n where n is the iteration number u03bc is the stability factor and e n is x n u2212 y n u00b7 f m x n it should be pointed out that addressing already generated can be reused for indexing y n 105 which is a distorted signal able to cause another error due to incorrect indexing during this procedure the samples x n 103 should bypass by the piecewise pre equalizers 107 after convergence of this indirect learning lms algorithm the equalizers 107 are activated an indirect learning method with an lms algorithm has also been utilized for adaptation of the piecewise filter coefficients the input of the multiple equalizers 107 in the feedback path is written in vector format as y fi n y f n y f n u2212 1 y f n u2212 k 1 where y f n is the post lut output that is y n u00b7 f m y n therefore the multiple fir filter outputs yfo n can be derived in vector format using the following equations y fo n w m u00b7 y fi n t adaptation of the tap coefficients of the pre equalizers 107 can be obtained as follows w m u n 1 w m.