Data encoding and decoding
A video data encoding method for encoding an array of video data values includes frequency-transforming the video data values according to a frequency transform, to generate an array of frequency-transformed values by a matrix-multiplication process using a transform matrix having a data precision greater than six bits.
1. A video data encoding method for encoding an array of video data values, the method comprising:
frequency-transforming the video data values according to a frequency transform; and
generating an array of frequency-transformed values by a matrix-multiplication process using a transform matrix having a data precision greater than six bits, the transform matrix being matched to an inverse transform that has a data precision of six bits and is used to decode the video data values, the transform matrix having coefficients defined by at least a subset of the following values, wherein each letter indicates a respective coefficient value:
(a) when the frequency transform is a discrete cosine transform:
(b) when the frequency transform is a discrete sine transform:
a
b
c
d
c
c
e
-
c
d
-
a
-
c
b
b
-
d
c
-
a
the coefficient values being selected according to the data precision from values equal to values listed in the following tables:
(a) when the frequency transform is a discrete cosine transform:
7-bit
8-bit
9-bit
10-bit
11-bit
12-bit
13-bit
14-bit
a
128
256
512
1024
2048
4096
8192
16384
b
166
332
665
1329
2658
5317
10633
21266
c
72
144
288
576
1153
2306
4612
9224
d
178
356
713
1426
2852
5703
11407
22813
e
150
301
601
1203
2406
4811
9622
19244
f
100
200
399
798
1596
3192
6385
12769
g
36
71
143
285
570
1141
2282
4563
h
181
361
722
1445
2890
5780
11560
23120
i
172
345
689
1379
2758
5516
11032
22063
j
160
320
639
1278
2556
5113
10225
20450
k
140
281
562
1123
2246
4493
8986
17972
l
114
229
458
915
1830
3660
7321
14642
m
87
174
347
694
1389
2777
5555
11109
n
50
101
201
403
806
1612
3223
6446
o
18
36
72
145
290
579
1158
2316
p
181
361
722
1444
2888
5777
11553
23106
q
179
357
714
1428
2856
5713
11426
22852
r
175
351
701
1403
2806
5611
11222
22445
s
171
341
683
1365
2731
5462
10924
21848
t
164
328
656
1312
2624
5249
10497
20995
u
155
310
619
1238
2476
4952
9905
19810
v
145
291
581
1163
2325
4650
9301
18601
w
134
268
536
1071
2143
4286
8571
17143
x
123
246
491
982
1965
3929
7859
15718
y
108
216
433
866
1732
3463
6927
13853
z
92
184
367
734
1469
2937
5875
11749
A
77
154
308
615
1231
2461
4923
9846
B
62
124
247
494
988
1977
3954
7908
C
44
87
174
348
697
1393
2787
5573
D
26
51
103
205
410
820
1641
3281
E
7
15
30
59
118
236
473
946
15-bit
16-bit
17-bit
18-bit
19-bit
a
32768
65536
131072
262144
524288
b
42532
85065
170129
340259
680517
c
18448
36896
73791
147582
295164
d
45627
91253
182507
365014
730028
e
38489
76977
153954
307909
615817
f
25538
51077
102153
204306
408612
g
9126
18252
36504
73009
146018
h
46240
92479
184958
369917
739833
i
44126
88253
176506
353011
706022
j
40901
81802
163603
327207
654413
k
35944
71887
143775
287550
575099
l
29283
58566
117132
234265
468530
m
22219
44437
88874
177749
355498
n
12892
25784
51569
103137
206275
o
4632
9264
18528
37057
74113
p
46212
92424
184849
369697
739394
q
45704
91407
182815
365630
731260
r
44890
89779
179559
359118
718236
s
43695
