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7.3.2Component code
The component code Cp is based on punctured convolutional coding with a mother code of rate 1/6 and constraint
length 7. The mother convolutional encoder generates from the vector (x p,i )iM=0p −1 = (ai )iI=−01 a codeword {(b0,i ,b1,i ,b2,i ,b3,i ,b4,i ,b5,i )}iI=+05 . This codeword is defined by:
b0,i = ai ai− 2 ai−3 ai−5 ai−6 ; b1,i = ai ai−1 ai− 2 ai−3 ai−6 ; b2,i = ai ai−1 ai− 4 ai−6 ;
b3,i = ai ai− 2 ai−3 ai−5 ai−6 ; b4,i = ai ai−1 ai− 2 ai−3 ai−6 ; b5,i = ai ai−1 ai− 4 ai−6 ;
for i = 0, 1, 2, to I + 5.
When i does not belong to the set {0, 1, 2, to I-1}, ai is equal to zero by definition.
The encoding can be achieved using the convolutional encoder presented in figure 25.
ai
1 Bit |
1 Bit |
1 Bit |
1 Bit |
1 Bit |
1 Bit |
delay |
delay |
delay |
delay |
delay |
delay |
b0,i
b1,i
b2,i
b3,i
b4,i
b5,i
Figure 25: Convolutional encoder
The octal forms of the generator polynomials are 133, 171, 145, 133, 171 and 145, respectively.
The vector (a−6 , a−5 , a−4 , a−3, a−2 , a−1) corresponds to the all-zero initial state of the shift register and the vector (aI , aI +1, aI +2 , aI +3, aI +4 , aI +5 ) corresponds to the all-zero final state of the shift register.
In addition to the mother code the system shall allow punctured rates. Table 27 shows the puncturing patterns.
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Table 27: Puncturing patterns |
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Code rates Rp |
Numerator RXp |
Denominator RYp |
Puncturing pattern |
Transmitted sequence |
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1/6 |
1 |
6 |
B0: 1 |
b0,0 b1,0 b2,0 b3,0 b4,0 b5,0 etc. |
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B1: 1 |
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B2: 1 |
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B3: 1 |
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B4: 1 |
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B5: 1 |
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1/4 |
1 |
4 |
B0: 1 |
b0,0 b1,0 b2,0 b3,0 etc. |
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B1: 1 |
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B2: 1 |
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B3: 1 |
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B4: 0 |
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B5: 0 |
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3/10 |
3 |
10 |
B0: 1 1 1 |
b0,0 b1,0 b2,0 b3,0 b0,1 b1,1 b2,1 |
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B1: 1 1 1 |
b0,2 b1,2 b2,2 etc. |
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B2: 1 1 1 |
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B3: 1 0 0 |
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B4: 0 0 0 |
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B5: 0 0 0 |
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1/3 |
1 |
3 |
B0: 1 |
b0,0 b1,0 b2,0 etc. |
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B1: 1 |
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B2: 1 |
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B3: 0 |
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B4: 0 |
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B5: 0 |
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4/11 |
4 |
11 |
B0: 1 1 1 1 |
b0,0 b1,0 b2,0 b0,1 b1,1 b2,1 b0,2 |
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B1: 1 1 1 1 |
b1,2 b2,2 b0,3 b1,3 etc. |
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B2: 1 1 1 0 |
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B3: 0 0 0 0 |
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B4: 0 0 0 0 |
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B5: 0 0 0 0 |
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2/5 |
2 |
5 |
B0: 1 1 |
b0,0 b1,0 b2,0 b0,1 b1,1 etc. |
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B1: 1 1 |
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B2: 1 0 |
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B3: 0 0 |
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B4: 0 0 |
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B5: 0 0 |
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1/2 |
1 |
2 |
B0: 1 |
b0,0 b1,0 etc. |
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B1: 1 |
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B2: 0 |
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B3: 0 |
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B4: 0 |
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B5: 0 |
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4/7 |
4 |
7 |
B0: 1 1 1 1 |
b0,0 b1,0 b0,1 b2,1 b0,2 b1,2 b0,3 |
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B1: 1 0 1 0 |
etc. |
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B2: 0 1 0 0 |
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B3: 0 0 0 0 |
