Cryptography Reference
In-Depth Information
schemes. As an example, at a binary error rate of
10
−
4
, we observe a gap of
0.9 dB for a coding rate
R
=1
/
2
, and 0.2 dB for
R
=3
/
4
.
Figure 10.14 - Performance in binary error rate (BER) and packet error rate (PER) of
the pragmatic association of a 16-QAM and a 16-state double-binary turbo code, for
the transmission of blocks of 54 bytes over a Gaussian channel. Coding rates 1/2 and
3/4. Max-Log-MAP decoding, inputs of the decoder quantized on 6 bits, 8 decoding
iterations.
For low and very low error rates, the scheme favouring the protection of the
redundancy gives the best performance. This behaviour is dicult to prove by
simulation for the lowest rates, as the assumed crossing point of the curves is
situated at an error rate that is dicult to obtain by simulation (
PER
10
−
8
for
R
=1
/
2
). The interpretation of this result requires analysis of the erroneous
paths in trellises with a high signal to noise ratio. We have observed that, in
the majority of cases, the erroneous sequences contain a fairly low number of
erroneous systematic bits and a rather high number of erroneous redundancy
bits. In other words, the erroneous sequences generally have a low input weight.
In particular, the erroneous paths in question mainly correspond to rectangular
patterns of errors (see Section 7.3.2). The result, from the point of view of
the asymptotic behaviour of turbo coded modulation, is that it is preferable to
ensure better protection of the parity bits.
The curves shown in Figure 10.14 were obtained with the help of the simpli-
fied Max-Log-MAP decoding algorithm, using data quantized on 6 bits at the
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