87391
174781
349562
699125
t
41990
83979
167959
335918
671836
u
39619
79239
158477
316955
633909
v
37202
74404
148808
297616
595233
w
34285
68570
137140
274281
548561
x
31436
62871
125743
251486
502971
y
27706
55412
110825
221650
443299
z
23498
46997
93993
187986
375972
A
19692
39384
78767
157535
315070
B
15816
31631
63263
126525
253051
C
11146
22292
44584
89168
178337
D
6562
13124
26248
52497
104993
E
1891
3782
7564
15129
30258
20-bit
21-bit
22-bit
23-bit
24-bit
a
1048576
2097152
4194304
8388608
16777216
b
1361035
2722070
5444140
10888280
21776560
c
590328
1180657
2361314
4722627
9445255
d
1460056
2920112
5840224
11680448
23360895
e
1231635
2463269
4926539
9853077
19706155
f
817225
1634450
3268899
6537799
13075597
g
292035
584070
1168141
2336282
4672564
h
1479667
2959333
5918667
11837334
23674667
i
1412045
2824090
5648179
11296358
22592717
j
1308827
2617653
5235307
10470613
20941227
k
1150199
2300397
4600795
9201590
18403179
l
937060
1874119
3748238
7496477
14992954
m
710995
1421991
2843981
5687962
11375925
n
412549
825098
1650196
3300393
6600785
o
148227
296454
592908
1185815
2371630
p
1478788
2957576
5915152
11830305
23660609
q
1462520
2925040
5850080
11700160
23400319
r
1436472
2872944
5745888
11491775
22983550
s
1398249
2796498
5592996
11185992
22371984
t
1343671
2687342
5374684
10749368
21498736
u
1267818
2535636
5071272
10142545
20285089
v
1190466
2380931
4761862
9523724
19047449
w
1097123
2194246
4388491
8776982
17553965
x
1005942
2011884
4023769
8047537
16095074
y
886598
1773197
3546394
7092787
14185574
z
751944
1503889
3007778
6015555
12031111
A
630139
1260278
2520556
5041112
10082224
B
506101
1012202
2024405
4048809
8097618
C
356674
713348
1426696
2853391
5706783
D
209987
419973
839947
1679894
3359787
E
60515
121030
242061
484122
968243
(b) when the frequency transform is a discrete sine transform:
7-bit
8-bit
9-bit
10-bit
11-bit
12-bit
13-bit
14-bit
a
58
116
232
464
928
1856
3712
7424
b
110
220
440
880
1760
3520
7040
14081
c
148
295
590
1181
2362
4723
9447
18893
d
168
336
672
1344
2688
5376
10753
21505
e
0
0
0
0
0
0
0
0
15-bit
16-bit
17-bit
18-bit
19-bit
a
14849
29698
59396
118791
237583
b
28162
56323
112647
225294
450588
c
37787
75573
151146
302292
604584
d
43011
86021
172043
344085
688170
e
0
0
0
0
0
20-bit
21-bit
22-bit
23-bit
24-bit
a
475165
950330
1900660
3801320
7602640
b
901175
1802350
3604700
7209400
14418800
c
1209169
2418337
4836675
9673350
19346700
d
1376340
2752680
5505360
11010720
22021440
e
0
0
0
0
0
the method further comprising setting the data precision of the transform matrix to three bits less than a bit depth of the video data values but greater than six bits.
2. The method according to claim 1 , wherein
the coefficient values are equal to the selected values from the respective table.
3. The method according to claim 1 , wherein,
for a discrete cosine transform of an array of N×N values, where N is a power of 2 smaller than 32, the subset M N [x][y] of values is defined by
M N [ x ][ y ]= M 32 [ x ][(2 (5-log 2(N)) ) y ] for x,y= 0 . . . ( N −1).
4. The method according to claim 3 , wherein
N is 4, 8 or 16.
5. A non-transitory computer readable medium including computer program instructions which when executed by a computer cause the computer to perform the method of claim 1 .
