{ "id": "ep9j82km4e", "slug": "pulse-position-modulation", "title": "Pulse-position modulation", "updated": "2026-10-15", "topic_path": [ { "id": "technology", "label": "Technology and the built world", "api_url": "https://www.edgepedia.org/api/v1/topics/technology" }, { "id": "technology.communication", "label": "Communications and everyday technology", "api_url": "https://www.edgepedia.org/api/v1/topics/technology.communication" }, { "id": "technology.communication.wireless-signal-processing-techniques", "label": "Wireless signal processing techniques", "api_url": "https://www.edgepedia.org/api/v1/topics/technology.communication.wireless-signal-processing-techniques" } ], "geo": [ { "id": "geo.nongeo.t1946.technology", "label": "Non-geographic · 1946 to 2000: Technology and the built world", "api_url": "https://www.edgepedia.org/api/v1/geo/geo.nongeo.t1946.technology", "path": [ { "id": "geo.nongeo", "label": "Non-geographic", "api_url": "https://www.edgepedia.org/api/v1/geo/geo.nongeo" }, { "id": "geo.nongeo.t1946", "label": "Non-geographic · 1946 to 2000", "api_url": "https://www.edgepedia.org/api/v1/geo/geo.nongeo.t1946" }, { "id": "geo.nongeo.t1946.technology", "label": "Technology and the built world", "api_url": "https://www.edgepedia.org/api/v1/geo/geo.nongeo.t1946.technology" } ] } ], "excerpt": "Pulse-position modulation (PPM) is a digital modulation method that encodes information in a pulse's position within a time frame, used in deep-space and lunar optical links.", "snippet": "Pulse-position modulation (PPM) is a digital modulation method that encodes information in a pulse's position within a time frame, used in deep-space and lunar optical links.", "node": "technology.communication.wireless-signal-processing-techniques", "markdown": "# Pulse-position modulation\n\nPulse-position modulation (PPM) is a digital modulation method that encodes information in the temporal position of a pulse: each group of \\( \\log_{2} M \\) bits selects one of \\( M \\) adjacent time slots in a fixed frame, and a pulse is transmitted in that slot and in no other.[1](https://ntrs.nasa.gov/api/citations/19680025702/downloads/19680025702.pdf) • [2](https://ipnpr.jpl.nasa.gov/progress_report/42-154/154K.pdf) Because only one slot in \\( M \\) carries energy, PPM exchanges bandwidth for average power, which suits channels where photons rather than bandwidth are the scarce resource. It is used in deep-space and lunar optical links, optical fiber, indoor infrared, ultra-wideband impulse radio, and underwater optical communications.[3](https://www.frontiersin.org/journals/physics/articles/10.3389/fphy.2022.987994/full) • [4](https://www.mdpi.com/2076-3417/15/8/4222) • [5](https://www.nature.com/articles/s41598-025-18406-y) • [6](https://eprints.gla.ac.uk/384047/1/384047.pdf)\n\n| Property | Value |\n| --- | --- |\n| Symbol mapping | \\( \\log_{2} M \\) user bits select the position of one pulsed slot in an \\( M \\)-slot frame [2](https://ipnpr.jpl.nasa.gov/progress_report/42-154/154K.pdf) |\n| Information rate | \\( \\log_{2}(M)/(M \\cdot \\Delta T) \\) bits/s for slot width \\( \\Delta T \\) [1](https://ntrs.nasa.gov/api/citations/19680025702/downloads/19680025702.pdf) |\n| Photon efficiency | 12.5 bits per photon demonstrated at PPM order \\( 2^{19} \\) with free-running clocks (2025) [7](https://arxiv.org/html/2503.13161) |\n| Coded sensitivity | SCPPM designed to operate within about 1 dB of Poisson-channel capacity [8](https://tda.jpl.nasa.gov/progress_report/42-161/161T.pdf) |\n| Lunar link | NASA's LLCD reached 622 Mbps with 16-PPM and single-photon detector