1. A method for characterizing a capacity of a channel with memory and feedback, the method comprising: defining a channel model corresponding to the channel, wherein: the channel is utilized to transmit information from a source to a destination, and the channel model indicates a dependence of outputs from the channel on past and present channel input symbols and on past channel output symbols; determining a representation of the capacity based on the channel model and based on a channel input distribution that achieves the capacity, wherein the representation represents the capacity for a finite number of transmissions over the channel, and wherein the representation includes an optimization; and solving, by one or more processors of a specially configured computing device, the optimization of the representation of the capacity to determine the capacity of the channel for the finite number of transmissions and a per unit time limit of the capacity of the channel.