A Mathematical Theory of Communication

This paper opened the new area the information theory. Before this paper, most people believed that the only way to make the error probability of transmission as small as desired is to reduce the data rate (such as a long repetition scheme). However, surprisingly this paper revealed that it does not need to reduce the data rate for achieving that much of small errors. It proved that we can get some positive data rate that has the same small error probability and also there is an upper bound of the data rate, which means we cannot achieve the data rate with any encoding scheme that has small enough error probability over the upper bound.