This research is devoted to developing the pulse position modulation (PPM) modem, which utilizes an extremely small 40 ps position width to achieve a theoretical bitrate above 149 Mbps. In this work, we present a PPM modulator, implemented using software-controlled digital delay lines (DDLs) and the demodulator based on the high-precision event timer-based time-to-digital converter (TDC) with streaming capabilities. The versatility of the proposed solution is achieved by relying on software-defined radio (SDR) approach where the majority of modem functions are performed in software running on personal computer (PC) connected to the modem by USB3 interface. Unlike the traditional SDR, the proposed design relies on precise digital-to-time and time-to-digital conversion, which can cope with signals having up to 100 GHz bandwidth. Along with the design description, the use of Consultative Committee for Space Data Systems (CCSDS) standard-compliant Reed-Solomon error correcting code (ECC) for mitigating the timing errors is discussed. Results of laboratory testing of the PPM modem hardware prototype are presented and explained.