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
k− 1
1
2
E b
N 0 )
PER
≈
(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
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