he "survivor" path. A transition from a previous state to a new state is marked by an incremental met- ric, usually a number. Typical metrics are the transition probability or the transi- tion cost. The metric is cumulative over a path, that is, the metric of a path is the sum of the metric of each transition belonging to the path. On the grounds of these hypotheses the algorithm associates a number to each state. When an event occurs, in our case every time a new sample is received at the decision level, the algorithm knows the state in which the system is and the previous sequence of states. Starting from them it examines a new set of states that are reachable from the initial state and that are compatible with the observed event, for each state combines the weight associated to the start- ing state with the metric of the transition and chooses the transition that creates the better combined value. This transition results in a new starting state that enriches the state sequence. Technology for Telecommunications: Integrated Optics and Microelectronics The incremental metric associated with a transition depends on the transition probabil- ity from the old state to the new state conditioned to the observed event and from the state transition history for a length equal to the channel memory. After computing the combinations of incremental metric and state metric, only the best survives and all other paths are discarded. It is to be underlined that, since it is the path weight that is at the center of the Viterbi algorithm, the path history must be stored in order to work the algorithm. In the case of an equalizer for the distortion of the optical channel, whatever technique is used to identify a finite number of states within the continuous response of the optical channel, the core issue is that the state graph is too big to be completely represented into the memory of the signal processor. Thus the key issue of this kind of equalizers, besides the sampling at very high rate, is the reduction of the Viterbi algori