arrays (2013) [3](https://www.frontiersin.org/journals/physics/articles/10.3389/fphy.2022.987994/full) |\n| DPPM gain | 16-DPPM gives a 3 dB average-power gain over 4-PPM, the IrDA 4 Mb/s format [9](https://ee.stanford.edu/~jmk/pubs/dppm.pdf) |\n| UWB demonstration | 28 GHz TR-PPM over radio-over-fiber, BER below \\( 8.17 \\times 10^{-7} \\) with 200 ps bins [4](https://www.mdpi.com/2076-3417/15/8/4222) |\n\n## How it works\n\nIn an M-ary PPM symbol of duration \\( M \\cdot T_{s} \\), a laser pulse occupies one of \\( M = 2^{m} \\) slots of duration \\( T_{s} \\), carrying \\( m \\) bits.[10](https://tda.jpl.nasa.gov/progress_report/42-161/161R.pdf) The symbol set is the binary constant-weight code of length \\( Q \\), weight one, and minimum distance two, with \\( Q \\) codewords; multipulse PPM instead uses the weight-\\( K \\) code with \\( M = \\binom{Q}{K} \\) codewords.[11](https://arxiv.org/pdf/1301.3369) For slot time \\( T_{s} \\), the average signal photons per pulse are \\( n_{s} = \\eta \\cdot \\lambda_{s} \\cdot M \\cdot T_{s} \\) and the noise photons per slot are \\( n_{b} = \\eta \\cdot \\lambda_{b} \\cdot T_{s} \\).[2](https://ipnpr.jpl.nasa.gov/progress_report/42-154/154K.pdf)\n\nMoving the pulse in time conveys information because a photon count's timing identifies the symbol directly. Pierce's photon-counting PPM creates a discrete memoryless channel equivalent to the \\( M \\)-ary erasure channel (a channel where symbols are either received or lost entirely), whose capacity grows with the alphabet size \\( M \\).[12](https://ipnpr.jpl.nasa.gov/progress_report/42-60/60H.PDF) For fixed \\( n_{s} \\) and \\( n_{b} \\), capacity approaches \\( D(p_{1} \\| p_{0}) = (n_{s} + n_{b}) \\log(1 + n_{s}/n_{b}) - n_{s} \\) as \\( M \\to \\infty \\).[13](https://archive.dimacs.rutgers.edu/archive/Workshops/Storage/slides/moision.pdf) In the idealized background-free case, where the only impairment is an erasure when no photon is recorded over an entire frame, the information recoverable from one frame is \\( [1 - \\exp(-n_{f})] \\cdot \\log_{2} M \\), so photon information efficiency (PIE) approaches \\( \\log_{2} M \\) bits per photon as the pulse energy \\( n_{f} \\to 0 \\); with nonzero background this limit does not generally hold.[7](https://arxiv.org/html/2503.13161) With complete decoding, PIE stays constant as signal power vanishes, while simple decoding, which treats multi-count frames as erasures, loses it; at 10 AU with \\( n_{b} = 0.1 \\) the difference is nearly a hundredfold.[14](https://nanolithography.spiedigitallibrary.org/conference-proceedings-of-spie/11180/111805V/Range-dependence-of-pulse-position-modulation-in-the-presence-of/10.1117/12.2536130.full) Quantum pulse gating, a nonlinear noise-rejection technique, can raise the PIE limit by removing noise photons whose temporal modes do not match the PPM pulse mode.[7](https://arxiv.org/html/2503.13161)\n\n## How it is done\n\nAn analog PPM transmitter samples the signal and converts each sample into a time delay using a voltage-to-time converter or a monostable multivibrator; demodulation recovers timing with a [phase-locked loop](https://www.edgepedia.org/phase-locked-loop) followed by a time-to-voltage converter.[15](https://next.gr/tutorials/analog-communication/pulse-position-modulation-ppm-in-communications-tutorial) In digital optical PPM the transmitter fires the laser in the selected slot. The receiver measures the optical energy in each slot and selects the maximum; with direct photodetection this means counting released electrons per slot, modeled as Poisson variables with mean \\( K_{S} + K_{N} \\) in the signaling slot and \\( K_{N} \\) elsewhere.