of them. Embodiments of the disclosure can be implemented in a computer program product tangibly embodied in a machine-readable storage device for execution by a programmable processor; and method steps of the disclosure can be performed by a programmable processor executing a program of instructions to perform functions of the disclosure by operating on input data and generating output. The disclosure can be implemented advantageously in one or more computer programs that are executable on a programmable system including at least one programmable processor coupled to receive data and instructions from, and to transmit data and instructions to, a data storage system, at least one input device, and at least one output device. Each computer program can be implemented in a high-level procedural or object-oriented programming language, or in assembly or machine language if desired; and in any case, the language can be a compiled or interpreted language. Suitable processors include, by way of example, both general and special purpose microprocessors. Generally, a processor will receive instructions and data from a read-only memory and/or a random access memory. Generally, a computer will include one or more mass storage devices for storing data files; such devices include magnetic disks, such as internal hard disks and removable disks; magneto-optical disks; and optical disks. Storage devices suitable for tangibly embodying computer program instructions and data include all forms of non-volatile memory, including by way of example semiconductor memory devices, such as EPROM, EEPROM, and flash memory devices; magnetic disks such as internal hard disks and removable disks; magneto-optical disks; and CD-ROM disks. Any of the foregoing can be supplemented by, or incorporated in, ASICs (application-specific integrated circuits). 
         [0027]    A number of implementations of the disclosure have been described. 
         [0028]    Nevertheless, it will be understood that various modifications may be made without departing from the spirit and scope of the disclosure. Accordingly, other implementations are within the scope of the following claims.