The Shannon-Hartley theorem gives an upper bound for the channel capacity $C$ of a single transmission channel as
$$C = B \log_2 (1 + S/N),$$
where $B$ is bandwidth and $S/N$ is the signal to noise ratio.
Is there a generalization for this theorem for multiple (correlated) channels? It seems that correlations between channel signals would reduce the total amount of information, while correlations in noise across channels would increase it. However I haven't found a mathematical framework for dealing with this case.