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4. Robert Lucky’s Adaptive Equalization, From the 1960s    7




                     (A)























                     (B)
                                                k e




                                                                Positive stable
                            +                       +           equilibrium point
                                                                                y k
                                             –                       –      ( SUM )
                       Negative stable
                                                    Unstable
                       equilibrium point
                                                    equilibrium point

                  FIGURE 1.4
                  Bootstrap learning. (A) The quantized output, the sum, and the error as a function of
                  (SUM). (B) The error versus (SUM).




                  4. ROBERT LUCKY’S ADAPTIVE EQUALIZATION, FROM THE
                     1960s
                  In the early 1960s, as Widrow’s group at Stanford was developing bootstrap
                  learning, at the same time, independently, a project at Bell laboratories led by Robert
                  W. Lucky was developing an adaptive equalizer for digital data transmission over
                  telephone lines [10,11]. His adaptive algorithm incorporated what he called “deci-
                  sion directed learning,” which has similarities to bootstrap learning.
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