Mathematicians often visualize this problem in terms of spheres. You can think of each code word as a high-dimensional point at the center of a sphere. If an error-filled message (when represented as a high-dimensional point) lives inside a given sphere, you know that the code word at the sphere’s center was the intended message. You don’t want these spheres to overlap — otherwise, a received message might be interpreted in more than one way. But the spheres shouldn’t be too far apart, either. Packing the spheres tightly means you can communicate more efficiently.
Anyone able to explain with an ELI5[1] what the link between error-correcting codes and the spheres is? I don't understand this paragraph.
The rest of the article is quite accessible, even though it is really hard to imagine what this should look like in higher dimensions...
Wow, these look like nice links. I'll start with the first one due to the more professional editing before deciding if I wanna dive into the professor's lecture... tnx
Anyone able to explain with an ELI5[1] what the link between error-correcting codes and the spheres is? I don't understand this paragraph.
The rest of the article is quite accessible, even though it is really hard to imagine what this should look like in higher dimensions...
EDIT: seems like it's also at the top of HN[2]
more accurately, explain it to me like I am not a mathematician ↩
#852273 Just having fun with footnotes now. ↩
The Hidden Geometry of Error-Free Communication
Einstein Lectures: Maryna Viazovska - Sphere packings in high dimensions and error correcting codes
not really ELI5, but interesting :)
Seems like I'll have to make time for the second one too. This
Another Roofchannel has some pretty good content...Wow, these look like nice links. I'll start with the first one due to the more professional editing before deciding if I wanna dive into the professor's lecture... tnx