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B4: 0 0 0 0 |
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B5: 0 0 0 0 |
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Code rates Rp |
Numerator RXp |
Denominator RYp |
Puncturing pattern |
Transmitted sequence |
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3/5 |
3 |
5 |
B0: 1 1 1 |
b0,0 b1,0 b0,1 b0,2 b1,2 etc. |
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B1: 1 0 1 |
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B2: 0 0 0 |
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B3: 0 0 0 |
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B4: 0 0 0 |
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B5: 0 0 0 |
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2/3 |
2 |
3 |
B0: 1 1 |
b0,0 b1,0 b0,1 etc. |
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B1: 1 0 |
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B2: 0 0 |
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B3: 0 0 |
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B4: 0 0 |
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B5: 0 0 |
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8/11 |
8 |
11 |
B0: 1 1 1 1 1 1 1 1 |
b0,0 b1,0 b0,1 b0,2 b0,3 b1,3 b0,4 |
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B1: 1 0 0 1 0 0 1 0 |
b0,5 b0,6 b1,6 b0,7 etc. |
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B2: 0 0 0 0 0 0 0 0 |
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B3: 0 0 0 0 0 0 0 0 |
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B4: 0 0 0 0 0 0 0 0 |
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B5: 0 0 0 0 0 0 0 0 |
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3/4 |
3 |
4 |
B0: 1 1 1 |
b0,0 b1,0 b0,1 b0,2 etc. |
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B1: 1 0 0 |
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B2: 0 0 0 |
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B3: 0 0 0 |
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B4: 0 0 0 |
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B5: 0 0 0 |
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4/5 |
4 |
5 |
B0: 1 1 1 1 |
b0,0 b1,0 b0,1 b0,2 b0,3 b0,4 etc. |
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B1: 1 0 0 0 |
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B2: 0 0 0 0 |
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B3: 0 0 0 0 |
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B4: 0 0 0 0 |
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B5: 0 0 0 0 |
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7/8 |
7 |
8 |
B0: 1 1 1 1 1 1 1 |
b0,0 b1,0 b0,1 b0,2 b0,3 b0,4 b0,5 |
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B1: 1 0 0 0 0 0 0 |
b0,6 etc. |
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B2: 0 0 0 0 0 0 0 |
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B3: 0 0 0 0 0 0 0 |
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B4: 0 0 0 0 0 0 0 |
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B5: 0 0 0 0 0 0 0 |
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8/9 |
8 |
9 |
B0: 1 1 1 1 1 1 1 1 |
b0,0 b1,0 b0,1 b0,2 b0,3 b0,4 b0,5 |
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B1: 1 0 0 0 0 0 0 0 |
b0,6 b0,7 etc. |
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B2: 0 0 0 0 0 0 0 0 |
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B3: 0 0 0 0 0 0 0 0 |
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B4: 0 0 0 0 0 0 0 0 |
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B5: 0 0 0 0 0 0 0 0 |
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For the FAC, all bits are punctured according to table 27. For the MSC and the SDC, the last 36 bits (the tailbits) of the serial mother codeword shall be punctured as follows. The index rp shall be used with table 27 to find the puncturing vector for the tailbits for each level. This index is calculated with the following formula:
SM:
rp = (2N2 |
− 12)− RYp |
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2N2 − 12 |
for p {0,1,2} |
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HMsym: |
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2(N1 + N 2 )− 12 |
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r0 = (2(N1 + N 2 )− 12)− RY0 |
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RY0 |
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rp = (2N2 |
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2N2 −12 |
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RYp |
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HMmix: |
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r Re = (N |
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−12)− RY Re |
N1 + N2 −12 |
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RY Re |
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rpRe = (N2 −12)− RYpRe |
N2 −12 |
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RYp |
