Data processing device and data processing method using low density parity check encoding for decreasing signal-to-noise power ratio
The present technology relates to a data processing device and a data processing method which can ensure high communication quality in data transmission using LDPC codes. In group-wise interleaving, an LDPC code having a code length N of 64800 bits and a coding rate r of 9/15 is interleaved in a unit of a bit group of 360 bits. In group-wise deinterleaving, a sequence of bit groups of the LDPC code which has been subjected to the group-wise interleaving is returned to an original sequence. The present technology can be applied to, for example, a case in which data transmission is performed using LDPC codes.
1. A receiving device comprising:
a receiver configured to receive a digital television broadcast signal including a mapped group-wise interleaved low density parity check (LDPC) code word; and
circuitry configured to:
process the mapped group-wise interleaved LDPC code word to obtain a group-wise interleaved LDPC code word, wherein each unit of 2 bits of the group-wise interleaved LDPC code word is mapped to one of 4 signal points of a modulation scheme,
process the group-wise interleaved LDPC code word in units of bit groups of 360 bits to obtain an LDPC code word of a LDPC code, wherein an (i+1)-th bit group from a head of the LDPC code word of the LDPC code is indicated by a bit group i, the LDPC code word of the LDPC code has a sequence of bit groups 0 to 179, and the group-wise interleaved LDPC code word has a following sequence of bit groups,
0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44, 46, 48, 50, 52, 54, 56, 58, 60, 62, 64, 66, 68, 70, 72, 74, 76, 78, 80, 82, 84, 86, 88, 90, 92, 94, 96, 98, 100, 102, 104, 106, 108, 110, 112, 114, 116, 118, 120, 122, 124, 126, 128, 130, 132, 134, 136, 138, 140, 142, 144, 146, 148, 150, 152, 154, 156, 158, 160, 162, 164, 166, 168, 170, 172, 174, 176, 178, 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 45, 47, 49, 51, 53, 55, 57, 59, 61, 63, 65, 67, 69, 71, 73, 75, 77, 79, 81, 83, 85, 87, 89, 91, 93, 95, 97, 99, 101, 103, 105, 107, 109, 111, 113, 115, 117, 119, 121, 123, 125, 127, 129, 131, 133, 135, 137, 139, 141, 143, 145, 147, 149, 151, 153, 155, 157, 159, 161, 163, 165, 167, 169, 171, 173, 175, 177, 179,
decode the LDPC code word of the LDPC code to obtain a decoded LDPC code word, and
process the decoded LDPC code word for presentation of the digital television broadcast signal, wherein
the LDPC code has a code length N of 64800 bits and a code rate r of 9/15 and is based on a parity check matrix initial value table listed as follows:
113 1557 3316 5680 6241 10407 13404 13947 14040
14353 15522 15698 16079 17363 19374 19543 20530 22833
24339
271 1361 6236 7006 7307 7333 12768 15441 15568 17923
18341 20321 21502 22023 23938 25351 25590 25876 25910
73 605 872 4008 6279 7653 10346 10799 12482 12935
13604 15909 16526 19782 20506 22804 23629 24859 25600
1445 1690 4304 4851 8919 9176 9252 13783 16076 16675
17274 18806 18882 20819 21958 22451 23869 23999 24177
1290 2337 5661 6371 8996 10102 10941 11360 12242
14918 16808 20571 23374 24046 25045 25060 25662 25783
25913
28 42 1926 3421 3503 8558 9453 10168 15820 17473
19571 19685 22790 23336 23367 23890 24061 25657 25680
0 1709 4041 4932 5968 7123 8430 9564 10596 11026
14761 19484 20762 20858 23803 24016 24795 25853 25863
29 1625 6500 6609 16831 18517 18568 18738 19387
20159 20544 21603 21941 24137 24269 24416 24803 25154
25395
55 66 871 3700 11426 13221 15001 16367 17601 18380
22796 23488 23938 25476 25635 25678 25807 25857 25872
1 19 5958 8548 8860 11489 16845 18450 18469 19496
20190 23173 25262 25566 25668 25679 25858 25888 25915
