Simultaneous wireless information and power transfer (SWIPT) has emerged as a viable technique to energize and connect low-power autonomous devices and enable future Internet of Things (IoT). A major challenge of SWIPT is the energy consumption of the receiver of such low-power devices. An attractive low-power solution consists in an integrated information decoder (ID) and energy harvester (EH) architecture for SWIPT receiver (IntRx) where the received RF signal is first rectified before being used for information decoding. Such architecture eliminates the need for energy-consuming RF components such as local oscillators and mixers. This paper proposes a novel modulation and demodulation method for the IntRx SWIPT architecture based on pulse position modulation (PPM) where information is encoded in the position of the pulse. The new method transmits high amplitude pulses to increase the Peak-to-Average Power Ratio (PAPR) of the transmit signal and exploits the EH's nonlinearity so as to boost the harvested DC power. Simultaneously, the information can be decoded from the rectifier signal by simply finding the position of the pulse in a certain symbol duration. We have analyzed both the information and the power transfer performance of the newly proposed PPM for IntRx SWIPT theoretically, numerically, and experimentally. To that end, we have established a SWIPT system testbed in an indoor environment by prototyping a base station to transfer information-power signal and the IntRx SWIPT receiver including ID and EH blocks. The performance evaluation of the PPM was carried out in various conditions, and the results have been compared and contrasted to conventional signals. Theoretical, numerical, and experimental results highlight the significant benefits of the proposed PPM scheme to enhance the power transfer performance and operate information decoding with low-power consumption.