In the transmission of digital data at a relatively high rate over a particular band limited channel, it is normally necessary to employ an equalizer at the receiver in order to correct the signal distortion introduced by the channel .ISI (inter symbol interference) leads to large error probability if it is not suppressed .The possible solutions for coping with ISI such as equalization technique. Maximum Likelihood Sequence Estimation (MLSE) implemented with Viterbi algorithm is the optimal equalizer for this ISI problem sense it minimizes the sequence of error rate. This estimator involves a very considerable amount of equipment complexity especially when detecting a multilevel digital signal having large alphabet, and/or operating under a channel with long impulse response, this arises a need to develop detection algorithms with reduced complexity without losing the performance. The aim of this work is to study the various ways to remove the ISI, concentrating on the decision-based algorithms (DFE, MLSE, and near MLSE), analyzing the difference between them from both performance and complexity point of view. An Improved non linear equalizer with Perturbation algorithm has been suggested which trying to enhance the performance and reduce the computational complexity by comparing it with the other existing detection algorithms.