and the dotted curve denotes contribution of the wiretap code. Note that in general there is a tradeoff between these two terms. To maximize the conditional entropy we set $P_0 = P_1=P/2$, while to maximize the wiretap codebook rate we need to set $P_0 = 0$ and $P_1 = P$. The resulting secret-key rate is maximized by selecting a power allocation that balances these two terms. The optimum fraction of power transmitted in the state ${\mathsf{s}_{r}}=0$ as a function of the signal to noise ratio is shown in Fig. \[fig:opt\]. Note that no power is transmitted when the signal-to-noise ratio is below $\approx -2.5 dB$. In this regime the channels are sufficiently noisy so that $H({\mathsf{s}_{r}}|\rvye,{\mathsf{s}_{e}}=1)
\approx 1$ even with $P_0 = 0$ and hence all the available power is used for transmitting the secret-message. As the signal-to-noise ratio increases more information regarding ${\mathsf{s}_{r}}$ gets leaked to the eavesdropper and to compensate for this effect, a non-zero fraction of power is transmitted when ${\mathsf{s}_{r}}= 0$.

Secret key generation with noncausal Transmitter CSI 
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In this section we provide Proofs of Theorem \[thm:lbNoDisc\] and \[thm:ubNoDisc\] i.e., the coding scheme and the upper bound for the secret key agreement problem.

Proof of 