[1](https://ntrs.nasa.gov/api/citations/19680025702/downloads/19680025702.pdf)\n\nAccurate slot observables require the receiver slot clock to track the received slot boundaries. A decision-directed tracking loop derives the timing error signal without guard time using a chopping function and a numerically controlled oscillator.[10](https://tda.jpl.nasa.gov/progress_report/42-161/161R.pdf) The Mars Laser Communication Demonstration instead embedded periodic synchronization symbols as a pilot, at a throughput cost.[10](https://tda.jpl.nasa.gov/progress_report/42-161/161R.pdf)\n\n## Origin\n\nA NASA technical report worked out the design of a PPM optical communication system, including a deep-space television example.[1](https://ntrs.nasa.gov/api/citations/19680025702/downloads/19680025702.pdf) In 1978 J. Pierce proposed M-ary PPM with direct photon-counting detection for the optical channel, dividing the T-second symbol interval into \\( M \\) slots with a pulse in only one.[16](https://doi.org/10.1109/tcom.1978.1094043) • [12](https://ipnpr.jpl.nasa.gov/progress_report/42-60/60H.PDF) In 1981 R. McEliece proposed Reed-Solomon codes for this photon-counting PPM channel, showing code rates up to 2 or 3 nats per photon are feasible,[17](https://doi.org/10.1109/tit.1981.1056380) • [12](https://ipnpr.jpl.nasa.gov/progress_report/42-60/60H.PDF) and J. Massey analyzed capacity, cutoff rate, and coding for the direct-detection optical channel the same year.[18](https://doi.org/10.1109/tcom.1981.1094916) I. Garrett analyzed PPM for transmission over optical fibers with direct or heterodyne detection in 1983.[19](https://doi.org/10.1109/tcom.1983.1095842)\n\n## Variants\n\n**Differential PPM** (DPPM), analyzed by Da-Shan Shiu and J. M. Kahn in 1999, deletes all off chips following the on chip, giving variable-length symbols that need no symbol synchronization and higher power and bandwidth efficiency than PPM.[20](https://doi.org/10.1109/26.780456) • [9](https://ee.stanford.edu/~jmk/pubs/dppm.pdf) A single-chip error shifts all subsequent bits, so ordinary bit error rate is meaningless and packet-error rate is used; DPPM's power spectral density does not approach zero at dc, so highpass filtering against fluorescent-light noise distorts it more than PPM.[9](https://ee.stanford.edu/~jmk/pubs/dppm.pdf) 16-DPPM provides a 3 dB optical average-power gain over 4-PPM at only slightly more bandwidth.[9](https://ee.stanford.edu/~jmk/pubs/dppm.pdf)\n\n**Multipulse PPM** (MPPM) uses all \\( \\binom{n}{w} \\) binary n-tuples of weight \\( w \\) as codewords, carrying \\( \\log_{2} \\binom{N}{k} \\) bits per codeword; **overlapping PPM** (OPPM) restricts valid codewords to those with the \\( w \\) ones consecutive; both reduce to conventional PPM when \\( w = 1 \\).[21](https://barry.ece.gatech.edu/pubs/conference/pimrc.pdf) • [22](https://pure.hud.ac.uk/ws/portalfiles/portal/70886374/FARHAT_THESIS.pdf) Coded multipulse PPM with reduced-layer multilevel coding was applied to free-space optical communications by Trung Nguyen and Lutz Lampe in 2010.[23](https://doi.org/10.1109/tcomm.2010.04.090007) **Self-synchronizing PPM**, proposed by Yuichiro Fujiwara in 2013, achieves synchronization with marker overhead smaller than the periodic-marker method, and expurgated PPM generalizes PPM to provide error correction at the modulation stage while keeping the same \\( M = Q \\) symbols.[24](https://doi.org/10.1109/tit.2013.2262094) • [11](https://arxiv.org/pdf/1301.3369)\n\n## Applications\n\n**Deep space and lunar links.