Cryptography Reference
In-Depth Information
algorithm, are all different from each other:
C
i
s
i
M
(0,1,1,1)
(0,1,1,1,0,0,0)
-2.7
(0,1,1,0)
(0,1,1,0,1,1,0)
-2.7+1.0+0.2=-1.5
(0,1,0,1)
(0,1,0,1,0,1,1)
-2.7+1.2-0.6=-2.1
(0,0,1,1)
(0,0,1,1,1,0,1)
-2.7+1.4+0.2=-1.1
(1,1,1,1)
(1,1,1,1,1,1,1)
-2.7+1.8+0.0=-0.9
(0,1,0,0)
(0,1,0,0,1,0,1)
-2.7+2.2+0.2=-0.3
(0,0,1,0)
(0,0,1,0,0,1,1)
-2.7+2.4-0.6=-0.9
(0,0,0,1)
(0,0,0,1,1,1,0)
-2.7+2.6+0.2=0.1
(1,1,1,0)
(1,1,1,0,0,0,1)
-2.7+2.8-0.2=-0.1
(1,1,0,1)
(1,1,0,1,1,0,0)
-2.7+3.0+0.6=0.9
(1,0,1,1)
(1,0,1,1,0,1,0)
-2.7+3.2-0.2=0.3
(0,0,0,0)
(0,0,0,0,0,0,0)
-2.7+3.6+0.0=0.9
(1,1,0,0)
(1,1,0,0,0,1,0)
-2.7+4.0-0.2=1.1
(1,0,1,0)
(1,0,1,0,1,0,0)
-2.7+4.2+0.6=2.1
(1,0,0,1)
(1,0,0,1,0,0,1)
-2.7+4.4-0.2=1.5
(1,0,0,0)
(1,0,0,0,1,1,1)
-2.7+5.4+0.0=2.7
•
Step 5:
j
F
P
(
j
)
1
((-0.9)-(-2.7))/4=0.475
2
((-1.1)-(-2.7))/4=0.4
3
((-2.1)-(-2.7))/4=0.15
4
((-1.5)-(-2.7))/4=0.3
5
((-1.5)-(-2.7))/4=0.3
6
((-1.5)-(-2.7))/4=0.3
7
((-2.1)-(-2.7))/4=0.15
J
E
J
1
0.3-0.5=-0.2
2
0.4-0.7=-0.3
3
-0.475-(-0.9)=0.525
4
-0.3-0.2=-0.5
5
-0.3-(-0.3)=0.0
6
-0.15-0.1=-0.25
7
0.15-0.6=-0.4
The Fang-Battail algorithm is theoretically maximum likelihood. However,
that will not necessarily suce for the algorithm applied for decoding product
codes to be maximum likelihood itself.