7520 7690 8855 9183 14654 16695 17121 17854 18083
18428 19633 20470 20736 21720 22335 23273 25083 25293
25403
48 58 410 1299 3786 10668 18523 18963 20864 22106
22308 23033 23107 23128 23990 24286 24409 24595 25802
12 51 3894 6539 8276 10885 11644 12777 13427 14039
15954 17078 19053 20537 22863 24521 25087 25463 25838
3509 8748 9581 11509 15884 16230 17583 19264 20900
21001 21310 22547 22756 22959 24768 24814 25594 25626
25880
21 29 69 1448 2386 4601 6626 6667 10242 13141 13852
14137 18640 19951 22449 23454 24431 25512 25814
18 53 7890 9934 10063 16728 19040 19809 20825 21522
21800 23582 24556 25031 25547 25562 25733 25789 25906
4096 4582 5766 5894 6517 10027 12182 13247 15207
17041 18958 20133 20503 22228 24332 24613 25689 25855
25883
0 25 819 5539 7076 7536 7695 9532 13668 15051 17683
19665 20253 21996 24136 24890 25758 25784 25807
34 40 44 4215 6076 7427 7965 8777 11017 15593 19542
22202 22973 23397 23423 24418 24873 25107 25644
1595 6216 22850 25439
1562 15172 19517 22362
7508 12879 24324 24496
6298 15819 16757 18721
11173 15175 19966 21195
59 13505 16941 23793
2267 4830 12023 20587
8827 9278 13072 16664
14419 17463 23398 25348
6112 16534 20423 22698
493 8914 21103 24799
6896 12761 13206 25873
2 1380 12322 21701
11600 21306 25753 25790
8421 13076 14271 15401
9630 14112 19017 20955
212 13932 21781 25824
5961 9110 16654 19636
58 5434 9936 12770
6575 11433 19798
2731 7338 20926
14253 18463 25404
21791 24805 25869
2 11646 15850
6075 8586 23819
18435 22093 24852
2103 2368 11704
10925 17402 18232
9062 25061 25674
18497 20853 23404
18606 19364 19551
7 1022 25543
6744 15481 25868
9081 17305 25164
8 23701 25883
9680 19955 22848
56 4564 19121
5595 15086 25892
3174 17127 23183
19397 19817 20275
12561 24571 25825
7111 9889 25865
19104 20189 21851
549 9686 25548
6586 20325 25906
3224 20710 21637
641 15215 25754
13484 23729 25818
2043 7493 24246
16860 25230 25768
22047 24200 24902
9391 18040 19499
7855 24336 25069
23834 25570 25852
1977 8800 25756
6671 21772 25859
3279 6710 24444
24099 25117 25820
5553 12306 25915
48 11107 23907
10832 11974 25773
2223 17905 25484
16782 17135 20446
475 2861 3457
16218 22449 24362
11716 22200 25897
8315 15009 22633
13 20480 25852
12352 18658 25687
3681 14794 23703
30 24531 25846
4103 22077 24107
23837 25622 25812
3627 13387 25839
908 5367 19388
0 6894 25795
20322 23546 25181
8178 25260 25437
2449 13244 22565
31 18928 22741
1312 5134 14838
6085 13937 24220
66 14633 25670
47 22512 25472
8867 24704 25279
6742 21623 22745
147 9948 24178
8522 24261 24307
19202 22406 24609.
2. The receiving device of claim 1 , wherein
the LDPC encoding is performed in accordance with an Advanced Television Systems Committee (ATSC) 3.0 standard.
3. The receiving device of claim 1 , wherein
the LDPC code word of the LDPC code is encoded according to a parity check matrix of the LDPC code,
the parity check matrix includes an information matrix part corresponding to information bits and a parity matrix part corresponding to parity bits,
the information matrix part is represented by the parity check matrix initial value table, and
each row of the parity check matrix initial value table indicating positions of elements ‘1’ in corresponding 360 columns of an information matrix part corresponding to a subset of the information bits used in calculating the parity bits.
4. The receiving device of claim 3 , wherein
a row of the parity check matrix initial value table is represented by i and a length of the parity bits of the LDPC code word of the LDPC code is represented by M, a 2+360×(i−1)-th column of the parity check matrix is obtained by a cyclic shift of a 1+360×(i−1)-th column of the parity check matrix downward by q=M/360.
