  The Viterbi algorithm, presented in 1967, allows a maximum likelihood
decoding of partial response codes. This study focuses on the duobinary code
which is the first member of this family and has been specified for the digital
part of television systems recommended by International Organizations. Up to
now the error-rate, which is the main criterion of the performance, has been
evaluated by simulation. Although there exist theoretical bounds, these bounds
are not satisfactory for a channel such as broadcasting (by terrestrial
transmitters, cable networks or satellite) which is strongly impaired by noise,
and linear and non-linear distortions. Analytical methods, verified by
simulation, are presented here in order to evaluate the theoretical and exact
values of the error-rate, in the form of series of numerical integrations, for
a transmission in baseband or in radio-frequency with quadriphase modulation
(or AM/VSB for cable networks) and coherent demodulation, in presence of noise
and several distortions. This methodology can be later extended to other
partial response codes, to convolutional codes and their concatenations.
