[HN Gopher] How many photons are received per bit transmitted fr...
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How many photons are received per bit transmitted from Voyager 1?
Author : williamsmj
Score : 762 points
Date : 2024-06-03 12:07 UTC (10 hours ago)
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| notorandit wrote:
| It's really nice! Both the question and the answer!
| jsjohnst wrote:
| Didn't realize the math would be that straightforward. Is there
| something the author isn't taking into account or is that a
| decent plausible range?
| krylon wrote:
| I was surprised, too. Knowing little about physics, this was a
| pleasant surprise, however.
| rcxdude wrote:
| It looks like a pretty reasonable order of magnitude estimate
| to me. Energy arguments tend to be quite neat for that because
| if the efficiency is at all reasonable they constrain things
| well with fairly simple calculations. The antenna
| directionality is also reasonably well understood and
| characterised. The exact noise level discussed later on is
| probably where things get a bit more uncertain (but aren't
| directly needed to answer the question).
| magicalhippo wrote:
| One thing that seems missing to me is that while the probe
| might send 160 bits/sec of useful data, those bits are not sent
| directly as such[1]:
|
| _The TMU encodes the high rate data stream with a
| convolutional code having constraint length of 7 and a symbol
| rate equal to twice the bit rate (k=7, r=1 /2)._
|
| So the effective symbol rate is 320 baud[2], and thus a factor
| of two should be included in the calculations from what I can
| gather.
|
| Note that the error correction was changed after Jupiter to use
| Reed-Solomon[3] (255,223) to lower the effective bit error
| rate, so effectively I guess the data rate is more like 140
| bps.
|
| [1]:
| https://web.archive.org/web/20130215195832/http://descanso.j...
|
| [2]: https://destevez.net/2021/09/decoding-voyager-1/
|
| [3]: https://destevez.net/2021/12/voyager-1-and-reed-solomon/
| ooterness wrote:
| For the "photons per bit" question, the useful throughput of
| 140 bps is the only thing that matters.
|
| For the "how many photons are needed" question, I agree that
| 320 baud (i.e., the effective analog bandwidth of 320 Hz)
| should have been used for the Shannon-Hartley calculations.
| lordnacho wrote:
| I love these kinds of questions. So what does that conclusion
| mean about when the probe will be so far away that we are below
| the Shannon limit?
|
| And can we beat the Shannon limit somehow, eg collect for longer,
| put the dish outside the atmosphere, and so on?
| fsmv wrote:
| Seems like we can just build a bigger receiving dish
| rcxdude wrote:
| There's not a lot of appetite for that, though. the 70m
| receiver is already one of the largest ever built, and for
| most use cases it's looking better to use an array of smaller
| ones. Which works fine for receiving but not so much for
| transmitting (while there are multiple sites in the world
| capable of receiving from voyager 2, there's only one dish
| which can actually transmit to it)
|
| (I recall seeing a video on that dish, and the director
| seemed confident there was enough noise margin left that
| voyager's power would fail before they lost contact with it)
| Asraelite wrote:
| I guess we could just program Voyager 1 to lower the data
| bitrate, adding more redundancy / error correction. I think
| there's no real limit to how far it could get if we keep doing
| that.
| ethbr1 wrote:
| Not my field, but assuming transmitting hardware (including
| beam forming) is constant and that atmosphere can mostly be
| ignored (see comments about it usually being a non-impact in
| the transmission frequencies), two approaches would suggest:
|
| 1. Increase the effective receiving dish size, to capture more
| of the signal. Essentially, this would be effective in direct
| proportion to beam spread (the more beam spread, the bigger
| dish you can use to capture signal).
|
| In practice, this would use multiple geographically-displaced
| dishes to construct a virtually-larger dish, to allow for
| better noise-cancellation magic (and at lower cost than one
| huge dish). I believe the deep space network (DSN) already does
| this? _Edit_ : It certainly has arrayed antennae [0], though
| not sure how many are Voyager-tasked.
|
| 2. Increase the resilience of the signal, via encoding. The
| math is talking about bits and photons, but not encoded
| information. By trading lower bit-efficiency for increased
| error tolerance (i.e. including redundant information) we can
| extract a coherent signal even accounting for losses.
|
| Someone please point out if I'm wrong, but afaik the Shannon-
| Hartley limit speaks to "lower" in the physical stack than
| error coding. I.e. one can layer arbitrary error coding on top
| of it to push limits (at the expense of rate)?
|
| If the above understanding is correct, is there a way to
| calculate maximum signal distance _assuming a theoretically
| maximally efficient error coding_ (is that a thing?) ? Or is
| that distance effectively infinite, assuming you 're willing to
| accept an increasingly slow bit receiving rate?
|
| [0]
| https://en.m.wikipedia.org/wiki/NASA_Deep_Space_Network#Ante...
| retrac wrote:
| There's another major factor. I suppose it falls under the
| encoding. Frequency stability. In a certain sense, having an
| extremely precise oscillator at both the receiver and the
| transmitter, is the same thing as just having a better more
| frequency-stable antenna, or less noise in the channel
| (because you know what the signal you're listening for should
| look like).
|
| I'm no physicist here so take this with a major grain of
| salt. I think the limit might ultimately arise from the
| uncertainty principle? Eventually the signal becomes so weak
| that measuring it, overwhelms the signal. This is why the
| receiver of space telescopes is cooled down with liquid
| helium. The thermally-generated background RF noise (black
| bodies radiate right down into the radio spectrum) would
| drown everything else out otherwise.
|
| Along those lines, while I'm still not quite sure where the
| limit is, things become discrete at the micro level, and the
| smallest possible physical state change appears to be
| discrete in nature:
| https://en.wikipedia.org/wiki/Landauer%27s_principle Enough
| work physically must occur to induce a state change of some
| kind at the receiver, or no communication can occur. (But
| this interpretation is disputed!)
| lxgr wrote:
| Coding counters the uncertainty principle by allowing
| multiple measurements, which can then be averaged. Thant
| counters the contribution of random noise.
|
| There are practical signals we use every day that are
| "below the noise floor" before we decode them.