5. The receiving device of claim 4 , wherein
for the 1+360×(i−1)-th column of the parity check matrix,
an i-th row of the parity check matrix initial value table includes one or more values each representing a different row number of element 1 of the 1+360×(i−1)-th column of the parity check matrix, and
for each column from the 2+360×(i−1)-th column to a 360×i-th column being a column other than the 1+360×(i−1)-th column of the parity check matrix,
an i-th row and j-th column value of the parity check matrix initial value table is represented as Hi, j and a row number of a j-th element 1 of a w-th column of the parity check matrix H is represented as Hw−j,
the row number Hw−j of the element 1 of the w-th column being a column other than the 1+360×(i−1)-th column of the parity check matrix is represented by the equation
Hw−j =mod( Hi,j +mod(( w− 1),360)× M/ 360, M ).
6. The receiving device of claim 3 , wherein the parity matrix part is a lower bidiagonal matrix, in which elements of “1” are arranged in a step-wise fashion.
7. The receiving device of claim 3 , wherein
the parity check matrix has no cycle-4.
8. The receiving device of claim 3 , wherein
the parity check matrix of the LDPC code belongs to an ensemble in which a performance threshold being a ratio of signal power to noise power at which a bit error rate starts to decrease is a predetermined value or smaller is found by multi-edge type density evolution.
9. A method comprising:
receiving a digital television broadcast signal including a mapped group-wise interleaved low density parity check (LDPC) code word;
processing the mapped group-wise interleaved LDPC code word to obtain a group-wise interleaved LDPC code word, wherein each unit of 2 bits of the group-wise interleaved LDPC code word is mapped to one of 4 signal points of a modulation scheme;
processing the group-wise interleaved LDPC code word in units of bit groups of 360 bits to obtain an LDPC code word of a LDPC code, wherein an (i+1)-th bit group from a head of the LDPC code word of the LDPC code is indicated by a bit group i, the LDPC code word of the LDPC code has a sequence of bit groups 0 to 179, and the group-wise interleaved LDPC code word has a following sequence of bit groups,
0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44, 46, 48, 50, 52, 54, 56, 58, 60, 62, 64, 66, 68, 70, 72, 74, 76, 78, 80, 82, 84, 86, 88, 90, 92, 94, 96, 98, 100, 102, 104, 106, 108, 110, 112, 114, 116, 118, 120, 122, 124, 126, 128, 130, 132, 134, 136, 138, 140, 142, 144, 146, 148, 150, 152, 154, 156, 158, 160, 162, 164, 166, 168, 170, 172, 174, 176, 178, 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 45, 47, 49, 51, 53, 55, 57, 59, 61, 63, 65, 67, 69, 71, 73, 75, 77, 79, 81, 83, 85, 87, 89, 91, 93, 95, 97, 99, 101, 103, 105, 107, 109, 111, 113, 115, 117, 119, 121, 123, 125, 127, 129, 131, 133, 135, 137, 139, 141, 143, 145, 147, 149, 151, 153, 155, 157, 159, 161, 163, 165, 167, 169, 171, 173, 175, 177, 179,
decoding, by decoding circuitry, the LDPC code word of the LDPC code to obtain a decoded LDPC code word; and
processing the decoded LDPC code word for presentation of the digital television broadcast signal, wherein
the LDPC code has a code length of N of 64800 bits and a code rate r of 9/15 and is based on a parity check matrix initial value table listed as follows:
113 1557 3316 5680 6241 10407 13404 13947 14040
14353 15522 15698 16079 17363 19374 19543 20530 22833
24339
271 1361 6236 7006 7307 7333 12768 15441 15568 17923
18341 20321 21502 22023 23938 25351 25590 25876 25910
73 605 872 4008 6279 7653 10346 10799 12482 12935
13604 15909 16526 19782 20506 22804 23629 24859 25600
1445 1690 4304 4851 8919 9176 9252 13783 16076 16675
17274 18806 18882 20819 21958 22451 23869 23999 24177
1290 2337 5661 6371 8996 10102 10941 11360 12242
14918 16808 20571 23374 24046 25045 25060 25662 25783
