have knowledge of $\rvs^n$. The second term $H(\rvs|\rvye)$ is the rate of the additional secret key that can be produced by exploiting the fact that $\rvs^n$ is only known to the sender and the legitimate terminal. This scheme is causal since the multiplexed code uses only current state to decide which codebook to use. Furthermore, since the state is known to the sender and receiver, the second term is also causal.

We note that the capacity expression  captures an interesting tension between two competing forces in choosing the optimal distribution. To maximize the contribution of the rate obtained from the multiplexed wiretap codebook, it is desirable to select $\rvu$ to be strongly correlated with $\rvs$. However doing so will leak more information about $\rvs$ to the wiretapper and reduce the rate contribution of the second codebook. To maximize the contribution of the common state sequence, we need to select an input that masks the state sequence from the eavesdropper [@merhavShamai]. We illustrate this tradeoff via an example in section \[subsec:NumericalExample\].

Finally it can be easily verified that the the expression  simplifies in the following special case.

\[corol:LessNoisySymCap\] Suppose that for each $s \in \cS$ the channel $p_{\rvyr,\rvye|\rvs=s, \rvx}(y_r,y_e|s,x)$ is such 