|
| So while there is an ultimate limit of the maximum coding
| rate for a given signal-to-noise ratio, this is expressed
| in terms of a data rate (i.e. bits per second). If you're
| fine with lowering your data rate, there is no fundamental
| theoretical limit, as far as I understand.
| shagie wrote:
| The resilience of the signal part...
|
| https://www.allaboutcircuits.com/news/voyager-mission-
| annive...
|
| > The uplink carrier frequency of Voyager 1 is 2114.676697
| MHz and 2113.312500 MHz for Voyager 2. The uplink carrier can
| be modulated with command and/or ranging data. Commands are
| 16-bps, Manchester-encoded, biphase-modulated onto a 512 HZ
| square wave subcarrier.
|
| The "Manchester encoding" brings us to
| https://www.allaboutcircuits.com/technical-
| articles/manchest...
|
| https://en.wikipedia.org/wiki/Manchester_code
|
| Note that "16 bps" while the system runs at 160 bps. This
| suggests that the data is repeated ten times and xor'ed with
| a clock running at 10 HZ.
|
| While there's no VOY set up now,
| https://eyes.nasa.gov/dsn/dsn.html will occasionally show it.
| When that happens, you will likely see two set up for it.
| I've not seen them set up across multiple facilities - the
| facilities are 120deg apart and only one has a spacecraft
| above the horizon for any given length of time.
|
| ---
|
| In the "sensitivity to photons" category, I'll also mention h
| ttps://en.wikipedia.org/wiki/Lunar_Laser_Ranging_experiment..
| .
|
| At the Moon's surface, the beam is about 6.5 kilometers (4.0
| mi) wide[24][i] and scientists liken the task of aiming the
| beam to using a rifle to hit a moving dime 3 kilometers (1.9
| mi) away. The reflected light is too weak to see with the
| human eye. Out of a pulse of 3x10^17 photons aimed at the
| reflector, only about 1-5 are received back on Earth, even
| under good conditions. They can be identified as originating
| from the laser because the laser is highly monochromatic.
|
| While there's no signal there, we're still looking at very
| sensitive equipment.
| RetroTechie wrote:
| 3. Use relays.
|
| Of course that would mean sending (a) giant receiver dish(es)
| in the general direction a probe is sent. On the flip side,
| if using a single relay it could travel at roughly 1/2 the
| speed of the probe.
|
| Note that signal strength weakens with distance^2. So if eg.
| you'd have 2 relays (1/3 and 2/3 between Earth & the probe),
| each relay would receive 9x stronger signal.
|
| No doubt the 'logistics' (trajectory, gravity assist options,
| mission cost etc) make this impractical. But it _is_ an
| option.
| ethbr1 wrote:
| That'd be really cool! And definitely helped by the fact
| that you'd only need to head out at a fraction of Voyagers
| speeds to get the benefit.
|
| There's some details on the Voyager gravity-assist
| mechanics here [0], but you'd also need the escape
| trajectory to be pointed in the Voyager direction which
| would further constrain...
|
| That said, Earth-Jupiter-Saturn alignments don't seem that
| rare (on a decades scale).
|
| [0] http://www.gravityassist.com/IAF3-2/Ref.%203-143.pdf
| nsguy wrote:
| TIL from another comment that the Shannon limit assumes
| Gaussian noise so it's not actually always the theoretical
| limit.
|
| You can't work around the Shannon limit by using encoding.
| It's the theoretical information content limit. But you can
| keep reducing the bandwidth and one way of doing that is
| adding error correction. So intuitively I'd say yes to your
| question, the distance can go to infinity as long as you're
| willing to accept an increasingly low receive bit rate.
| What's less clear to me is whether error correction on its
| own can be used to approach the Shannon limit for a given S/N
| ratio - I think the answer is no because you're not able to
| use the entire underlying bandwidth. But you can still
| extract a digital signal from noise given enough of a
| signal...
|
| EDIT: There is a generalization of the Shannon limit to non-
| white Gaussian noise here:
| https://dsp.stackexchange.com/a/82840
| mlok wrote:
| Maybe some kind of relay in space (maybe it could follow
| Voyager 1, slightly faster) which amplifies the signal and
| retransmits to Earth ?
| mpreda wrote:
| Maybe multiple receiving antennas could be used, spaced widely
| apart (e.g. one on Earth, one on the moon, one in orbit
| somewhere); each would receive some signal affected by noise,
| but the noise would be different for each (such as the
| atmosphere affecting only the on-ground antenna). Also given
| that we know the precise location of the transmitter, we can
| work-out the exact phase difference between the antennas. Some
| digital post-processing would combine the raw signal+noise from
| the multiple receivers and extract the signal.
|
| In fact, I assume that at this distance, even a very narrow
| signal would spread wide enough to illuminate more than just
| the Earth diameter.
| Symmetry wrote:
| The Shannon Limit is fundamental so you can't get around it
| directly. But yes, there are things you can do to receive
| information from further away.
|
| 1) A bigger dish is the most obvious one.
|
| 2) Use a lower bitrate to send more energy per bit at the same
| transmitter power.
|
| 3) Reduce the effective receiver temperature. This is a case
| where putting it outside the atmosphere might help in reducing
| noise.
| 7373737373 wrote:
| If the current number of photons per bit is 1500 and the
| effective limit at 8.3GHz is 25, that is a factor of 60.
|
| With each doubling of distance the number decreases by the
| inverse square law, so with the current setup we'd have a
| maximum distance of log2(60) = 5.9 times the current distance
| (about 163 astronomical units (AU)) which is 961 AU.
|
| In comparison, the closest star to our sun, Proxima Centauri,
| is 268774 AU away!
|
| Which means we would need something 268774/961 ~= 280 times
| SQUARED = 78222 times more sensitive than the current setup at
| the Shannon limit to communicate with it if it managed to get
| that far.
| kibwen wrote:
| _> So what does that conclusion mean about when the probe will
| be so far away that we are below the Shannon limit?_
|
| I think the practical limit right now is that the Voyagers are
| losing power.