6. A data encoding apparatus for encoding an array of video data values, the apparatus comprising:
frequency transform circuitry configured to frequency-transform the video data values according to a frequency transform, to generate an array of frequency-transformed values by a matrix-multiplication process using a transform matrix having a data precision greater than six bits, the transform matrix being matched to an inverse transform that has a data precision of six bits and is used to decode the video data values, the transform matrix having coefficients defined by at least a subset of the following values, wherein each letter indicates a respective coefficient value:
(a) when the frequency transform is a discrete cosine transform:
(b) when the frequency transform is a discrete sine transform:
a
b
c
d
c
c
e
-
c
d
-
a
-
c
b
b
-
d
c
-
a
the coefficient values being selected according to the data precision from values equal to values listed in the following tables:
(a) when the frequency transform is a discrete cosine transform:
7-bit
8-bit
9-bit
10-bit
11-bit
12-bit
13-bit
14-bit
a
128
256
512
1024
2048
4096
8192
16384
b
166
332
665
1329
2658
5317
10633
21266
c
72
144
288
576
1153
2306
4612
9224
d
178
356
713
1426
2852
5703
11407
22813
e
150
301
601
1203
2406
4811
9622
19244
f
100
200
399
798
1596
3192
6385
12769
g
36
71
143
285
570
1141
2282
4563
h
181
361
722
1445
2890
5780
11560
23120
i
172
345
689
1379
2758
5516
11032
22063
j
160
320
639
1278
2556
5113
10225
20450
k
140
281
562
1123
2246
4493
8986
17972
l
114
229
458
915
1830
3660
7321
14642
m
87
174
347
694
1389
2777
5555
11109
n
50
101
201
403
806
1612
3223
6446
o
18
36
72
145
290
579
1158
2316
p
181
361
722
1444
2888
5777
11553
23106
q
179
357
714
1428
2856
5713
11426
22852
r
175
351
701
1403
2806
5611
11222
22445
s
171
341
683
1365
2731
5462
10924
21848
t
164
328
656
1312
2624
5249
10497
20995
u
155
310
619
1238
2476
4952
9905
19810
v
145
291
581
1163
2325
4650
9301
18601
w
134
268
536
1071
2143
4286
8571
17143
x
123
246
491
982
1965
3929
7859
15718
y
108
216
433
866
1732
3463
6927
13853
z
92
184
367
734
1469
2937
5875
11749
A
77
154
308
615
1231
2461
4923
9846
B
62
124
247
494
988
1977
3954
7908
C
44
87
174
348
697
1393
2787
5573
D
26
51
103
205
410
820
1641
3281
E
7
15
30
59
118
236
473
946
15-bit
16-bit
17-bit
18-bit
19-bit
a
32768
65536
131072
262144
524288
b
42532
85065
170129
340259
680517
c
18448
36896
73791
147582
295164
d
45627
91253
182507
365014
730028
e
38489
76977
153954
307909
615817
f
25538
51077
102153
204306
408612
g
9126
18252
36504
73009
146018
h
46240
92479
184958
369917
739833
i
44126
88253
176506
353011
706022
j
40901
81802
163603
327207
654413
k
35944
71887
143775
287550
575099
l
29283
58566
117132
234265
468530
m
22219
44437
88874
177749
355498
n
12892
25784
51569
103137
206275
o
4632
9264
18528
37057
74113
p
46212
92424
184849
369697
739394
q
45704
91407
182815
365630
731260
r
44890
89779
179559
359118
718236
s
43695
87391
174781
349562
699125
t
41990
83979
167959
335918
671836
u
39619
79239
158477
316955
633909
v
37202
74404
148808
297616
595233
w
34285
68570
137140
274281
548561
x
31436
62871
125743
251486
502971
y
27706
55412
110825
221650
443299
z
23498
46997
93993
187986
375972
A
19692
39384
78767
157535
315070
B
15816
31631
63263
126525
253051
C
11146
22292
44584
89168
178337
D
6562
13124
26248
52497
104993
E
1891
3782
7564
15129
30258
20-bit
21-bit
22-bit
23-bit
24-bit
a
1048576
2097152
4194304
8388608
16777216
b
1361035
2722070
5444140
10888280
21776560
c
590328
1180657
2361314
4722627
9445255
d
1460056
2920112
5840224
11680448
23360895
e
1231635
2463269
4926539
9853077
19706155
f
817225
1634450
3268899
6537799
13075597
g
292035
584070
1168141
2336282
4672564
h
1479667
2959333
5918667
11837334
23674667
i
1412045
2824090
5648179
11296358
22592717
j
1308827
2617653
5235307
10470613
20941227
k
1150199
2300397
4600795
9201590
18403179
l
937060
1874119
3748238
7496477
14992954
m
710995
1421991
2843981
5687962
11375925
n
412549
825098
1650196
3300393
6600785
o
148227
296454
592908
1185815
2371630
p
1478788
2957576
5915152
11830305
23660609
q
1462520
2925040
5850080
11700160
23400319
r
1436472
2872944
5745888
11491775
22983550
s
1398249
2796498
5592996
11185992
22371984
t
1343671
2687342
5374684
10749368
21498736
u
1267818
2535636
5071272
10142545
20285089
v
1190466
2380931
4761862
9523724
19047449
w
1097123
2194246
4388491
8776982
17553965
x
1005942
2011884
4023769
8047537
16095074
y
886598
1773197
3546394
7092787
14185574
z
751944
1503889
3007778
6015555
12031111
A
630139
1260278
2520556
5041112
10082224
B
506101
1012202
2024405
4048809
8097618
C
356674
713348
1426696
2853391
5706783
D
209987
419973
839947
1679894
3359787
E
60515
121030
242061
484122
968243
(b) when the frequency transform is a discrete sine transform:
7-bit
8-bit
9-bit
10-bit
11-bit
12-bit
13-bit
14-bit
a
58
116
232
464
928
1856
3712
7424
b
110
220
440
880
1760
3520
7040
14081
c
148
295
590
1181
2362
4723
9447
18893
d
168
336
672
1344
2688
5376
10753
21505
e
0
0
0
0
0
0
0
0
15-bit
16-bit
17-bit
18-bit
19-bit
a
14849
29698
59396
118791
237583
b
28162
56323
112647
225294
450588
c
37787
75573
151146
302292
604584
d
43011
86021
172043
344085
688170
e
0
0
0
0
0
20-bit
21-bit
22-bit
23-bit
24-bit
a
475165
950330
1900660
3801320
7602640
b
901175
1802350
3604700
7209400
14418800
c
1209169
2418337
4836675
9673350
19346700
d
1376340
2752680
5505360
11010720
22021440
e
0
0
0
0
0
the frequency transform circuitry further configured to set the data precision of the transform matrix to three bits less than a bit depth of the video data values but greater than six bits.