** NASA's LLCD used 16-PPM with single-photon detector arrays for 622 Mbps lunar-Earth communication in 2013.[3](https://www.frontiersin.org/journals/physics/articles/10.3389/fphy.2022.987994/full) NASA's DSOC technology demo aboard Psyche completed its final pass on September 2, 2025, having achieved a peak 267 Mbps downlink at 0.2 AU and 8.3 Mbps at 400 million km using binary PPM; possible reactivation in late 2026 has been discussed but no plan is approved.[3](https://www.frontiersin.org/journals/physics/articles/10.3389/fphy.2022.987994/full)\n\n**Fiber and indoor infrared.** Digital PPM is a preferred format for the ideal photon-counting channel and optical intersatellite links, and homodyne digital PPM at 1.5 μm should improve receiver sensitivity by typically 5 dB over homodyne PSK PCM.[25](https://onlinelibrary.wiley.com/doi/10.1002/ett.4460030405) Over 46 measured indoor infrared channels at 10 and 30 Mb/s, 16-PPM with maximum-likelihood sequence detection gave the best average-power efficiency against on-off keying.[26](https://ee.stanford.edu/~jmk/pubs/ppm.tcomm.pdf)\n\n**Ultra-wideband and underwater.** A 28 GHz IR-UWB TR-PPM system over analog radio-over-fiber used 200 ps time bins and 100 ps pulses, reaching BER below \\( 8.17 \\times 10^{-7} \\) over a 5 m wireless link with and without 20 km of fiber; a reference pulse at the start of each frame aids symbol decoding, and the transceiver can double as a joint radar-communication system measuring range and velocity.[4](https://www.mdpi.com/2076-3417/15/8/4222) In SPAD-based underwater photon-counting systems, PPM gives the longest transmission distance at a fixed BER when \\( M > 2 \\) but the lowest rate at fixed bandwidth and power.[27](https://www.frontiersin.org/journals/physics/articles/10.3389/fphy.2021.815343/full) M-ary PPM's power efficiency and simple detection without adaptive thresholding suit battery-powered underwater sensor nodes.[6](https://eprints.gla.ac.uk/384047/1/384047.pdf)\n\n## Limitations and alternatives\n\nPPM's major drawback is large bandwidth expansion, which lowers data rate for a given bandwidth and motivated the derivative schemes.[22](https://pure.hud.ac.uk/ws/portalfiles/portal/70886374/FARHAT_THESIS.pdf) It is vulnerable to loss of slot synchronization, potentially causing a severe error floor or throughput penalty even with little or no noise.[11](https://arxiv.org/pdf/1301.3369) PPM-based schemes are also significantly more sensitive to multipath dispersion than on-off keying: for 2-PPM at \\( R_{b}/W = 0.5 \\), channel capacity falls from 0.95 to 0.18 bits per codeword at SNR 3.3 dB.[21](https://barry.ece.gatech.edu/pubs/conference/pimrc.pdf) [Background radiation](https://www.edgepedia.org/background-radiation) entering the photodetector acts as erroneous energy and makes the channel M-ary symmetric; even with no background, the word error probability approaches \\( \\exp(-K_{s})/2 \\).[1](https://ntrs.nasa.gov/api/citations/19680025702/downloads/19680025702.pdf)\n\nAgainst neighboring schemes, NRZ-OOK requires factors of 2, 3, and 4 more power than 4-PPM, 8-PPM, and 16-PPM respectively, but PPM's bandwidth efficiency declines as the order grows, whereas M-PAM's rises and M-PAM needs more SNR for more than 2 bits per symbol.[28](https://doi.org/10.5120/13786-1838) In 2025 underwater simulations at 520 nm with a SiPM receiver, PPM was the most energy-efficient intensity modulation, but OOK achieved the longest range, 123.73 m in pure seawater at BER \\( 10^{-5} \\), and DPIM offered better bandwidth efficiency and peak-to-average power ratio at higher demodulation complexity.