Cryptography Reference
In-Depth Information
Figure 7.24 - Measured and estimated PER (UB) of the DVB-RCS turbo code for
the transmission of MPEG (188 bytes) blocks with coding rates
2
/
3
and
4
/
5
.4-PSK
modulation and Gaussian channel.
cable to any linear code, for any blocksize and any coding rate, and it requires
only a few seconds to a few minutes calculation on an ordinary computer, the
calculation time being a linear function of the blocksize or of its period
P
.
When the decoding is not maximum likelihood, this method is no longer rig-
orous and produces only an estimation of the minimum distance. In addition,
the multiplicity of the codewords at distance
d
min
is not provided and Equa-
tion (7.57) cannot be applied without particular hypotheses about the prop-
erties of the code. In the case of turbo codes, two realistic hypotheses can be
formulated to estimate multiplicity: a single codeword at distance
A
i
has its
i
-th
information bit at 1 (unicity), and the
A
i
values corresponding to all positions
i
come from distinct codewords (non-overlapping).
An estimation of the PER is then given by:
erfc
(
RA
i
kâ
1
1
2
E
b
N
0
)
PER
â
(7.58)
i
=0
The first hypothesis (unicity) under-evaluates the value of the error rate, unlike
the second (non-overlapping) that over-evaluates it and, overall, the two effects
compensate each other. As an example, Figure 7.24 compares the measured per-
formance of the DVB-RCS turbo code, for two coding rates, with their estimate