In information theory, the capacity of a memoryless channel is defined as the mutual information between the input and output distributions, maximized over all possible input symbol distributions. In fact, no known concrete family of codes has rate asymptotically approaching the capacity but a completely random family of codes, with symbols drawn randomly from a distribution that maximizes the mutual information between input and output distributions of the channel, does! I published this in 1948.

In information theory, the capacity of a memoryless channel is defined as the mutual information between the input and output distributions, maximized over all possible input symbol distributions. In fact, no known concrete family of codes has rate asymptotically approaching the capacity but a completely random family of codes, with symbols drawn randomly from a distribution that maximizes the mutual information between input and output distributions of the channel, does! Shannon published this in 1948.