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rpIm = (N2 −12)− RYpIm |
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RYp |
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Table 28: Puncturing patterns of the tailbits
rp |
Puncturing pattern |
Transmitted sequence |
0 |
B0: 1 1 1 1 1 1 |
b0,0 b1,0 b0,1 b1,1 b0,2 b1,2 b0,3 b1,3 b0,4 b1,4 b0,5 b1,5, etc. |
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B1: 1 1 1 1 1 1 |
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B2: 0 0 0 0 0 0 |
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B3: 0 0 0 0 0 0 |
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B4: 0 0 0 0 0 0 |
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B5: 0 0 0 0 0 0 |
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1 |
B0: 1 1 1 1 1 1 |
b0,0 b1,0 b2,0 b0,1 b1,1 b0,2 b1,2 b0,3 b1,3 b0,4 b1,4 b0,5 b1,5, etc. |
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B1: 1 1 1 1 1 1 |
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B2: 1 0 0 0 0 0 |
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B3: 0 0 0 0 0 0 |
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B4: 0 0 0 0 0 0 |
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B5: 0 0 0 0 0 0 |
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B0: 1 1 1 1 1 1 |
b0,0 b1,0 b2,0 b0,1 b1,1 b0,2 b1,2 b0,3 b1,3 b2,3 b0,4 b1,4 b0,5 b1,5, |
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B1: 1 1 1 1 1 1 |
etc. |
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B2: 1 0 0 1 0 0 |
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B3: 0 0 0 0 0 0 |
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B4: 0 0 0 0 0 0 |
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B5: 0 0 0 0 0 0 |
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B0: 1 1 1 1 1 1 |
b0,0 b1,0 b2,0 b0,1 b1,1 b2,1 b0,2 b1,2 b0,3 b1,3 b2,3 b0,4 b1,4 b0,5 |
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B1: 1 1 1 1 1 1 |
b1,5, etc. |
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B2: 1 1 0 1 0 0 |
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B3: 0 0 0 0 0 0 |
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B4: 0 0 0 0 0 0 |
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B5: 0 0 0 0 0 0 |
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B0: 1 1 1 1 1 1 |
b0,0 b1,0 b2,0 b0,1 b1,1 b2,1 b0,2 b1,2 b0,3 b1,3 b2,3 b0,4 b1,4 b2,4 |
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B1: 1 1 1 1 1 1 |
b0,5 b1,5, etc. |
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B2: 1 1 0 1 1 0 |
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B3: 0 0 0 0 0 0 |
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B4: 0 0 0 0 0 0 |
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B5: 0 0 0 0 0 0 |
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rp |
Puncturing pattern |
Transmitted sequence |
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5 |
B0: 1 1 1 1 1 1 |
b0,0 b1,0 b2,0 b0,1 b1,1 b2,1 b0,2 b1,2 b2,2 b0,3 b1,3 b2,3 b0,4 b1,4 |
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B1: 1 1 1 1 1 1 |
b2,4 b0,5 b1,5, etc. |
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B2: 1 1 1 1 1 0 |
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B3: 0 0 0 0 0 0 |
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B4: 0 0 0 0 0 0 |
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B5: 0 0 0 0 0 0 |
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B0: 1 1 1 1 1 1 |
b0,0 b1,0 b2,0 b0,1 b1,1 b2,1 b0,2 b1,2 b2,2 b0,3 b1,3 b2,3 b0,4 b1,4 |
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B1: 1 1 1 1 1 1 |
b2,4 b0,5 b1,5 b2,5, etc. |
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B2: 1 1 1 1 1 1 |
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B3: 0 0 0 0 0 0 |
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B4: 0 0 0 0 0 0 |
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B5: 0 0 0 0 0 0 |
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B0: 1 1 1 1 1 1 |
b0,0 b1,0 b2,0 b3,0 b0,1 b1,1 b2,1 b0,2 b1,2 b2,2 b0,3 b1,3 b2,3 b0,4 |
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B1: 1 1 1 1 1 1 |
b1,4 b2,4 b0,5 b1,5 b2,5, etc. |
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B2: 1 1 1 1 1 1 |
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B3: 1 0 0 0 0 0 |
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B4: 0 0 0 0 0 0 |
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B5: 0 0 0 0 0 0 |
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B0: 1 1 1 1 1 1 |
b0,0 b1,0 b2,0 b3,0 b0,1 b1,1 b2,1 b0,2 b1,2 b2,2 b0,3 b1,3 b2,3 b3,3 |
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B1: 1 1 1 1 1 1 |
b0,4 b1,4 b2,4 b0,5 b1,5 b2,5, etc. |
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B2: 1 1 1 1 1 1 |
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B3: 1 0 0 1 0 0 |
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B4: 0 0 0 0 0 0 |
