[[Claude Shannon]] showed a simple but impracticalasymptotically optimal [[code]] that couldcan reach the theoretical capacity of a [[communication channel]]. It requires assigning a random code word to every possible <math>n</math>-bit message, then decoding by finding the closest code word. If <math>n</math> is chosen large enough, this beats any existing code and can get arbitrarily close to the capacity of the channel. Unfortunately, any <math>n</math> big enough to beat existing codes is also completely impractical.<ref>{{cite web |url=https://news.mit.edu/2010/explained-shannon-0115 |title=Explained: The Shannon limit |publisher=MIT News Office |author=Larry Hardesty |date=January 19, 2010}}</ref> These codes, though never used, inspired decades of research into more practical algorithms that today can achieve rates arbitrarily close to channel capacity.<ref>{{cite web |url=https://ocw.mit.edu/courses/6-451-principles-of-digital-communication-ii-spring-2005/1a3ad00d83d1d042da3328a8edd9edc2_chap13.pdf |title=Capacity-approaching codes (Chapter 13 of ''Principles Of Digital Communication II'') |publisher=[[MIT OpenCourseWare]] |date=2005}}</ref>
