Is it possible for a superluminal signal velocity without violating   causality?
  We present a model for a vacuum-like effective medium composed of the absorbing and gain media under the special designed parameters. Within the linear response theory, we prove that any pulse signal (with or without a discontinuity) through such a kind of vacuum-like effective media is always equal to the light speed in vacuum () without any distortion. As well known that the group velocity in anomalous or normal dispersive media may be smaller or larger than, or even become negative, but the discontinuous point always propagates at the velocity . Therefore we present some discussions on different definitions of the signals, based on the light pulses with a well-defined shape or with a sudden change, for trying to understand two possibilities for the signal velocity without violating the causality. 
Li-Gang Wang