25913
28 42 1926 3421 3503 8558 9453 10168 15820 17473
19571 19685 22790 23336 23367 23890 24061 25657 25680
0 1709 4041 4932 5968 7123 8430 9564 10596 11026
14761 19484 20762 20858 23803 24016 24795 25853 25863
29 1625 6500 6609 16831 18517 18568 18738 19387
20159 20544 21603 21941 24137 24269 24416 24803 25154
25395
55 66 871 3700 11426 13221 15001 16367 17601 18380
22796 23488 23938 25476 25635 25678 25807 25857 25872
1 19 5958 8548 8860 11489 16845 18450 18469 19496
20190 23173 25262 25566 25668 25679 25858 25888 25915
7520 7690 8855 9183 14654 16695 17121 17854 18083
18428 19633 20470 20736 21720 22335 23273 25083 25293
25403
48 58 410 1299 3786 10668 18523 18963 20864 22106
22308 23033 23107 23128 23990 24286 24409 24595 25802
12 51 3894 6539 8276 10885 11644 12777 13427 14039
15954 17078 19053 20537 22863 24521 25087 25463 25838
3509 8748 9581 11509 15884 16230 17583 19264 20900
21001 21310 22547 22756 22959 24768 24814 25594 25626
25880
21 29 69 1448 2386 4601 6626 6667 10242 13141 13852
14137 18640 19951 22449 23454 24431 25512 25814
18 53 7890 9934 10063 16728 19040 19809 20825 21522
21800 23582 24556 25031 25547 25562 25733 25789 25906
4096 4582 5766 5894 6517 10027 12182 13247 15207
17041 18958 20133 20503 22228 24332 24613 25689 25855
25883
0 25 819 5539 7076 7536 7695 9532 13668 15051 17683
19665 20253 21996 24136 24890 25758 25784 25807
34 40 44 4215 6076 7427 7965 8777 11017 15593 19542
22202 22973 23397 23423 24418 24873 25107 25644
1595 6216 22850 25439
1562 15172 19517 22362
7508 12879 24324 24496
6298 15819 16757 18721
11173 15175 19966 21195
59 13505 16941 23793
2267 4830 12023 20587
8827 9278 13072 16664
14419 17463 23398 25348
6112 16534 20423 22698
493 8914 21103 24799
6896 12761 13206 25873
2 1380 12322 21701
11600 21306 25753 25790
8421 13076 14271 15401
9630 14112 19017 20955
212 13932 21781 25824
5961 9110 16654 19636
58 5434 9936 12770
6575 11433 19798
2731 7338 20926
14253 18463 25404
21791 24805 25869
2 11646 15850
6075 8586 23819
18435 22093 24852
2103 2368 11704
10925 17402 18232
9062 25061 25674
18497 20853 23404
18606 19364 19551
7 1022 25543
6744 15481 25868
9081 17305 25164
8 23701 25883
9680 19955 22848
56 4564 19121
5595 15086 25892
3174 17127 23183
19397 19817 20275
12561 24571 25825
7111 9889 25865
19104 20189 21851
549 9686 25548
6586 20325 25906
3224 20710 21637
641 15215 25754
13484 23729 25818
2043 7493 24246
16860 25230 25768
22047 24200 24902
9391 18040 19499
7855 24336 25069
23834 25570 25852
1977 8800 25756
6671 21772 25859
3279 6710 24444
24099 25117 25820
5553 12306 25915
48 11107 23907
10832 11974 25773
2223 17905 25484
16782 17135 20446
475 2861 3457
16218 22449 24362
11716 22200 25897
8315 15009 22633
13 20480 25852
12352 18658 25687
3681 14794 23703
30 24531 25846
4103 22077 24107
23837 25622 25812
3627 13387 25839
908 5367 19388
0 6894 25795
20322 23546 25181
8178 25260 25437
2449 13244 22565
31 18928 22741
1312 5134 14838
6085 13937 24220
66 14633 25670
47 22512 25472
8867 24704 25279
6742 21623 22745
147 9948 24178
8522 24261 24307
19202 22406 24609.
10. The method of claim 9 , wherein
the LDPC encoding is performed in accordance with an Advanced Television Systems Committee (ATSC) 3.0 standard.
11. The method of claim 9 , wherein
the LDPC code word of the LDPC code is encoded according to a parity check matrix of the LDPC code,
the parity check matrix includes an information matrix part corresponding to information bits and a parity matrix part corresponding to parity bits,
the information matrix part is represented by the parity check matrix initial value table, and
each row of the parity check matrix initial value table indicating positions of elements ‘1’ in corresponding 360 columns of an information matrix part corresponding to a subset of the information bits used in calculating the parity bits.