|
| _" The radioisotope thermoelectric generator on each
| spacecraft puts out 4 watts less each year. [...] The two
| Voyager spacecraft could remain in the range of the Deep Space
| Network through about 2036, depending on how much power the
| spacecraft still have to transmit a signal back to Earth."_
|
| https://voyager.jpl.nasa.gov/frequently-asked-questions/
| Dylan16807 wrote:
| > And can we beat the Shannon limit somehow, eg collect for
| longer
|
| If you turn on a faucet for longer, you're not beating the
| "gallon limit" of the system. The limit is not a fixed number,
| it's directly based on how much you do to improve the signal.
|
| And they have already slowed down the transmission speed
| repeatedly.
| amirhirsch wrote:
| TLDR; 4e22 photons per second 2.6e22 per bit.
|
| For comparison, ~2e26 photons will be received through your iris
| in your life
| KeplerBoy wrote:
| Does this number account for all photons or just those in the
| rather narrow optical band?
|
| Then again RF photons just don't fit through the pupils and
| will get backscattered, i guess.
| amelius wrote:
| How many of them come from Voyager 1?
| amirhirsch wrote:
| Someone's asking the hard questions! According to the oracle,
| 1 in 4 people will experience one photon from voyager in
| their lifetime.
| rcxdude wrote:
| That's how many are _sent_ by Voyager. Only about 1500 or 400
| photons per bit are actually received by the radio dish
| (depending on which frequency is being used).
| croemer wrote:
| Maybe OP sends photons from their eyes in addition to
| receiving them
| pcdoodle wrote:
| I am confused. I thought photons were just visible light but I
| guess these little buggers are everywhere. Also very surprised
| voyager is using 2.3ghz, that's crazy saturated on earth due to
| wifi. How these engineers make this all work, is magic to me.
| mpreda wrote:
| _Electromagnetic radiation_ includes visible light, radio
| spectrum, X-rays, etc. Photons.
| nilamo wrote:
| > Also very surprised voyager is using 2.3ghz, that's crazy
| saturated on earth due to wifi
|
| Wifi didn't exist when Voyager was launched...
| thsksbd wrote:
| But the band was free for use, wasn't it? (Obviously not
| crowded)
| anotherhue wrote:
| Available for microwaves since 1947, intentional emission
| came later in the 80s.
| ianburrell wrote:
| The ISM band is 2.4-2.5 GHz. Voyager at 2.3Ghz is outside
| the band.
| drmpeg wrote:
| WiFi is at 2.4 GHz. LTE band 30, satellite radio (XM/Sirius)
| and aeronautical telemetry all exist between the deep space
| downlink at 2290 to 2300 MHz and WiFi at 2400 MHz.
| noneeeed wrote:
| Nope. It's one of those things that can take a bit to get used
| to, but everything on the electromagnetic spectrum is just
| light in the general sense. The only difference between radio-
| waves, x-rays, infra-red and (human) visible light is the
| frequency/wavelength.
|
| If the frequency is high enough then the waves of light can be
| detected by things as small as cells in the back of your eye,
| or the pixels in a camera sensor. If it is too low then you
| need much larger detectors.
|
| Other animals have detectors for different
| frequencies/wavelengths, allowing them to see either infra-red
| (mosquitos) or ultraviolet (bees, butterflies etc).
|
| What we call "visible light" is just the particular range that
| our eyes can detect (about 400 to 800THz). If we were the size
| of a planet, and our eye cells were the size of a radio-
| telescope dish we would be able to "see" in those wavelengths.
| In fact, when we see images taken by radio telescopes, those
| have been essentially pitch-shifted up to something we can see,
| like the reverse of what we do when listening for bat clicks
| (where the pitch is downshifted to our hearing range).
|
| The wikipedia article has a nice little diagram putting the
| wavelengths into perspective.
| https://en.wikipedia.org/wiki/Electromagnetic_spectrum
| pcdoodle wrote:
| Thanks for the reply.
|
| This makes me think of the dual slit experiment. Does the
| universe treat everything as a wave to save CPU cycles or
| something?
|
| If we think of light as little balls (at our size i think
| that would make sense). If we were much bigger, we would
| think of these longer waves as balls too?
| SJC_Hacker wrote:
| Wave-particle duality/quantum mechanics have different
| interpretations, but since "the math works" and there's
| nothing better, thats what they go with.
|
| One way of thinking of it - everything is a wave until you
| make a measurement. Then you get a "collapse"
| (localization) of the wavefunction. Which leads to the
| question of why the wave function collapses - i.e. how does
| nature know we want to make a measurement.
|
| Which leads to all sorts of crazy ideas like the simulation
| hypothesis. Which is not a scientific theory, because you
| can't falsify it, but even very educated people like Neil
| DeGrasse Tyson have remarked on it.
| pythonguython wrote:
| Photons and waves both model electromagnetism. Photons are just
| the quantization of electromagnetic radiation, where E=hv. This
| is the whole idea of wave-particle duality. We often describe
| radio frequencies with waves because they act more like waves
| than particles (Diffraction, spherical propagation, have an
| easily measureable wavelength)
| einsteinx2 wrote:
| Photons are just the quanta or particles of electromagnetic
| radiation, of which visible light is a small portion of the
| overall spectrum. So you can have photons of microwaves as
| well, such as in this case. Or photons of X-rays or gamma rays
| or infrared light or ultraviolet light or whatever. It's pretty
| wild actually just how small a section of the EM spectrum our
| eyes are sensitive to!
| BenjiWiebe wrote:
| 2.3 GHz is not saturated due to WiFi. Wifi is 2.4GHz and up.
| Even the harmonics will be above 2.4 GHz (by definition).
| moffkalast wrote:
| You know, I never really thought of lower wavelengths than light
| as being carried by photons, but I suppose it's all EM. Antennas
| are technically just really red light bulbs.
| gjstein wrote:
| This is true enough, though remember that material properties
| change dramatically when you start moving through wavelengths
| by orders of magnitude. Silicon is transparent in the mid-
| infrared, which is what makes silicon photonics possible [1]
|
| [1] https://en.wikipedia.org/wiki/Silicon_photonics
| bandrami wrote:
| It's crazy to me how many theoretical limits Shannon predicted
| way before the hardware was there.
