Turbo codes
1. Introduction
At the 1993 IEEE International Conference on Communications in
Geneva two French scientists Claude Berrou and Alain Glavieux from
ENSTBretagne in Brest presented a digital coding scheme that could
provide virtually errorfree communications at data rates and transmittingpower
efficiencies well beyond what most experts thought possible. The
new error correction coding scheme, named turbo codes, has revolutionized
errorcorrection coding. The new scheme let engineers design systems
that are very close to the socalled channel capacity – the
maximum rate, in bit per second, of a communications channel for
a given power level at the transmitter. This threshold was discovered
by the Claude Shannon in 1948.
Turbo codes are iteratively decoded parallel concatenated convolutional
codes which consist of two convolutinal encoders, the first of which
encodes the information bits directly, while the second one encodes
the information bits following interleaving. Maximum likelihood
decoding (Viterbi algorithm) of these codes is prohibitively complex
because they are equivalent to a timevarying convolutional codes
with very high number of states (e.g. about 21000 states). The key
to solving the decoding complexity of these concatenated codes is
the existence of suboptimal decoding algorithm which achieves performance
very close to that of a maximum likelihood decoder.
In 1995 the serial analogues of turbo codes were introduced. The
serially concatenated convolutional codes are constructed from the
same constituent codes and interleaver elements as turbo codes,
but are concatenated in a serial fashion. Serial schemes achieve
comparable performance to parallel schemes.
