Timeline for Theorems that are essentially impossible to guess by empirical observation
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Dec 31, 2021 at 18:37 | comment | added | paul garrett | @PhilFreedenberg Wow! I had not been keeping track of such developments for several years now...! Amazing. | |
| Dec 31, 2021 at 18:34 | comment | added | Phil Freedenberg | In 2009 polar codes were shown to achieve 100% channel capacity. These are now being implemented in 5G cellular networks. | |
| Dec 30, 2021 at 14:16 | comment | added | Timothy Chow | @BubbleZ The catch is that most codes don't have an efficient decoding algorithm. I guess that one could imagine an alternative universe in which, prior to proving Shannon's theorem, people performed an empirical investigation by generating random codes and laboriously decoding them to discover that they have close to the channel capacity. But it's hard to imagine people executing exponential time decoding algorithms in the 1940s in order to test a hypothesis that they have no a priori reason to believe is true. | |
| Dec 30, 2021 at 10:09 | comment | added | BubbleZ | " "most"/"random" codes achieve close to channel capacity, " Doesn't that means that data supports Shannon's theorems ? | |
| S Dec 30, 2021 at 3:11 | history | answered | paul garrett | CC BY-SA 4.0 | |
| S Dec 30, 2021 at 3:11 | history | made wiki | Post Made Community Wiki by paul garrett |