Pulse-position modulation  Pulse-position modulation (PPM) is a form of signal modulation in which "M" message bits are encoded by transmitting a single pulse in one of formula_1 possible required time shifts. This is repeated every "T" seconds, such that the transmitted bit rate is formula_2 bits per second. It is primarily useful for optical communications systems, which tend to have little or no multipath interference. An ancient use of pulse-position modulation was the Greek hydraulic semaphore system invented by Aeneas Stymphalus around 350 B.C. that used the water clock principle to time signals. In this system, the draining of water acts as the timing device, and torches are used to signal the pulses. The system used identical water-filled containers whose drain could be turned on and off, and a float with a rod marked with various predetermined codes that represented military messages. The operators would place the containers on hills so they could be seen from each other at a distance. To send a message, the operators would use torches to signal the beginning and ending of the draining of the water, and the marking on the rod attached to the float would indicate the message. In modern times, pulse-position modulation has origins in telegraph time-division multiplexing, which dates back to 1853, and evolved alongside pulse-code modulation and pulse-width modulation. In the early 1960s, Don Mathers and Doug Spreng of NASA invented pulse-position modulation used in radio-control (R/C) systems. PPM is currently being used in fiber-optic communications, deep-space communications, and continues to be used in R/C systems. One of the key difficulties of implementing this technique is that the receiver must be properly synchronized to align the local clock with the beginning of each symbol. Therefore, it is often implemented differentially as "differential pulse-position modulation", whereby each pulse position is encoded relative to the previous, such that the receiver must only measure the difference in the arrival time of successive pulses. It is possible to limit the propagation of errors to adjacent symbols, so that an error in measuring the differential delay of one pulse will affect only two symbols, instead of affecting all successive measurements. Aside from the issues regarding receiver synchronization, the key disadvantage of PPM is that it is inherently sensitive to multipath interference that arises in channels with frequency-selective fading, whereby the receiver's signal contains one or more echoes of each transmitted pulse. Since the information is encoded in the time of arrival (either differentially, or relative to a common clock), the presence of one or more echoes can make it extremely difficult, if not impossible, to accurately determine the correct pulse position corresponding to the transmitted pulse.