Cryptography Reference
In-Depth Information
the encoding scheme adopted in many countries for digital terrestrial television
[6.1].
Figure 6.1 - serial concatenated code, (a) without and (b) with permutation. In both
cases, the output of the outer encoder is entirely recoded by the inner encoder.
Nowadays, this first version of concatenated codes is called
serial concatena-
tion
(SC). Its decoding, presented in Figures 6.1 is not optimal. Indeed, even if,
locally, the two elementary decoders are optimal, the simple sequencing of these
two decodings is not globally optimal as the inner decoder does not take any
advantage of the redundancy produced by the outer code. It is this observation,
that occurred fairly late in the history of information theory, that led to the
development of new decoding principles, beginning with turbo decoding. We
now know how to decode, quasi-optimally, all sorts of concatenated schemes,
with the sole condition that the decoders of elementary codes are of the SISO
(
soft-in/soft-out
) type. In this sense, we can note that the concept of concate-
nation has greatly evolved in the last few years, moving towards a wider notion
of multi-dimensional encoding. Here, the
dimension of a code
, which should not
be confused with the length (
k
) of the information message that we also call
dimension, is the number of elementary codes used in the production of the final
codeword.
Figure 6.2 - Parallel concatenation of systematic encoders.
