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Dielectric barrier discharge excitated by unipolar pulsed power is a promising approach for producing non-thermal plasma at atmospheric pressure. A magnetic compression solid-state pulse power generator is used to produce dielectric barrier discharge (DBD). The generator is capable of providing repetitive pulses with the voltage of up to 30 kV and duration of 70 ns at a 300 Ω resistive load. This paper illustrates electrical characteristic and luminous emissions of DBD excitated by repetitive unipolar nanosecond-pulses in atmospheric air. Different from common DBD excitated by high-voltage AC sources, discharge current of DBD in the experimental investigation can be on an order of tens of amperes. When the DBD is created using two liquid electrodes, the luminous emissions from the obverse and flank sides of liquid electrodes show that no filament is observed and the discharge is homogeneous and diffuse in the whole discharge regime.