A method for characterizing a capacity of a channel with memory and feedback comprises 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. The method further includes 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 the optimization of the representation of the capacity to determine the capacity of the channel for the finite number of transmissions.