Cryptography Reference
In-Depth Information
2. The role of SISO decoding is to increase the equivalent signal to noise ratio
of the LLR, that is, to provide more reliable extrinsic information at output
z
output
than at input (
z
input
). The convergence of the iterative process
(see Section 7.6) will depend on the transfer function SNR
(
z
output
)=
G
(
SNR
(
z
input
))
of each of the decoders.
When data is not available at the input of the SISO decoder, due to punc-
turing for example, a neutral value (analogue zero) is substituted for this
missing data.
3. When the elementary decoding algorithm is not the optimal MAP algo-
rithm but a sub-optimal simplified version, the extrinsic information has
to undergo some transformations before being used by a decoder:
•
multiplying the extrinsic information by factor
γ
, lower than 1, guar-
antees the stability of the looped structure.
γ
can vary over the itera-
tions, for example, from 0.7 at the beginning of the iterative process,
to 1 for the last iteration.
•
clipping the extrinsic information solves both the issue of limiting the
size of the memories and that of participating in the stability of the
process. A typical value of the maximum dynamics of the extrinsic
information is twice the input dynamics of the decoder.
4. Binary decision taking is performed by thresholding at value 0.
The number of iterations required by turbo decoding depends on the size
of the block and on the coding rate. Generally, the larger the decoded
block and the slower the convergence, the higher the MHD of the code.
The same occurs when the coding rates are low. In practice, we limit the
number of iterations to a value between 4 and 10, according to the speed,
latency and consumption constraints imposed by the application.
Figure 7.14 gives an example of the performance of a binary turbo code,
taken from the UMTS standard [7.3]. We can observe a decrease in packet error
rates (PER), just close to the theoretical limit (that is, around 0,5 dB, taking
into account the size of the block), but also a fairly pronounced change in slope,
due to an MHD that is not very high (
d
min
=26
) for a rate of 1/3.
7.4.2 SISO decoding and extrinsic information
Here we present processing performed in practice in a SISO decoder using the
MAP algorithm [7.6] or its simplified version, the Max-log-MAP algorithm, also
called the SubMAP algorithm [7.37], to decode RSC
m
-binary codes and imple-
ment iterative decoding. For binary codes and turbo codes, all these equations
can be simplified by taking
m
=1
.