7. The apparatus according to claim 6 , wherein
the coefficient values are equal to the selected values from the respective table.
8. The apparatus according to claim 6 , wherein,
for a discrete cosine transform of an array of N×N values, where N is a power of 2 smaller than 32, the subset M N [x][y] of values is defined by:
M N [ x ][ y ]= M 32 [ x ][(2 (5-log 2(N)) ) y ] for x,y= 0 . . . ( N −1).
9. The apparatus according to claim 8 , wherein
N is 4, 8 or 16.
10. A video data capture, transmission, display or storage apparatus comprising the apparatus according to claim 6 .
11. A video data decoding method for decoding an array of video data values, the decoding method comprising:
using an inverse transform that has a data precision of six bits to decode the array of video data values, wherein
the array of video data values have been encoded by:
frequency-transforming video data values according to a frequency transform; and
generating an array of frequency-transformed values by a matrix-multiplication process using a transform matrix having a data precision greater than six bits, the transform matrix being matched to the inverse transform having the data precision of six bits that is used to decode the video data values, the transform matrix having coefficients defined by at least a subset of the following values, wherein each letter indicates a respective coefficient value:
(a) when the frequency transform is a discrete cosine transform:
(b) when the frequency transform is a discrete sine transform:
[
a
c
d
b
b
c
-
a
-
d
c
e
-
c
c
d
-
c
b
-
a
]
the coefficient values being selected according to the data precision from values equal to values listed in the following tables:
(a) when the frequency transform is a discrete cosine transform:
7-bit
8-bit
9-bit
10-bit
11-bit
12-bit
13-bit
14-bit
a
128
256
512
1024
2048
4096
8192
16384
b
166
332
665
1329
2658
5317
10633
21266
c
72
144
288
576
1153
2306
4612
9224
d
178
356
713
1426
2852
5703
11407
22813
e
150
301
601
1203
2406
4811
9622
19244
f
100
200
399
798
1596
3192
6385
12769
g
36
71
143
285
570
1141
2282
4563
h
181
361
722
1445
2890
5780
11560
23120
i
172
345
689
1379
2758
5516
11032
22063
j
160
320
639
1278
2556
5113
10225
20450
k
140
281
562
1123
2246
4493
8986
17972
1
114
229
458
915
1830
3660
7321
14642
m
87
174
347
694
1389
2777
5555
11109
n
50
101
201
403
806
1612
3223
6446
o
18
36
72
145
290
579
1158
2316
p
181
361
722
1444
2888
5777
11553
23106
q
179
357
714
1428
2856
5713
11426
22852
r
175
351
701
1403
2806
5611
11222
22445
s
171
341
683
1365
2731
5462
10924
21848
t
164
328
656
1312
2624
5249
10497
20995
u
155
310
619
1238
2476
4952
9905
19810
v
145
291
581
1163
2325
4650
9301
18601
w
134
268
536
1071
2143
4286
8571
17143
x
123
246
491
982
1965
3929
7859
15718
y
108
216
433
866
1732
3463
6927
13853
z
92
184
367
734
1469
2937
5875
11749
A
77
154
308
615
1231
2461
4923
9846
B
62
124
247
494
988
1977
3954
7908
C
44
87
174
348
697
1393
2787
5573
D
26
51
103
205
410
820
1641
3281
E
7
15
30
59
118
236
473
946
15-bit
16-bit
17-bit
18-bit
19-bit
a
32768
65536
131072
262144
524288
b
42532
85065
170129
340259
680517
c
18448
36896
73791
147582
295164
d
45627