| ziofill wrote:
| That's because his results are about pure information (and in
| the limit for infinite string lengths), so sooner or later some
| hardware will hit onto those limits or tend to them.
| bandrami wrote:
| Agreed, but: he's still understudied. I think in retrospect
| any 21st-century math course has to include Shannon, and they
| don't all, yet.
| sebzim4500 wrote:
| On some level he's a victim of his own success. He invents
| information theory in the same paper that proves the most
| interesting results, so who else will work on it?
| aidenn0 wrote:
| Even the practical work was done surprisingly early. I
| have a book on error correcting codes from the 1950s and
| it's missing very little (Most notably trellis codes and
| LDPC; the former being invented in the '70s and the
| latter in 1963).
| sebzim4500 wrote:
| There's been much more progress on compression though
| (Arithmetic Coding, ANS, etc.)
| moffkalast wrote:
| Shannon: "I'm about to make and end this field's whole
| career."
| Strilanc wrote:
| Wasn't expecting my question to hit top of HN. I guess I'll give
| some context for why I asked it.
|
| I work in quantum error correction, and was trying to collect
| interesting and quantitative examples of repetition codes being
| used implicitly in classical systems. Stuff like DRAM storing a 0
| or 1 via the presence or absence of 40K electrons [1], undersea
| cables sending X photons per bit (don't know that one yet), some
| kind of number for a transistor switching (haven't even decided
| on the number for that one yet), etc.
|
| A key reason quantum computing is so hard is that by default
| repetition makes things worse instead of better, because every
| repetition is another chance for an unintended measurement. So
| protecting a qubit tends to require special physical properties,
| like the energy gap of a superconductor, or complex error
| correction strategies like surface codes. A surface code can
| easily use 1000 physical qubits to store 1 logical qubit [2], and
| I wanted to contrast that with the sizes of implicit repetition
| codes used in classical computing.
|
| 1: https://web.mit.edu/rec/www/dramfaq/DRAMFAQ.html
|
| 2: https://arxiv.org/abs/1208.0928
| nico wrote:
| Very cool. It's interesting to realize that at some level,
| every system is a quantum system if you "zoom in" enough
| Ringz wrote:
| I would spontaneously respond that you are right and at the
| same time have no problem if someone explains to me that it
| is not so.
| empyrrhicist wrote:
| I think the point is the model though - if a system's
| behavior can be modeled/described classically, it's a bit
| silly to to call it a "quantum" system in the same way that
| it's reductive to say Biology is just applied particle
| physics. Sure, but that's not a very useful level of
| abstraction.
| jessriedel wrote:
| If you want to understand the transition between a
| fundamental theory and its effective description in some
| limiting regime, you need to be able to describe a system
| in the limiting regime using the fundamental theory. It's
| not "silly" to talk about an atom having a gravitational
| field even if it's unmeasurably small (currently).
| fsckboy wrote:
| > _at some level, every system is a quantum system_
|
| if we consider "quantum" to mean our quantum theory, at the
| level of general relativity, gravity is not a quantum system.
| and the qualifier "yet" is also not known.
| grog454 wrote:
| > by default repetition makes things worse instead of better
|
| Can you elaborate on this a bit? My intuition is that, by
| default, statistical models benefit from larger N. But I have
| no experience in quantum physics.
| ziofill wrote:
| It actually depends how this sentence is intended. There
| exist quantum repetition codes: the Shor code is the simplest
| example that uses 9 physical qubits per logical qubit. Since
| the information is quantum it needs majority voting over two
| independent bases (hence 3x3=9 qubits to encode a logical
| one).
| Strilanc wrote:
| It's because unintended measurement is a type of error in a
| quantum computer. Like, if an electron passing near your
| qubit would get pushed left if your qubit was 0 and right if
| was 1, then you will see errors when electrons pass by.
| Repeating the 0 or 1 a thousand times just means there's
| 1000x more places that electrons passing by would cause a
| problem. That kind of redundancy makes that kind of error
| mechanism worse instead of better.
|
| There _are_ ways of repeating quantum information that
| protect against accidental measurement errors. For example,
| if your logical 0 is |000 > + |110> + |011> + |101> and your
| logical 1 is |111> + |001> + |100> + |010> then can recover
| from one accidental measurement. And there are more complex
| states that protect against both bitflip errors and
| accidental measurements simultaneously. They're just more
| complicated to describe (and implement!) than "use 0000000
| instead of 0 and 1111111 instead of 1".
| Kerbonut wrote:
| If there's interference, could you do something like when
| using 7 repetition for each bit, take whatever 5 of 7 is,
| e.g. 1111100 is 1 and 1100000 is 0.
| nomel wrote:
| Is this the correct interpretation?
|
| Classical systems: You measure some state, with the
| measurement containing some error. Averaging the
| _measurement error_ usually gets closer to the actual
| value.
|
| Quantum systems: Your measurement influences/can influence
| the state, which can cause an error in the state itself.
| Multiple measurements means more possible influence.
| Strilanc wrote:
| Yeah that's roughly it. In classical computers all errors
| can be simplified as being bit flip errors (0 instead of
| 1, 1 instead of 0). Like, power loss is a lot of bit flip
| errors that happened to target the bits that should have
| been 1. In quantum computers this simplification does not
| work, there is another type of error called a phase flip.
| Measurements cause phase flip errors. You can exchange
| the phase flip and bit flip bases by using a gate called
| the Hadamard gate. So if you surround measurements with
| Hadamard gates, you will see bit flip errors. The
| existence of gates like Hadamard is what makes it
| possible to see these kinds of things at all, and
| correspondingly its availability can be thought of as the
| thing that makes a quantum computer a quantum computer,
| instead of a classical computer.
| Sniffnoy wrote:
| You might be making the mistake of thinking that quantum
| mechanics runs on probabilities, which work in the way you
| are used to, when in fact it runs on amplitudes, which work
| quite differently.
