The Art of Error Correcting Coding phần 1 ppsx
The Art of Error Correcting Coding phần 1 ppsx
... standard array of the binary linear (4, 2, 2) code is the following:
¯s 00 01 10 11
00 0000 011 0 10 11 110 1
11 10 00 11 10 0 011 010 1
10 010 0 0 010 11 11 10 01
01 00 01 011 1 10 10 11 00
Decoding with the standard ... =
11 1
and parity-check matrix
H =
11 0
10 1
.
Accordingly, its standard array is the following:
¯s 01
00 000 11 1
11 10 0 011
10 0...
The Art of Error Correcting Coding phần 2 pps
... generator matrix for RM (1, 3) is thus given by
G (1, 3) =
¯
1
¯x
1
¯x
2
¯x
3
=
11 111 111
000 011 11
0 011 0 011
010 1 010 1
. (2.5)
Note that code RM (1, 3) can be also obtained ... constructed from Boolean functions of degree up to one in three variables:
{1, x
1
,x
2
,x
3
}, so that
¯
1 = 11 111 111
¯x
1
= 000 011 11
¯x
2
= 0 011 0 011...
The Art of Error Correcting Coding phần 3 doc
... 0000
1 00 01
α 0 010
α
2
010 0
α
3
10 00
α
4
0 011
α
5
011 0
α
6
11 00
α
7
10 11
α
8
010 1
α
9
10 10
α
10
011 1
α
11
11 10
α
12
11 11
α
13
11 01
α
14
10 01
68 BINARY CYCLIC CODES AND BCH CODES
1e -12
1e -10
1e-08
1e-06
1e-04
1e-02
1e+00
10 ... also Example 3 .1. 5),
H =
11 111 111
011 1 010 0
0 011 1 010
00 011 1 01
.
It can be easily verified...
The Art of Error Correcting Coding phần 4 docx
... encoder.
00
01
10
11
11
00
10
01
00
11
10
01
00
01
10
11
00
01
10
11
00
01
10
11
00
01
10
11
00
01
10
11
00
01
10
11
11 01 00 10 11 01
Figure 5.5 A path in the trellis of a memory-2 rate -1/ 2 convolutional ... x
3
+ 1.
Power Vector
0 0000
1 00 01
α 0 010
α
2
010 0
α
3
10 00
α
4
10 01
α
5
10 11
α
6
11 11
α
7
011 1
α
8
11 10
α
9
01...
The Art of Error Correcting Coding phần 5 docx
... = 10 ¯u = 01 ¯u = 11
000 00000 10 110 010 11 111 01
110 10 000 0 011 0
11 011 011 01
011 010 00 11 110 00 011
10 1 01
100 0 010 0 10 010
011 11 110 01
010 00 010 10 100
010 01 111 11
0 01 000 01 1 011 1 010 10
11 100
10 1 ... d
f
1/ 2
1
1
v
(0)
i
,v
(1)
i
10
2/3
10
11
v
(0)
i
,v
(1)
i
,v
(1)
i +1
6
3/4
10 1
11 0
v
(0)
i
,v
(1)
i
,v
(1)...
The Art of Error Correcting Coding phần 6 pot
... (10 ,11 ,00)
y = (11 , 01, 01)
y = (10 ,11 ,11 )
y = (11 ,11 , 01)
3
3
3
3
00
01
10
11
00
01
10
11
00
01
10
11
00
01
10
11
00
01
10
11
00
01
10
11
00
11
00
10
01
10
00
01
10
11
1 1 +1 1 +1 1 +1 +1 1 ... (11 ,11 , 01, 10 ,10 ,10 )
00
01
10
11
00
01
10
11
00
01
10
11
00
01
10
11
00
01
10
11
00
01
10
11
00
11
00
10
01
10...
The Art of Error Correcting Coding phần 7 ppt
... 00
10
00
10
11
01
00
10
11
01
00
10
11
01
00
01
00
5
+5
2
+2
+1
+1
1
+5
5
5
+5
6
6
+6
0
0
0
0
+4
41+ 60
+6
6
2
+20
+26
0
+ 21
+14
+19
5
+13
+5
+3
9
+3
+5
+9
1
+7
+4
+4
+12
2
+2
2
+4
+10
2
+4
2
+18
+8
4
+4
+10
2
+2
+24
0
+26
4 ,1 1,3 +2,3 +3,+3 3,+3 3, +1
1 ,1 +1, 1 +1, 1 +1, +1 1, +1 1 ,1
Received
Figure 7 .11 Trellis ... at the input is sent to...
The Art of Error Correcting Coding phần 8 pptx
... 0000
0000 11 11 0000 0000 0000
0000 0000 11 11 0000 0000
0000 0000 0000 11 11 0000
0000 0000 0000 0000 11 11
1000 10 00 10 00 10 00 0000
010 0 010 0 010 0 0000 10 00
0 010 0 010 0000 010 0 010 0
00 01 0000 0 010 0 010 ... C
SC
is
G
SC
=
11
¯
0
12
¯
0
12
11
10 00
0 010
010 0
00 01
10 1
011
¯
0
23
¯
0
23
10 1
011
...
The Art of Error Correcting Coding phần 9 potx
... 213
11 11 11
00
01
10
11
00
01
10
000
10 0
011
11 1
000
10 0
011
11 1
010
11 0
0 01
1 01
0 01 1 01
010
11 0
00
01
10
000
10 0
011
11 1
000
10 0
011
11 1
010
11 0
0 01
1 01
0 01 1 01
010
11 0
00
01
10
000
10 0
011
11 1
000
10 0
011
11 1
010
11 0
0 01
1 01
0 01 ... MODULATION 217
x
y
0 011 011 1
11 11
1 011
0 010 011 0
11 10
10 10
00 010...
The Art of Error Correcting Coding phần 10 potx
... 10 7339 513 152943 011 744 918 412 82048
64 11 420796 414 34358842 413 615 8689350
wd .12 8 .11 3.006
6 3 413 76
8 87288624
10 13 842455424
12 14 4 818 0487936
14 10 614 1978256640
16 5697 211 389035256
18 2 314 62 916 338 818 304
20 ... 17 58650583498 215 85 715 411 392357 912 576
64 18 711 832845256 314 92099 910 44344449600
wd .12 8 .12 7.002
2 812 8
4 10 668000
6 5423 611 200...