Slot synthesis for high cardinality pulse position modulation

A communication system including a slot clock generator for high data rate pulse position modulation (PPM), comprising:

• a set of clocks with a set of predetermined harmonically related frequencies, harmonically related to a fundamental period and having rates that are mutually prime in pairs, said set of clocks configured such that the frequency of the fastest clock of the set of harmonically related frequencies is minimized with the fundamental period divided into a number of periods where a number of synthetic divisions of the period of the fundamental frequency exceeds a specified power of two which synthesizes and accumulates changes in clock states at a rate corresponding to a slot rate that is greater than a slot rate of any single clock in said set, wherein a lookup table is used to synthesize said slot rate of said clock states by solving a set of simultaneous modular equations on said clock states by producing a composite modulus that is larger than a cardinality of a PPM signal selected from wavelength and polarization, optionally with pulse-position modulating at a set of four wavelengths;
• and
• further comprising:
• a precession counter which maintains phasing of a PPM slot rate to said synthetic slot clock, by at least one of re-mapping said synthetic clock slot to a modulus slot, resetting clock-set counters at an end of each PPM word, or introducing dead times after each PPM word to align each of said clock states to a PPM word boundary, thereby lowering a data rate whereby a corresponding single scalar PPM slot rate differs for each modulated wavelength with the vector-PPM word rate held to a predetermined ratio.