| cycomanic wrote:
| Subsea cables don't use repetition codes (they are very much
| suboptimal), but typically use large overhead (20%) LDPC codes
| (as do satellite comms systems for that matter (the dvb-s2
| standard is a good example). Generally to get anywhere close to
| Shannon we always need sophisticated coding.
|
| Regarding the sensitivity of Subsea systems they are still
| significantly above 1 photon/bit, the highest sensitivity
| experiments have been done for optical space comms (look e.g.
| for the work from Mit Lincoln Labs, David Geisler, David Kaplan
| and Bryan Robinson are some of the people to look for.
| Strilanc wrote:
| I think you're picturing a different level of the network
| stack than I had in mind. Yes, above the physical level they
| will be explicitly using very sophisticated codes. But I
| think physically it is the case that messages are transmitted
| using pulses of photons, where a pulse will contain many
| photons and will lose ~5% of its photons per kilometer when
| travelling through fiber (which is why amplifiers are needed
| along the way). In this case the "repetition code" is the
| number of photons in a pulse.
| cycomanic wrote:
| But we are classical, so I think it's wrong (or at least
| confusing) to talk about the many photons as repetition
| codes. Then we might as well start to call all classical
| phenomena repetition codes. Also how would you define SNR
| when doing this?
|
| Repetition codes have a very clearly defined meaning in
| communication theory, using them to mean something else is
| very confusing.
| jessriedel wrote:
| > Then we might as well start to call all classical
| phenomena repetition codes
|
| All classical phenomena _are_ repetition codes (e.g.,
| https://arxiv.org/abs/0903.5082 ). And this is perfectly
| compatible with the meaning in communication theory,
| except that the symbols we're talking about are the
| states of the fundamental physical degrees of freedom.
|
| In the exact same sense, the von Neumann entropy of a
| density matrix is the Shannon entropy of its spectrum,
| and no one says "we shouldn't call that the Shannon
| entropy because Shannon originally intended to apply it
| to macroscopic signals on a communication line".
| Strilanc wrote:
| Yeah, I agree it's unusual to describe "increased
| brightness" as "bigger distance repetition code". But I
| think it'll be a useful analogy in context, and I'd of
| course explain that.
| fsckboy wrote:
| > _How many photons are received per bit transmitted from
| Voyager 1?_
|
| wouldn't you also want to know how many photons are transmitted
| and how many bits transmitted are received?
| stracer wrote:
| All transmitted bits are also received, at least when
| everything works as intended.
| forgot-im-old wrote:
| No, with error correction, not all transmitted bits are
| received, but the message bits can be recovered.., and if
| not they must retransmit later.
| resters wrote:
| Isn't sending more than one photon always "repetition" in that
| sense? Classical systems probably don't do that because of the
| engineering complexity of sending a single photon at a time --
| we had oscillators and switches, not single photon emitters.
| jessriedel wrote:
| > Isn't sending more than one photon always "repetition" in
| that sense?
|
| Yes. But regardless of whether its feasible to send single
| quanta in any given circumstance, the redundant nature of the
| signals is key to understanding its much higher degree of
| robustness relative to quantum signals.
|
| And to be clear, you can absolutely send a classical signal
| with individual quanta.
| s1dev wrote:
| I believe that a classical radio receiver is measuring a
| coherent state. This is a much lower level notion than people
| normally think about in QEC since the physical DoF are usually
| already fixed (and assumed to be a qubit!) in QEC. The closest
| analogue might be different choices of qubit encodings in a
| bosonic code.
|
| In general, I'm not sure that the classical information theory
| toolkit allows us to compare a coherent state with some average
| occupation number N to say, M (not necessarily coherent) states
| with average occupation number N' such that N' * M = N. For
| example, you could use a state that is definitely not
| "classical" / a coherent state or you could use photon number
| resolving measurements.
|
| A tangential remark: The classical information theory field
| uses this notion of "energy per bit" to be able to compare more
| universally between information transmission schemes. So they
| would ask something like "How many bits can I transmit with X
| bandwidth and Y transmission power?"
| Sharlin wrote:
| > Stuff like DRAM storing a 0 or 1 via the presence or absence
| of 40K electrons
|
| I'd assume that these days it's a couple of orders of magnitude
| fewer than that (the cited source is from 1996). Incidentally,
| 40k e- is roughly the capacity of a single electron well
| ("pixel") in a modern CMOS image sensor [1] - but those 40k
| electrons are able to represent a signal of up to ~14 bits,
| around 10k distinct luminance values, depending on temperature
| and other noise sources.
|
| [1] https://www.princetoninstruments.com/learn/camera-
| fundamenta...
| Strilanc wrote:
| If you have a more modern estimate I'll take it. Very
| interesting about the CMOS sensors distinguishing +- 2
| electrons (40K / 2^14).
| dheera wrote:
| I worked in quantum optics for a while. Our DARPA grant once
| had the "mission" to see how many bits of information could be
| theoretically crammed into 1 photon. It turns out to be an
| uninteresting question because you can theoretically cram
| infinite bits into one photon, encoded in the relative timing
| of the photon in a pulse train, limited only by the dispersion
| of your medium (in space, effectively zero).
|
| Even dispersion is a boring question because it is possible to
| reverse dispersion by sending the light through a parametric
| amplifier to conjugate the phases and then running it through
| the dispersion medium a second time locally.
|
| We later ended up working on other things.
| cycomanic wrote:
| Actually the limit predicted by Shannon can be significantly
| beaten, because Shannon assumes gaussian noise, but if we use
| photon counting receivers we need to use a poisson distribution.
| This is the Gordon-Holevo limit.
|
| To beat Shannon you need PPM formats and photon counters (single
| photon detectors).
|
| One can do significantly better than the numbers from voyager in
| the article using optics even without photon cpunting. Our group
| has shown 1 photon/bit at 10 Gbit/s [1] but others have shown
| even higher sensitivity (albeit at much lower data rates).