91253
182507
365014
730028
e
38489
76977
153954
307909
615817
f
25538
51077
102153
204306
408612
g
9126
18252
36504
73009
146018
h
46240
92479
184958
369917
739833
i
44126
88253
176506
353011
706022
j
40901
81802
163603
327207
654413
k
35944
71887
143775
287550
575099
1
29283
58566
117132
234265
468530
m
22219
44437
88874
177749
355498
n
12892
25784
51569
103137
206275
o
4632
9264
18528
37057
74113
p
46212
92424
184849
369697
739394
q
45704
91407
182815
365630
731260
r
44890
89779
179559
359118
718236
s
43695
87391
174781
349562
699125
t
41990
83979
167959
335918
671836
u
39619
79239
158477
316955
633909
v
37202
74404
148808
297616
595233
w
34285
68570
137140
274281
548561
x
31436
62871
125743
251486
502971
y
27706
55412
110825
221650
443299
z
23498
46997
93993
187986
375972
A
19692
39384
78767
157535
315070
B
15816
31631
63263
126525
253051
C
11146
22292
44584
89168
178337
D
6562
13124
26248
52497
104993
E
1891
3782
7564
15129
30258
20-bit
21-bit
22-bit
23-bit
24-bit
a
1048576
2097152
4194304
8388608
16777216
b
1361035
2722070
5444140
10888280
21776560
c
590328
1180657
2361314
4722627
9445255
d
1460056
2920112
5840224
11680448
23360895
e
1231635
2463269
4926539
9853077
19706155
f
817225
1634450
3268899
6537799
13075597
g
292035
584070
1168141
2336282
4672564
h
1479667
2959333
5918667
11837334
23674667
i
1412045
2824090
5648179
11296358
22592717
j
1308827
2617653
5235307
10470613
20941227
k
1150199
2300397
4600795
9201590
18403179
l
937060
1874119
3748238
7496477
14992954
m
710995
1421991
2843981
5687962
11375925
n
412549
825098
1650196
3300393
6600785
o
148227
296454
592908
1185815
2371630
p
1478788
2957576
5915152
11830305
23660609
q
1462520
2925040
5850080
11700160
23400319
r
1436472
2872944
5745888
11491775
22983550
s
1398249
2796498
5592996
11185992
22371984
t
1343671
2687342
5374684
10749368
21498736
u
1267818
2535636
5071272
10142545
20285089
v
1190466
2380931
4761862
9523724
19047449
w
1097123
2194246
4388491
8776982
17553965
x
1005942
2011884
4023769
8047537
16095074
y
886598
1773197
3546394
7092787
14185574
z
751944
1503889
3007778
6015555
12031111
A
630139
1260278
2520556
5041112
10082224
B
506101
1012202
2024405
4048809
8097618
C
356674
713348
1426696
2853391
5706783
D
209987
419973
839947
1679894
3359787
E
60515
121030
242061
484122
968243
(b) when the frequency transform is a discrete sine transform:
7-bit
8-bit
9-bit
10-bit
11-bit
12-bit
13-bit
14-bit
a
58
116
232
464
928
1856
3712
7424
b
110
220
440
880
1760
3520
7040
14081
c
148
295
590
1181
2362
4723
9447
18893
d
168
336
672
1344
2688
5376
10753
21505
e
0
0
0
0
0
0
0
0
15-bit
16-bit
17-bit
18-bit
19-bit
a
14849
29698
59396
118791
237583
b
28162
56323
112647
225294
450588
c
37787
75573
151146
302292
604584
d
43011
86021
172043
344085
688170
e
0
0
0
0
0
20-bit
21-bit
22-bit
23-bit
24-bit
a
475165
950330
1900660
3801320
7602640
b
901175
1802350
3604700
7209400
14418800
c
1209169
2418337
4836675
9673350
19346700
d
1376340
2752680
5505360
11010720
22021440
e
0
0
0
0
0
wherein the selecting further comprising setting the data precision of the transform matrix to three bits less than a bit depth of the video data values but greater than six bits.