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In this paper, we consider the problem of space-time (ST) coding with unipolar pulse position modulations (PPM). The proposed code satisfies a large number of construction constraints that render it superior to the existing PPM encoding schemes. In particular, the proposed 2 times 2 code achieves a full transmit diversity order while transmitting at a rate of 1 PPM-symbol per channel use. The proposed scheme can be associated with M-ary PPM constellations for all even values of M without introducing any constellation extension. This renders the proposed scheme suitable for low cost carrier-less ultra-wideband (UWB) systems where information must be conveyed only by the time delays of the modulated sub-nanosecond pulses without introducing any amplitude amplification or phase rotation. Finally, the proposed scheme is symbol-by-symbol decodable where the information can be reconstituted by performing simple linear operations at the receiver side. A possible extension to transmitters equipped with three antennas is also discussed in situations where a certain number of feedback bits is available.