|
| [1] https://www.nature.com/articles/s41377-020-00389-2
| nico wrote:
| Interesting. Is that related to compressed sensing? I wonder if
| compress sensing could be used for something like the Voyager
| signals
|
| It seems there might be multiple ways to go beyond Shannon's
| limit, depending on what you are trying to do
| cycomanic wrote:
| I don't think compressed sensing is really extracting more
| information than Shannon, it simply exploits the fact that
| the signal we are interested in is sparse so we don't need to
| sample "everything". But this is somewhat outside my area of
| expertise so my understanding could be wrong.
| nico wrote:
| Maybe I'm mixing Shannon's limit with the sampling rate
| imposed by the Nyquist-Shannon Sampling theorem
|
| > Around 2004, Emmanuel Candes, Justin Romberg, Terence
| Tao, and David Donoho proved that given knowledge about a
| signal's sparsity, the signal may be reconstructed with
| even fewer samples than the sampling theorem
| requires.[4][5] This idea is the basis of compressed
| sensing
|
| ...
|
| > However, if further restrictions are imposed on the
| signal, then the Nyquist criterion may no longer be a
| necessary condition. A non-trivial example of exploiting
| extra assumptions about the signal is given by the recent
| field of compressed sensing, which allows for full
| reconstruction with a sub-Nyquist sampling rate.
| Specifically, this applies to signals that are sparse (or
| compressible) in some domain
|
| From: https://en.m.wikipedia.org/wiki/Nyquist%E2%80%93Shann
| on_samp...
| sunk1st wrote:
| In so many words, Shannon gave a proof showing that _in
| general_ the sample rate of a digital sensor puts an
| upper bound on the frequency of any signal that sensor is
| able to detect.
|
| Unlike the Nyquist-Shannon theory, compressed sensing is
| not generally applicable: it requires a sparse signal.
|
| As with many other optimization techniques, it's a trade
| off between soundness and completeness.
| nico wrote:
| Great way to explain it!
|
| Loved this:
|
| > As with many other optimization techniques, it's a
| trade off between soundness and completeness
| ramraj07 wrote:
| Can't you calculate the CRLB for any given distribution if you
| wanted? That's what my lab did for microscopy anyway. Saying
| you're beating the Shannon limit is like saying you're beating
| the second law of thermodynamics to me.. but I could be wrong.
| Sanzig wrote:
| You are correct. People often say "Shannon limit" (the
| general case) when they are really referring to the "Shannon-
| Hartley Limit" (the simplified case of an additive white
| Gaussian noise channel).
|
| For example, MIMO appears to "break" the Shannon-Hartley
| limit because it does exceed the theoretical AWGN capacity
| for a simple channel. However, when you apply Shannon's
| theory to reformulate the problem for the case of a multipath
| channel with defined mutual coupling, you find that there is
| a higher limit you are still bounded by.
| s1dev wrote:
| I often wondered why MIMO was such an investigated topic.
| It would make sense if the Shannon limit is higher for this
| channel. Is there a foundational paper or review that shows
| this?
| cycomanic wrote:
| Shannon theory assumes Gaussian noise, however in the very
| low power regime that's just not true. I agree it's
| unintuitive. Have a look at the Gordon paper I posted
| earlier.
| aptitude_moo wrote:
| Very interesting, I studied telecommunications and I thought
| the Shannon limit was the absolute limit. I wonder now if this
| Gordon Holevo limit is applicable for "traditional"
| telecommunications (like 5G) as opposed to photon counting a
| deep space probe
|
| EDIT: This paper seems to answer my question [1]
|
| [1]
| https://opg.optica.org/directpdfaccess/8711ab35-bbc2-4d51-8e...
| stracer wrote:
| Can you please post another link? This one does not work.
| HappyPanacea wrote:
| I think it is https://arxiv.org/abs/2002.05766.
| richarme wrote:
| I think it's this one:
|
| https://opg.optica.org/jlt/viewmedia.cfm?uri=jlt-38-10-2741
| &...
|
| Quantum Limits in Optical Communications
|
| Konrad Banaszek, Ludwig Kunz, Michal Jachura, and Marcin
| Jarzyna
| adrian_b wrote:
| As also explained in the conclusion of the paper linked by
| you, "photon-counting" detectors are possible only when the
| energy of one photon is high enough, which happens only for
| infrared light or for higher frequencies.
|
| "Photon-counting" methods cannot be implemented at
| frequencies so low as used in 5G networks or in any other
| traditional radio communications.
| IndrekR wrote:
| /at room temperature/
|
| https://en.wikipedia.org/wiki/Johnson%E2%80%93Nyquist_noise
| stracer wrote:
| Is there some fundamental limit to the number of bits per
| photon that can be communicated via EM radiation? I think it
| does not exist, because photons aren't all equal, we can use
| very high frequency and X-ray quantum can probably carry much
| more information than RF quantum.
| resters wrote:
| this is called the Shannon limit. To discern signal from
| noise, a minimum sample rate of 2x the frequency of the
| signal is required. A signal is something that can be turned
| on or off to send a bit.
|
| Higher frequencies can carry more data as you infer but the
| engineering challenges of designing transmitters and
| receivers create tradeoffs in practical systems.
| ganzuul wrote:
| In addition to wavelength EM also has several polarization
| modes and near/far field characteristics that can carry
| information.
| resters wrote:
| Can individual photons be measured for polarization and
| phase or is there a similar limit that requires more than
| one photon to do so? I suppose both are relative to some
| previous polarization or phase?
| ganzuul wrote:
| Good induction to thinking about quantum gravity.
| im3w1l wrote:
| Send three photons A B C. They arrive at times ta, tb, tc.
| Compute fraction (tc - tb) / (tb - ta). This can encode any
| positive real number with arbitrary precision. But clearly
| you need either very precise measurements or send the photons
| at a very slow rate.
| yyyfb wrote:
| I guess not without a minimum bound on the communication
| speed.
|
| If you have a way to reliably transmit N bits in time T using
| P photons, you can transmit N+1 bits in time 2 * T using also
| P photons. What you would do to transmit X0,X1,...Xn is:
|
| - During the first time slot of duration T, transmit X1,...
