We rely on a Basis Expansion Model (BEM) for the channel, to design three Space-Time-Doppler (SID) codecs that enable maximum diversity gains, when block transmissions undergo time-selective fading effects. Within the constraints of each maximum-diversity design, it is also possible to achieve maximum coding gain, at least when the BEM parameters are i.i.d. The theoretical results are corroborated by simulation results and the BEM is validated.