  In this paper, we present a general formula for the capacity region of a
general interference channel with two pairs of users. The formula shows that
the capacity region is the union of a family of rectangles, where each
rectangle is determined by a pair of spectral inf-mutual information rates.
Although the presented formula is usually difficult to compute, it provides us
useful insights into the interference channels. In particular, when the inputs
are discrete ergodic Markov processes and the channel is stationary memoryless,
the formula can be evaluated by BCJR algorithm. Also the formula suggests us
that the simplest inner bounds (obtained by treating the interference as noise)
could be improved by taking into account the structure of the interference
processes. This is verified numerically by computing the mutual information
rates for Gaussian interference channels with embedded convolutional codes.
Moreover, we present a coding scheme to approach the theoretical achievable
rate pairs. Numerical results show that decoding gain can be achieved by
considering the structure of the interference.