12. The method of claim 11 , wherein
a row of the parity check matrix initial value table is represented by i and a length of the parity bits of the LDPC code word of the LDPC code is represented by M, a 2+360×(i−1)-th column of the parity check matrix is obtained by a cyclic shift of a 1+360×(i−1)-th column of the parity check matrix downward by q=M/360.
13. The method of claim 12 , wherein
for the 1+360×(i−1)-th column of the parity check matrix,
an i-th row of the parity check matrix initial value table includes one or more values each representing a different row number of element 1 of the 1+360×(i−1)-th column of the parity check matrix, and
for each column from the 2+360×(i−1)-th column to a 360×i-th column being a column other than the 1+360×(i−1)-th column of the parity check matrix,
an i-th row and j-th column value of the parity check matrix initial value table is represented as Hi, j and a row number of a j-th element 1 of a w-th column of the parity check matrix H is represented as Hw−j,
the row number Hw−j of the element 1 of the w-th column being a column other than the 1+360×(i−1)-th column of the parity check matrix is represented by the equation
Hw−j =mod( Hij +mod(( w− 1),360)× M/ 360, M ).
14. The method of claim 11 , wherein the parity matrix part is a lower bidiagonal matrix, in which elements of “1” are arranged in a step-wise fashion.
15. The method of claim 11 , wherein
the parity check matrix has no cycle-4.
16. The method of claim 11 , wherein
the parity check matrix of the LDPC code belongs to an ensemble in which a performance threshold being a ratio of signal power to noise power at which a bit error rate starts to decrease is a predetermined value or smaller is found by multi-edge type density evolution.
17. A non-transitory computer readable medium including computer executable instructions which, when executed by a computer, cause the computer to perform a method comprising:
receiving by a receiving device, a digital broadcast signal including a mapped group-wise interleaved low density parity check (LDPC) code word from a transmitting device;
processing the mapped group-wise interleaved LDPC code word to obtain a group-wise interleaved LDPC code word, wherein each unit of 2 bits of the group-wise interleaved LDPC code word is mapped to one of 4 signal points of a modulation scheme;
processing the group-wise interleaved LDPC code word in units of bit groups of 360 bits to obtain an LDPC code word of an LDPC code, wherein an (i+1)-th bit group from a head of the LDPC code word of the LDPC code is indicated by a bit group i, the LDPC code word of the LDPC code has a sequence of bit groups 0 to 179, and the group-wise interleaved LDPC code word has a following sequence of bit groups,
0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44, 46, 48, 50, 52, 54, 56, 58, 60, 62, 64, 66, 68, 70, 72, 74, 76, 78, 80, 82, 84, 86, 88, 90, 92, 94, 96, 98, 100, 102, 104, 106, 108, 110, 112, 114, 116, 118, 120, 122, 124, 126, 128, 130, 132, 134, 136, 138, 140, 142, 144, 146, 148, 150, 152, 154, 156, 158, 160, 162, 164, 166, 168, 170, 172, 174, 176, 178, 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 45, 47, 49, 51, 53, 55, 57, 59, 61, 63, 65, 67, 69, 71, 73, 75, 77, 79, 81, 83, 85, 87, 89, 91, 93, 95, 97, 99, 101, 103, 105, 107, 109, 111, 113, 115, 117, 119, 121, 123, 125, 127, 129, 131, 133, 135, 137, 139, 141, 143, 145, 147, 149, 151, 153, 155, 157, 159, 161, 163, 165, 167, 169, 171, 173, 175, 177, 179;
decoding the LDPC code word of the LDPC code to obtain a decoded LDPC code word, and
processing the decoded LDPC code word for presentation of the digital broadcast signal;
