Cryptography Reference
In-Depth Information
The distribution
f
s
is not Gaussian. It is therefore necessary to use a digital
calculation tool to determine it, which is the great drawback of this method.
If we view the MI of output IS as a function of IA and of the signal to noise
ratio
E
b
/N
0
, the transfer function of the extrinsic information is defined by:
IE
=
T
(
IA,E
b
/N
0
)
(7.63)
d. Practical method to obtain the transfer function of the extrinsic informa-
tion
Figure 7.26 shows the path taken to establish the transfer characteristic of
the extrinsic information of a SISO decoder.
•
step 1: Generation of the pseudo random message
d
to be transmitted; at
least 10000 bits are necessary for the statistical properties to be represen-
tative.
•
step 2: Encoding the data with rate
R
then 2-PSK modulation of the
signal; the systematic and redundancy data both belong to the alphabet
{-1,+1}.
•
step 3: Application of a Gaussian noise with signal to noise ratio
E
b
/N
0
(indB),withvariance
1
2
·
E
b
/
N
0
10
−
0
,
1
×
σ
=
R
•
step 4: Application to the data transmitted (stored in a file) of normal
law
N
(
μ
z
,σ
z
)
corresponding to the mutual information IA desired (see
Figure 7.25) to obtain the distribution of
a priori
extrinsic information.
•
step 5: Initialization of the SISO decoder with the
a priori
LLRs (it might
be necessary, depending on the decoding algorithm chosen, to transform
the LLRs into probabilities).
•
step 6: Recovering the LLRs at the output of the SISO decoder (corre-
sponding to one half-iteration of the decoding process), in a file.
•
step 7: Utilization of digital calculation software to evaluate IS (relation
(7.62)).
•
Trace the histograms of the LLR distributions output as a function
of the bit transmitted (hence the necessity to store this information
in two files).
•
Evaluate the integral by the trapeze method.