| Xn if X0 = 0 and 0 otherwise (assuming absence of photons is
| one of the symbols, which we can label 0)
|
| - During the second time slot of duration T, transmit 0 if
| X0=0 and X1,... Xn otherwise
|
| This only uses P photons to transmit one more bit, but it
| takes twice as long. So if you're allowed to take all the
| time that you want to transmit, and have really good clocks,
| I guess that theoretically this is unbounded.
| sansseriff wrote:
| The Deep Space Optical Communication (Dsoc) between earth and
| the psyche spacecraft uses large-M PPM for this reason! This
| mission is currently ongoing.
|
| They send optical pulses in one of up to 128 possible time
| slots, thereby carrying 7 bits each. And each optical pulse on
| earth may only be received by 5-10 photons.
| ziofill wrote:
| What a lovely question. The estimate is 10-100 photons/bit
| (minimum).
|
| If you're curious about how many bits a _single_ photon can
| carry, in controlled settings (tabletop quantum optics) a single
| photon can carry log(n) bits where n is the size of the state
| space of the photon, which theoretically is infinite and in
| practice it can reach into the hundreds /thousands.
| layer8 wrote:
| No, the estimate is around 750 or 200 photons/bit received,
| depending on the transmission frequency. The answer to the
| question is B, not C. Your numbers are the estimated minimum
| needed, not the actual amount received, which is what the
| question was asking.
| mnw21cam wrote:
| Visible light is different, because each photon has a lot more
| energy than in the 2.3GHz range. Your average decent consumer-
| level camera has a sensor that can nominally just about detect
| single photons some proportion of the time (as in, some of them
| bounce off instead of being detected) though it can't
| technically _count_ them. The graininess on digital camera
| images is more from the Poisson noise of the incoming photons
| than it is from the applied noise of the sensor itself.
| HarHarVeryFunny wrote:
| The fact that we can communicate with Voyager, and in both
| directions, blows my mind. It's completely counter-intuitive.
|
| At least for Voyager->earth we can use giant radio telescopes to
| detect the faint signal, but how do we manage to focus on those
| few hundreds of photons per bit coming from a pinpoint source a
| light day away?!
|
| In the earth->Voyager direction it seems even less intuitive -
| sure we can broadcast a powerful signal, but it's being received
| by a 12' wide antenna 15 billion miles away. WTF?
|
| I guess radio communications in general is magic, a bit like (in
| nature of counter-intuition) quantum entanglement of particles
| arbitrarily far apart. It seems there is something deeply wrong
| about our mental models of space and time.
| cycomanic wrote:
| For anyone who is interested in the ultimate limits to
| communications the seminal paper by Jim Gordon is quite easy to
| understand even without a physics degree (unlike the Holevo paper
| IMO). He was incredibly good at writing in an accessible manner
| (apart from probably being the person who most deserved a Nobel
| prize but didn't get it).
|
| https://doi.org/10.1109%2FJRPROC.1962.288169
| prof-dr-ir wrote:
| > probably being the person who most deserved a Nobel prize but
| didn't get it
|
| You probably want to read up a bit on the remarkable life of
| Lise Meitner.
| superposeur wrote:
| The overwhelming loss in this calculation is from the antenna's
| radiated energy spreading out over a larger and larger area
| (despite the directional "gain" factor).
|
| I'm wondering: would a probe launched today instead employ a
| laser to communicate? This would seem to offer many orders of
| magnitude improvement in the directionality of the signal.
| deelowe wrote:
| I imagine it'd certainly employ some type of beamforming at the
| least.
| wongarsu wrote:
| Assuming you don't need fast steering, is a 3.7m transmitter
| array doing beamforming really better than a 3.7m dish
| transmitting at the same power?
|
| My intuition would have been that you are better off using a
| fairly standard transceiver and spending your engineering
| budget either increasing power or getting a bigger dish
| (either by launching on a wider rocket or with a folding
| design).
|
| Lasers might interesting for the downlink, but receiving a
| laser signal on the probe sounds difficult (earth is pretty
| bright).
| cycomanic wrote:
| Diffraction scales inversely proportional to wavelength so
| you gain significantly by going to optics, i.e. you can use
| a much smaller aperature in optics.
| outworlder wrote:
| There's some value in getting rid of mechanical devices (or
| reducing the need to rotate the entire spacecraft).
| CamperBob2 wrote:
| The array doing beamforming can be spread out much farther.
| If the DSN were being built now, I'd think its antennas
| would look more like the Square Kilometer Array.
| magicalhippo wrote:
| Seems they're already on to something like that[1][2]:
|
| _We envision deployment in three sites at or near the
| longitudes of the existing DSN sites._
|
| _As an example, a potential initial phase could deploy
| 40 12-m elements at each complex to duplicate the X-band
| performance of a DSN 70-m antenna._
|
| _Second and third phase deployments may bring the number
| of 12-m antennas to 200, then perhaps 400 per complex._
|
| [1]: https://ieeexplore.ieee.org/document/4374100
|
| [2]: https://ieeexplore.ieee.org/document/4374103
| londons_explore wrote:
| The main challenge is the earth to probe comms for distant
| probes, since the earth is often very close (in an angular
| sense) to the sun from the probes perspective, and the sun
| gives out a lot of black body radiation.
|
| However, due to the shape of the black body radiation curve,
| the sun gives out relatively less microwave radiation than it
| does visible light, which might outweigh the advantages of more
| directionality given by using a laser.
| jjk166 wrote:
| Further, we're good at building really big radio transceivers
| here on Earth, we don't have nearly the same technical
| experience with lasers of that scale.
| superposeur wrote:
| Ok what about using a maser instead of a laser?
| opwieurposiu wrote:
| The big dish antennas do use ruby masers, but not to
| transmit. The maser is used as the LNA on the receive side.
| Check out the picture on page 41 of the pdf, clearly this a
| flux capacitor, mislabeled to deceive us ;)
|
| https://descanso.jpl.nasa.gov/monograph/series10/03_Reid_ch
| a...
|
| https://www.rfcafe.com/references/popular-
| electronics/amazin...
| superposeur wrote:
| Cool use of maser for receive.
