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

Error-rate in Viterbi decoding of a duobinary signal in presence of noise and distortions: theory and simulation