wherein the LDPC code has a code length N of 64800 bits and a code rate r of 9/15 and is based on a parity check matrix initial value table listed as follows:
113 1557 3316 5680 6241 10407 13404 13947 14040
14353 15522 15698 16079 17363 19374 19543 20530 22833
24339
271 1361 6236 7006 7307 7333 12768 15441 15568 17923
18341 20321 21502 22023 23938 25351 25590 25876 25910
73 605 872 4008 6279 7653 10346 10799 12482 12935
13604 15909 16526 19782 20506 22804 23629 24859 25600
1445 1690 4304 4851 8919 9176 9252 13783 16076 16675
17274 18806 18882 20819 21958 22451 23869 23999 24177
1290 2337 5661 6371 8996 10102 10941 11360 12242
14918 16808 20571 23374 24046 25045 25060 25662 25783
25913
28 42 1926 3421 3503 8558 9453 10168 15820 17473
19571 19685 22790 23336 23367 23890 24061 25657 25680
0 1709 4041 4932 5968 7123 8430 9564 10596 11026
14761 19484 20762 20858 23803 24016 24795 25853 25863
29 1625 6500 6609 16831 18517 18568 18738 19387
20159 20544 21603 21941 24137 24269 24416 24803 25154
25395
55 66 871 3700 11426 13221 15001 16367 17601 18380
22796 23488 23938 25476 25635 25678 25807 25857 25872
1 19 5958 8548 8860 11489 16845 18450 18469 19496
20190 23173 25262 25566 25668 25679 25858 25888 25915
7520 7690 8855 9183 14654 16695 17121 17854 18083
18428 19633 20470 20736 21720 22335 23273 25083 25293
25403
48 58 410 1299 3786 10668 18523 18963 20864 22106
22308 23033 23107 23128 23990 24286 24409 24595 25802
12 51 3894 6539 8276 10885 11644 12777 13427 14039
15954 17078 19053 20537 22863 24521 25087 25463 25838
3509 8748 9581 11509 15884 16230 17583 19264 20900
21001 21310 22547 22756 22959 24768 24814 25594 25626
25880
21 29 69 1448 2386 4601 6626 6667 10242 13141 13852
14137 18640 19951 22449 23454 24431 25512 25814
18 53 7890 9934 10063 16728 19040 19809 20825 21522
21800 23582 24556 25031 25547 25562 25733 25789 25906
4096 4582 5766 5894 6517 10027 12182 13247 15207
17041 18958 20133 20503 22228 24332 24613 25689 25855
25883
0 25 819 5539 7076 7536 7695 9532 13668 15051 17683
19665 20253 21996 24136 24890 25758 25784 25807
34 40 44 4215 6076 7427 7965 8777 11017 15593 19542
22202 22973 23397 23423 24418 24873 25107 25644
1595 6216 22850 25439
1562 15172 19517 22362
7508 12879 24324 24496
6298 15819 16757 18721
11173 15175 19966 21195
59 13505 16941 23793
2267 4830 12023 20587
8827 9278 13072 16664
14419 17463 23398 25348
6112 16534 20423 22698
493 8914 21103 24799
6896 12761 13206 25873
2 1380 12322 21701
11600 21306 25753 25790
8421 13076 14271 15401
9630 14112 19017 20955
212 13932 21781 25824
5961 9110 16654 19636
58 5434 9936 12770
6575 11433 19798
2731 7338 20926
14253 18463 25404
21791 24805 25869
2 11646 15850
6075 8586 23819
18435 22093 24852
2103 2368 11704
10925 17402 18232
9062 25061 25674
18497 20853 23404
18606 19364 19551
7 1022 25543
6744 15481 25868
9081 17305 25164
8 23701 25883
9680 19955 22848
56 4564 19121
5595 15086 25892
3174 17127 23183
19397 19817 20275
12561 24571 25825
7111 9889 25865
19104 20189 21851
549 9686 25548
6586 20325 25906
3224 20710 21637
641 15215 25754
13484 23729 25818
2043 7493 24246
16860 25230 25768
22047 24200 24902
9391 18040 19499
7855 24336 25069
23834 25570 25852
1977 8800 25756
6671 21772 25859
3279 6710 24444
24099 25117 25820
5553 12306 25915
48 11107 23907
10832 11974 25773
2223 17905 25484
16782 17135 20446
475 2861 3457
16218 22449 24362
11716 22200 25897
8315 15009 22633
13 20480 25852
12352 18658 25687
3681 14794 23703
30 24531 25846
4103 22077 24107
23837 25622 25812
3627 13387 25839
908 5367 19388
0 6894 25795
20322 23546 25181
8178 25260 25437
2449 13244 22565
31 18928 22741
1312 5134 14838
6085 13937 24220
66 14633 25670
47 22512 25472
8867 24704 25279
6742 21623 22745
147 9948 24178
8522 24261 24307
19202 22406 24609.