TABLE OF CONTENTS The invention of turbocodes does not derive from a linear and limpid theory, much less a beautiful mathematical development. It is the product of a long search, whose origin is to be found in the intuitions and work of some European researchers: Gerard Battail, Joachim Hagenauer and Peter Hoeher who, at the end of the 1980s [BAT 87, BAT 89, HAG 89a, HAG 89b], announced the promise of probabilistic treatment in communication systems. Others before, in particular in the United States, such as Michael Tanner [TAN 81] and Robert Gallager [GAL 62], had earlier come up with coding and decoding processes that were the precursors of turbocodes.
In the laboratories of the Ecole Nationale Sup rieure de Telecommunications de Bretagne (Brittany National Telecommunications Graduate School) some sought the simplest way possible to translate the Viterbi algorithm with soft output (SOVA: Soft-output Viterbi Algorithm) proposed in [BAT 87], in MOS transistors. A suitable solution [BER 93a] was found after two years, which made it possible for the researchers to form an opinion on probabilistic decoding. Thus, they observed following Battail and Hagenauer that a decoder with soft input and output could be regarded as an amplifier of signal-to-noise ratio, which encouraged them to implement concepts commonly used in amplifiers, in particular, negative feedback. We must, however, note that this parallel with amplifiers only makes sense if the values considered at the input and the output of the decoder provide...