|
| Not having thought this through before, I see now that
| while a transmit maser may have efficiency advantages, it
| may not improve directionality relative to a standard
| parabolic radio transmitter. All methods of producing
| microwaves will have basically the same diffraction-
| limited gain for a given "aperture" (dish) size. That
| darn uncertainty principle! (However, an optical laser
| would still give way better directionality.)
| sebzim4500 wrote:
| Presumably though it would be useful to have a high bandwidth
| link back to earth even if we had to use conventional
| microwave transmitters to send data back.
|
| We want to download high resolution images/spectrographs
| whereas we only want to upload code/instructions.
| Out_of_Characte wrote:
| There's several projects for laser-based communication and
| research. It would also make it really difficult to aim since
| you can miss your target now.
|
| https://www.jpl.nasa.gov/news/nasas-deep-space-optical-comm-...
|
| https://en.m.wikipedia.org/wiki/Laser_Interferometer_Space_A...
| superposeur wrote:
| Interesting about the JPL program and I'm amazed this
| prototype was only launched last year! Apparently the answer
| to comms laser use is "not yet but soon".
| cycomanic wrote:
| All space agencies have optical comms in their road maps.
| Largely they are thinking about inter satellite communications
| (the atmosphere causes significant issues when going back to
| earth). So the main application is to have some relay satellite
| that can then transmit to earth via RF. The application is not
| mainly deep space ropes but Leo or meo satellites, the
| typically only have very short transit times over the ground
| stations, so can't get all their measurement data down. By
| using e.g. a geo relay they can transmit lots of data optically
| and the geo relay can more slowly transmit the data to earth
| until the leo satellite comes back in view.
| mordae wrote:
| Improving directionality also makes aiming much harder.
| sunk1st wrote:
| Perhaps we should consider relaying the signal through a third
| satellite.
| CobrastanJorji wrote:
| I'm curious about the feasibility of combining the two problems
| of propulsion alway from Earth and communication with Earth
| into beam-powered propulsion aimed directly at Earth, pulsed
| for use as communication.
|
| Probably infeasible for several reasons (only useful when
| accelerating DIRECTLY away from Earth, incoming light to power
| spaceship is probably coming from the sun and therefore likely
| also in the directly of Earth, so net zero acceleration at best
| from firing the photons back towards the sun), but it'd be
| pretty neat.
| hammock wrote:
| >Voyager sends 160 bits/second
|
| This makes me wonder, are the bits = the power turned on for
| exactly 1/320th sec, every 1/160th sec? Or is the power on/power
| off ratio something different? Does it vary by protocol? What are
| the pros and cons?
| danbruc wrote:
| Without looking up what kind of encoding and modulation they
| are using, I would assume that they are sending a continuous
| sine wave at the carrier frequency that has the bits - probably
| after encoding the raw data bits with some error correction
| code - modulated onto it by changing frequency, amplitude,
| phase, or a combination of them depending on the value of each
| bit or group of bits.
| ks2048 wrote:
| Nice question. Does anyone know what exactly data is being sent?
| What kind of compression it is using? etc
| mooktakim wrote:
| Why didn't they send out new relays as Voyager travelled out.
| somat wrote:
| An interesting thing about photons (which may not be true, I just
| enjoy this stuff amateurishly, that is, without the effort or
| rigor to actually understand it.) is that they might not exist.
| the em field is not quantized, or at least is not quantized at
| the level of photons. A "photon" only exists where the em field
| interacts with matter, where the electrons that create the
| disturbance can only pulse in discrete levels.
|
| https://www.youtube.com/watch?v=ExhSqq1jysg
|
| Not that this changes anything, we can only detect or create
| light with matter. but it does make me curious about single
| photon experiments and what they are actually measuring.
| leetrout wrote:
| Thanks for the link. I never conceptualized photons outside of
| the visual spectrum so the headline made me take a step back
| and get nerd sniped in the process.
|
| I stumbled upon this before seeing your comment:
|
| https://physics.stackexchange.com/questions/90646/what-is-th...
| golergka wrote:
| Isn't that simply the principle of particle-wave duality? When
| particle/wave in field X interacts with field X, it behaves
| like a wave, but interactions with other fields are quantised.
| croemer wrote:
| That's why I love Physics and was enamoured with it in my late
| teens.
| wwarner wrote:
| 23 watts.
| tb0ne wrote:
| Super interesting! But I feel like there is a bit of a conclusion
| missing for me.
|
| So 1500 Photons hit the receiver per bit send, but this is
| obviously way to few to keep processing the signal and it will
| just be drowned out by noise? Where do we go from here? Does
| voyager repeat its signal gazillions of times so we can average
| out the noise on our end? Where can I find more information on
| what is done with these few photons?
| SonOfLilit wrote:
| No, those 1500 photons are enough and we basically read the
| signal from them, from my reading of the comments here.
| PeterCorless wrote:
| I just wanted to chime in with a reminder that though Voyager 1
| is speeding away from Sol at a constant velocity because of the
| Earth's revolution around the sun it can be up to +-1 AU closer
| or further away, depending on the time of the year.
|
| This article is for Voyager 2, but the issue is the same. For a
| brief moment every year we actually get _closer_ to Voyager 1,
| then we pivot away in our revolution around the sun and the
| distance between Earth and Voyager 1 or 2 increases sharply. So
| distance, when plotted over time, looks like a wobbly line.
|
| https://earthsky.org/space/voyager-spacecraft-getting-closer...
| rocho wrote:
| Wow, I never thought about how Voyager communicates with Earth.
| But now I wonder: if Voyager just sends photons towards the
| Earth, at the receiving end how are we recognizing which photons
| are coming from Voyager and how is the "signal" decoded?
| RachelF wrote:
| Two main reasons for recognizing the photons: They have a
| specific frequency, 8.3GHz in this example. It's like tuning an
| FM radio to a station. The photons are coming from a specific
| direction.
|
| As to how they are decoded, you'll need to understand some
| modulation techniques.
| RachelF wrote:
| What is equally impressive is the number of photons received from
| radar imaging of asteroids.
|
| They are closer, but the radar equation received power is
| inversely proportional to range to the fourth power, not range
| squared as with Voyager.
|
| Anything proportional to 1/R^4 degrades very quickly.
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