[5](https://www.nature.com/articles/s41598-025-18406-y) PPM is therefore the choice for power-limited, photon-counting channels such as deep-space links, not for bandwidth-limited ones.\n\n## References\n\n1. [The Design of a Pulse Position Modulated (PPM) Optical Communication System (Karp & Gagliardi, NASA TN, 1968)](https://ntrs.nasa.gov/api/citations/19680025702/downloads/19680025702.pdf)\n2. [Deep-Space Optical Communications Downlink Budget: Modulation and Coding (JPL Progress Report)](https://ipnpr.jpl.nasa.gov/progress_report/42-154/154K.pdf)\n3. [Performance evaluation of the high-speed deep-space optical communication system assisted by preamplified thresholded pulse-position modulation (Frontiers in Physics, 2022)](https://www.frontiersin.org/journals/physics/articles/10.3389/fphy.2022.987994/full)\n4. [Ultra-Wideband Analog Radio-over-Fiber Communication System Employing Pulse-Position Modulation (Applied Sciences, 2025)](https://www.mdpi.com/2076-3417/15/8/4222)\n5. [Performance analysis and optimization of modulation techniques for underwater optical wireless communication in varied aquatic environments (Scientific Reports, 2025)](https://www.nature.com/articles/s41598-025-18406-y)\n6. [Performance of M-ary Pulse Position Modulated Underwater OWC Links With Turbulence and Path Loss Effects (University of Glasgow)](https://eprints.gla.ac.uk/384047/1/384047.pdf)\n7. [Photon information efficiency limits in deep-space optical communications (arXiv, 2025)](https://arxiv.org/html/2503.13161)\n8. [Coded Modulation for the Deep-Space Optical Channel: Serially Concatenated Pulse-Position Modulation (JPL DESCANSO)](https://tda.jpl.nasa.gov/progress_report/42-161/161T.pdf)\n9. [Differential pulse-position modulation for power-efficient optical communication (Shiu & Kahn, IEEE Trans. Communications, 1999)](https://ee.stanford.edu/~jmk/pubs/dppm.pdf)\n10. [Decision-Directed Slot Synchronization for Pulse-Position-Modulated Optical Signals (JPL)](https://tda.jpl.nasa.gov/progress_report/42-161/161R.pdf)\n11. [Self-synchronizing pulse position modulation with error tolerance (Fujiwara; IEEE Trans. Information Theory, 2013)](https://arxiv.org/pdf/1301.3369)\n12. [Capacity, Cutoff Rate, and Coding for Direct-Detection Optical Channel (JPL Progress Report)](https://ipnpr.jpl.nasa.gov/progress_report/42-60/60H.PDF)\n13. [Modulation codes for the deep-space optical channel (Moision, JPL, DIMACS workshop)](https://archive.dimacs.rutgers.edu/archive/Workshops/Storage/slides/moision.pdf)\n14. [Range dependence of pulse position modulation in the presence of background noise (SPIE)](https://nanolithography.spiedigitallibrary.org/conference-proceedings-of-spie/11180/111805V/Range-dependence-of-pulse-position-modulation-in-the-presence-of/10.1117/12.2536130.full)\n15. [Pulse Position Modulation (PPM) in Communications (electronics tutorial)](https://next.gr/tutorials/analog-communication/pulse-position-modulation-ppm-in-communications-tutorial)\n16. [J. Pierce (1978). Optical Channels: Practical Limits with Photon Counting. IRE Transactions on Communications Systems.](https://doi.org/10.1109/tcom.1978.1094043)\n17. [R. McEliece (1981). Practical codes for photon communication. IEEE Transactions on Information Theory.](https://doi.org/10.1109/tit.1981.1056380)\n18. [J. Massey (1981). Capacity, Cutoff Rate, and Coding for a Direct-Detection Optical Channel. IRE Transactions on Communications Systems.](https://doi.org/10.1109/tcom.1981.1094916)\n19. [I. Garrett (1983). Pulse-Position Modulation for Transmission Over Optical Fibers with Direct