Cryptography Reference
In-Depth Information
data shared by the two decoders is more penalizing than puncturing data that
are only useful to one of the decoders.
What must be closely considered when building a turbo code and decoding
it, are the RTZ sequences, whose output weights limit the minimum distance of
the code and fix its asymptotic performance. In what follows it will be assumed
that the error patterns that are not RTZ do not contribute to the MHD of the
turbo code and will therefore not have to be considered.
7.3.1 Termination of constituent codes
For a turbo code, there are two trellises to be terminated and the solutions
presented in Section 5.5.1 can be envisaged:
Doing nothing in particular concerning the terminal states: the data
situated at the end of the block, in either the natural order or in the permuted
order, are thus less well protected. This leads to a decrease in the asymptotic
gain, but this degradation, which is a function of the size of the block, may be
compatible with some applications. It should be noted that non-termination of
the trellis penalizes the PER (Packet Error Rates) more greatly than the BER.
Terminating the trellis of one or both elementary codes using tail
bits: CCSDS [7.4] and UMTS [7.3] standards use this technique. The bits
ensuring the termination of one of the two trellises are not used in the other
encoder. These bits are therefore not turbo encoded, which leads, but to a
lesser degree, to the same drawbacks as those presented in the previous case.
Moreover, the transmission of the tail bits causes a decrease in the coding rate
and therefore in the spectral eciency.
Using interleaving enables the automatic termination of the trellis:
it is possible to close the trellis of a turbo code automatically, without adding any
tail bits, by slightly transforming the coding scheme (self-concatenation) and by
using interleaving that respects certain periodicity rules. This solution described
in [7.15] does not decrease the spectral eciency but imposes constraints on the
interleaving which makes it dicult to control performance at low error rates.
Adopting circular encoding: a circular encoder for convolutional codes
guarantees that the initial state and the final state of the register are identical.
The trellis then takes the form of a circle, which, from the point of view of the
decoder, can be considered as a trellis with infinite length [7.32, 7.48]. This
termination process, already known as
tail-biting
for non-recursive codes, offers
two main advantages:
•
Unlike the other techniques, circular termination does not present any edge
effects: all the bits of the message are protected in the same way and are
all doubly encoded by the turbo code. Therefore, during the design of the
permutation, there is no need to give special importance to such and such
a bit, which leads to simpler permutation models.
