Cryptography Reference
In-Depth Information
Figure 8.9 - Internal architecture of the SISO decoder.
The algebraic decoding module uses the value of the syndrome to determine
the erroneous places in the concurrent vectors. In the case of BCH codes, it is
possible to use the Berlekamp-Massey algorithm or the extended Euclid algo-
rithm to make the correction. It should, however, be noted that this solution
is really only economical for block codes with high correcting power. For codes
with low error correction capability, it is less costly to store the bits to be cor-
rected in a local ROM, for each possible value of the syndrome.
The selection module must sort among the words generated by the algebraic
decoding module to determine the most probable ones. It must therefore calcu-
late the metric of each of these words (which it does sequentially by additions)
and determine, by computation of the minimum value, the most probable among
them (their number is generally limited, for the sake of space).
Finally, the module for calculating the weightings uses the list of concurrent
words chosen above to generate the weightings from the equation of step 6 of
the Chase-Pyndiah algorithm. This module has low complexity since the calcu-
lations to be done are relatively simple and, for each bit, it must keep only two
values sequentially (the smallest metric among the concurrent words having 0 as
the corresponding value for this bit in its binary development, and the smallest
metric for the candidate words having 1 as their binary value). This module also
contains value
β
. In the case of an FPGA (
Field Programmable Gate Array
)im-
plantation, all the iterations are generally executed on the same hardware which
is re-used from half-iteration to half-iteration. We must therefore anticipate a
procedure for loading value
β
.
Bibliography
[8.1] P. Adde, R. Pyndiah, and O. Raoul. Performance and complexity of
block turbo decoder circuits. In
Proceedings of Third International Con-
ference on Electronics, Circuits and Systems, (ICECS'96)
, pages 172-175,
Rhodes, Greece, 1996.
