4 ms·

I am not sure if you can use 1 photon per bit because (as I understand) emitting and capturing photons is a probabilistic process and when you have 1 photon, th

I am not sure if you can use 1 photon per bit because (as I understand) emitting and capturing photons is a probabilistic process and when you have 1 photon, there is a probability that it will not be captured by an antenna, but rather will be reflected or will turn into heat. Or am I wrong here?

eru 2y ago
In principle, you can send more than one photon per bit on average. Photons have a lot of ways they can encode additional bits, eg frequency, polarisation, timing. You are right that you can randomly lose some photons. That's what error correcting codes are. See https://en.wikipedia.org/wiki/Error_correction_code https://en.wikipedia.org/wiki/Error_correction_code As an example, assume every photon can encode 10 bits without losses, but you lose 10% of your photons. Then with a clever error correcting code you can encode just shy of 9 bits per photon. You can think of the error correcting code 'smearing' 9 * n bits of information over 10 * n photos, and as long as you collect 0.9 * n photons, you can recover the 9 * n bits of information. It's the same reason your CD still plays, even if you scratch it. In fact, you can glue a paper strip of about 1 cm width on the bottom of your CD, and it'll still play just fine. Go wider, and it won't, because you'll be exceeding the error correcting capacity of the code they are using for CDs.
- lebed2045 2y ago
  *typo: you can send more than one bit per photon on average I'm very curious to learn more about 1cm, what is the math behind it? Do you speak about classical music CD with ±700mb of capacity? I was always fascinating by ability of old super scratched optical disks still functioning without problems.
  - eru 2y ago
    > I'm very curious to learn more about 1cm, what is the math behind it? So I actually got that from a cool math talk I attended about 20 years ago. At the end the professor had a cool demonstration where he glued paper strips of various sizes radially on the CD, and exactly as the math he spend an hour explaining predicted, the CD player could cope with up to a 1cm width strip, but no more. Let me try to find some written material. https://en.wikipedia.org/wiki/Cross-interleaved_Reed%E2%80%93Solomon_coding https://en.wikipedia.org/wiki/Cross-interleaved_Reed%E2%80%9... is a good start, but doesn't go into the details. https://en.wikipedia.org/wiki/Reed%E2%80%93Solomon_error_correction https://en.wikipedia.org/wiki/Reed%E2%80%93Solomon_error_cor... might also be worth a read. In a nutshell, you arrive at the 1cm like this: you can look up what proportion of 'wrong' bits the CD's coding can correct and other overhead. Then you look up the circumference of a CD (about 28 cm), then you do some multiplication, and figure out that you can lose about 1cm out of every 28cm, and still be able to correct. Most of the interesting math happens at the first step of 'what proportion of errors can the music CD correct?' and more interestingly 'how does the CD player do that?' > I was always fascinating by ability of old super scratched optical disks still functioning without problems. Keep in mind that CD-ROMs have one additional layer of coding on top of what music CDs have. That's because if a bit error slips through the error correction chances are it still won't be audible to the human ear for music, but software might still crash with a single wrong bit. > Do you speak about classical music CD with ±700mb of capacity? Yes, that's because that's what I heard the talk about. I am sure more modern formats also have interesting error correction, but I don't know what they use and how much you could cover up.

eru 2y ago

In principle, you can send more than one photon per bit on average. Photons have a lot of ways they can encode additional bits, eg frequency, polarisation, timing. You are right that you can randomly lose some photons. That's what error correcting codes are. See https://en.wikipedia.org/wiki/Error_correction_code https://en.wikipedia.org/wiki/Error_correction_code As an example, assume every photon can encode 10 bits without losses, but you lose 10% of your photons. Then with a clever error correcting code you can encode just shy of 9 bits per photon. You can think of the error correcting code 'smearing' 9 * n bits of information over 10 * n photos, and as long as you collect 0.9 * n photons, you can recover the 9 * n bits of information. It's the same reason your CD still plays, even if you scratch it. In fact, you can glue a paper strip of about 1 cm width on the bottom of your CD, and it'll still play just fine. Go wider, and it won't, because you'll be exceeding the error correcting capacity of the code they are using for CDs.

lebed2045 2y ago
*typo: you can send more than one bit per photon on average I'm very curious to learn more about 1cm, what is the math behind it? Do you speak about classical music CD with ±700mb of capacity? I was always fascinating by ability of old super scratched optical disks still functioning without problems.
- eru 2y ago
  > I'm very curious to learn more about 1cm, what is the math behind it? So I actually got that from a cool math talk I attended about 20 years ago. At the end the professor had a cool demonstration where he glued paper strips of various sizes radially on the CD, and exactly as the math he spend an hour explaining predicted, the CD player could cope with up to a 1cm width strip, but no more. Let me try to find some written material. https://en.wikipedia.org/wiki/Cross-interleaved_Reed%E2%80%93Solomon_coding https://en.wikipedia.org/wiki/Cross-interleaved_Reed%E2%80%9... is a good start, but doesn't go into the details. https://en.wikipedia.org/wiki/Reed%E2%80%93Solomon_error_correction https://en.wikipedia.org/wiki/Reed%E2%80%93Solomon_error_cor... might also be worth a read. In a nutshell, you arrive at the 1cm like this: you can look up what proportion of 'wrong' bits the CD's coding can correct and other overhead. Then you look up the circumference of a CD (about 28 cm), then you do some multiplication, and figure out that you can lose about 1cm out of every 28cm, and still be able to correct. Most of the interesting math happens at the first step of 'what proportion of errors can the music CD correct?' and more interestingly 'how does the CD player do that?' > I was always fascinating by ability of old super scratched optical disks still functioning without problems. Keep in mind that CD-ROMs have one additional layer of coding on top of what music CDs have. That's because if a bit error slips through the error correction chances are it still won't be audible to the human ear for music, but software might still crash with a single wrong bit. > Do you speak about classical music CD with ±700mb of capacity? Yes, that's because that's what I heard the talk about. I am sure more modern formats also have interesting error correction, but I don't know what they use and how much you could cover up.