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

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.