3 ms·

The problem is a variation of that, which makes it possible, as explained in the post. The large caveat is that the accuracy is probabilistic, and it’s expected

by asxd 5y ago

The problem is a variation of that, which makes it possible, as explained in the post. The large caveat is that the accuracy is probabilistic, and it’s expected that the receiver is getting many 1-bit from various sensors that are all measuring the same phenomena. It’s a bit like the concept of dithering in images, where visually we can represent shades of grays just by using many 1 bit pixels.

oh_my_goodness 5y ago
Yes, it's a variation on the problem ... but sending many bits to the receiver is a really significant variation on just sending one bit. I'm not sure whether so many people would be intrigued to read "How to send a real number using arbitrarily many bits."
- asxd 5y ago
  I think the motivation here is still compression. You know you’re going to have a bunch of input values coming in, and this is about how to minimize the size of each value. So the overall throughput required does go down in the end.
- adrian_b 5y ago
  Yes, both the blog and the Arxiv paper are very confusing, because they speak about estimating a real number "Using a Single Bit". It is obvious that there is no way of guessing more than 1 bit of a number after receiving a single bit (unless you have previously established a convention like 0=any_other_number, 1=a_certain_number, when you can estimate many bits when you receive a "1", but no bits when you receive a "0"). Looking at the text of the article, it is obviously that it does not refer to sending "a Single Bit", but to sending "a Single Bit" many times, because only then the variance and the other statistics used by them can be computed. If the problem is rephrased as "How to Send a Real Number Using a Single Bit" at each of many transmissions, then the problem becomes banal and it has been studied for more than 60 years, in the field of analog-digital and digital-analog conversions, under names like "stochastic converters", "delta modulation", "delta-sigma modulation", and a few others, and much better solutions are known than discussed in the article. (The corresponding problem in that field is how to measure an analog signal, i.e. the real number, with a single analog comparator and a single reference value, when you get just 1 bit of information, i.e. whether the measured value is smaller or greater than the reference. The simplest solution is to sum a random noise with the value to be measured, and then compute the average of the 1-bit values, but there are much more sophisticated methods).

by asxd 5y ago

oh_my_goodness 5y ago

Yes, it's a variation on the problem ... but sending many bits to the receiver is a really significant variation on just sending one bit. I'm not sure whether so many people would be intrigued to read "How to send a real number using arbitrarily many bits."

asxd 5y ago
I think the motivation here is still compression. You know you’re going to have a bunch of input values coming in, and this is about how to minimize the size of each value. So the overall throughput required does go down in the end.
adrian_b 5y ago
Yes, both the blog and the Arxiv paper are very confusing, because they speak about estimating a real number "Using a Single Bit". It is obvious that there is no way of guessing more than 1 bit of a number after receiving a single bit (unless you have previously established a convention like 0=any_other_number, 1=a_certain_number, when you can estimate many bits when you receive a "1", but no bits when you receive a "0"). Looking at the text of the article, it is obviously that it does not refer to sending "a Single Bit", but to sending "a Single Bit" many times, because only then the variance and the other statistics used by them can be computed. If the problem is rephrased as "How to Send a Real Number Using a Single Bit" at each of many transmissions, then the problem becomes banal and it has been studied for more than 60 years, in the field of analog-digital and digital-analog conversions, under names like "stochastic converters", "delta modulation", "delta-sigma modulation", and a few others, and much better solutions are known than discussed in the article. (The corresponding problem in that field is how to measure an analog signal, i.e. the real number, with a single analog comparator and a single reference value, when you get just 1 bit of information, i.e. whether the measured value is smaller or greater than the reference. The simplest solution is to sum a random noise with the value to be measured, and then compute the average of the 1-bit values, but there are much more sophisticated methods).