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We introduce a multipulse multicarrier (MPMC) transceiver for packet transmissions over time-varying fading channels. The core of this system is an efficient Zak-transform implementation of the MPMC modulator/demodulator that uses optimized transmit/receive pulses. This implementation suggests a simple precoder that allows us to exploit the multipath/Doppler diversity offered by the channel. The transmit symbols are recovered via an MMSE equalizer and decoder. To obtain the required channel state information, we propose efficient LS and MMSE channel estimators that are based on pilot symbols. Numerical simulations verify the diversity gain of our MPMC transceiver as well as its superiority over conventional multicarrier systems for the case of highly dispersive channels.