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B5: 0 0 0 0 0 0 |
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B0: 1 1 1 1 1 1 |
b0,0 b1,0 b2,0 b3,0 b0,1 b1,1 b2,1 b3,1 b0,2 b1,2 b2,2 b0,3 b1,3 b2,3 |
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B1: 1 1 1 1 1 1 |
b3,3 b0,4 b1,4 b2,4 b0,5 b1,5 b2,5, etc. |
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B2: 1 1 1 1 1 1 |
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B3: 1 1 0 1 0 0 |
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B4: 0 0 0 0 0 0 |
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B5: 0 0 0 0 0 0 |
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10 |
B0: 1 1 1 1 1 1 |
b0,0 b1,0 b2,0 b3,0 b0,1 b1,1 b2,1 b3,1 b0,2 b1,2 b2,2 b0,3 b1,3 b2,3 |
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B1: 1 1 1 1 1 1 |
b3,3 b0,4 b1,4 b2,4 b0,5 b1,5 b2,5, b3,5, etc. |
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B2: 1 1 1 1 1 1 |
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B3: 1 1 0 1 0 1 |
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B4: 0 0 0 0 0 0 |
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B5: 0 0 0 0 0 0 |
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B0: 1 1 1 1 1 1 |
b0,0 b1,0 b2,0 b3,0 b0,1 b1,1 b2,1 b3,1 b0,2 b1,2 b2,2, b3,2, b0,3 |
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B1: 1 1 1 1 1 1 |
b1,3 b2,3 b3,3 b0,4 b1,4 b2,4 b0,5 b1,5 b2,5, b3,5, etc. |
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B2: 1 1 1 1 1 1 |
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B3: 1 1 1 1 0 1 |
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B4: 0 0 0 0 0 0 |
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B5: 0 0 0 0 0 0 |
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The puncturing shall be performed as follows:
SM:
The higher protected part of the transmitted sequence is punctured according to table 27 resulting in:
(vp,0 Kvp,2N1−1).
ETSI
102 ETSI ES 201 980 V4.1.2 (2017-04)
The lower protected part of the transmitted sequence is punctured according to table 27 resulting in: v p,2N1 Kv p,2(N1+ N2 )−13−rp .
The tailbits of the transmitted sequence are punctured according to table 28 resulting in: vp,2(N1+ N2 )−12−rp Kvp,2(N1+ N2 )−1 .
NOTE 1: If there is only one protection level the higher protected part is absent.
HMsym:
The VSPP part of the transmitted sequence is punctured according to table 27 resulting in: (v0,0 Kv0,2(N1+ N2 )−13−r0 ).
The tailbits for the VSPP part of the transmitted sequence are punctured according to table 28 resulting in:
(v0,2(N1+ N2 )−12−r0 Kv0,2(N1+ N2 )−1).
The higher protected part of the SPP part of the transmitted sequence is punctured according to table 27 resulting in:
(v p,0 Kv for p {1,2}.
The lower protected part of the SPP part of the transmitted sequence is punctured according to table 27 resulting in:
v p,2N1 Kv p,2(N1+ N2 )−13−rp for p {1,2}.
The tailbits for the SPP part of the transmitted sequence is punctured according to table 28 resulting in:
vp,2(N + N |
2 |
)−12−r |
p |
Kv p,2(N + N |
2 |
)−1 |
for Y ( p) = (y p,0 |
, y p,1, y p,2 |
,...y p,2(N + N |
2 |
)−1). |
1 |
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NOTE 2: If there is only one protection level the higher protected part is absent.
HMmix:
The VSPP part of the transmitted sequence is punctured according to table 27 resulting in:
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Re |
Kv |
Re |
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v |
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0,2(N1+ N2 )−13− r0 |
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0,0 |
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The tailbits for the VSPP part of the transmitted sequence are punctured according to table 28 resulting in:
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Re |
Kv |
Re |
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v |
0,2( N1+ N2 )−12− r0 |
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0,2( N1 + N2 )−1 |
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The real component of the higher protected part of the SPP part of the transmitted sequence is punctured according to table 27 resulting in:
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Re |
Kv |
Re |
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v |
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for Xin = 2N2 . |
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p,0 |
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p,2N1−1 |
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The real component of the lower protected part of the SPP part of the transmitted sequence is punctured according to table 27 resulting in:
vRe |
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KvRe |
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for |
p {1,2}. |
p,2N |
1 |
p,2(N1+ N2 )−13−rp |
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ETSI