or Heterodyne Detection. IRE Transactions on Communications Systems.](https://doi.org/10.1109/tcom.1983.1095842)\n20. [Da-Shan Shiu, J.M. Kahn (1999). Differential pulse-position modulation for power-efficient optical communication. IEEE Transactions on Communications.](https://doi.org/10.1109/26.780456)\n21. [Performance Analysis and Channel Capacity for Multiple-Pulse Position Modulation on Multipath Channels (Georgia Tech / PIMRC)](https://barry.ece.gatech.edu/pubs/conference/pimrc.pdf)\n22. [Design and System Implementation of Pulse Position Modulation (PPM) Based Coding Systems (PhD thesis, University of Huddersfield)](https://pure.hud.ac.uk/ws/portalfiles/portal/70886374/FARHAT_THESIS.pdf)\n23. [Trung Nguyen, Lutz Lampe (2010). Coded multipulse pulse-position modulation for free-space optical communications. IEEE Transactions on Communications.](https://doi.org/10.1109/tcomm.2010.04.090007)\n24. [Yuichiro Fujiwara (2013). Self-Synchronizing Pulse Position Modulation With Error Tolerance. IEEE Transactions on Information Theory.](https://doi.org/10.1109/tit.2013.2262094)\n25. [A comparison of coherent digital PPM with PCM (European Transactions on Telecommunications)](https://onlinelibrary.wiley.com/doi/10.1002/ett.4460030405)\n26. [Performance of Pulse-Position Modulation on Measured Non-Directed Indoor Infrared Channels (IEEE Trans. Communications, 1996)](https://ee.stanford.edu/~jmk/pubs/ppm.tcomm.pdf)\n27. [A Comprehensive Comparison and Analysis of Several Intensity Modulations Based on the Underwater Photon-Counting Communication System (Frontiers in Physics, 2021)](https://www.frontiersin.org/journals/physics/articles/10.3389/fphy.2021.815343/full)\n28. [Performance Comparison between OOK, PPM and PAM Modulation Schemes for Free Space Optical (FSO) Communication Systems: Analytical Study](https://doi.org/10.5120/13786-1838)\n\n---\n*Topic: Encyclopedia › Technology and the built world › Communications and everyday technology › Wireless signal processing techniques*\n\n*Initially written Sep 29, 2026 · Edited: Oct 15, 2026*\n\n*Copyright 2026 EdgeChat AI, a subsidiary of Biostate AI.*\n\nLicense: Edgepedia Community License 1.0, https://www.edgepedia.org/edgepedia/license\n", "same_as": [ "https://ee.stanford.edu/~jmk/pubs/dppm.pdf", "https://ee.stanford.edu/~jmk/pubs/ppm.tcomm.pdf" ], "url": "https://www.edgepedia.org/pulse-position-modulation", "markdown_url": "https://www.edgepedia.org/pulse-position-modulation.md", "license": { "name": "Edgepedia Community License 1.0", "url": "https://www.edgepedia.org/edgepedia/license", "summary": "Free with credit, commercial use included. AI training is open to everyone. For other uses, organizations over USD 100M in revenue or 100M monthly users license separately.", "spdx": "LicenseRef-Edgepedia-Community-1.0" }, "credit": "\"Pulse-position modulation\", Edgepedia (EdgeChat), https://www.edgepedia.org/pulse-position-modulation. Edgepedia Community License 1.0.", "credit_md": "\"[Pulse-position modulation](https://www.edgepedia.org/pulse-position-modulation)\", Edgepedia (EdgeChat), [https://www.edgepedia.org/pulse-position-modulation](https://www.edgepedia.org/pulse-position-modulation). [Edgepedia Community License 1.0](https://www.edgepedia.org/edgepedia/license).", "credit_html": "\"Pulse-position modulation\", Edgepedia (EdgeChat), https://www.edgepedia.org/pulse-position-modulation. Edgepedia Community License 1.0.", "speakable": "Pulse-position modulation is a digital modulation method that encodes information in a pulse's position within a time frame, used in deep-space and lunar optical links." }