Symmetric CSI Sample Clauses

Symmetric CSI. Numerical Example It can be easily seen that for the dirty paper coding example in section III-B, the secret-key capacity when s is also revealed to the legitimate receiver is infinity. More generally higher the entropy of s, higher will be the gains in the secret-key capacity with symmetric CSI. In this section illustrate the secret-key rate for an on-off channel for the receivers: yr = srx + zr (22) ye = sex + ze, ∈ { } where both sr, se 0, 1 , the random variables are mutu- ally independent and Pr(sr = 0) = Pr(se = 0) = 0.5. Furthermore we assume that sr is revealed to the legitimate terminals, whereas the eavesdropper is revealed y˜e = (se, ye). The noise random variables are mutually independent, zero ≤ mean and unit variance Gaussian random variables and the power constraint is that E[x 2] P . ∼ N ∼ We evaluate the secret-key rate expression for Gaussian inputs i.e., u = x (0, P0) when sr = 0 and u = x ≤ N (0, P1) when sr = 1. Further to satisfy the average power constraint we have that P0 + P1 2P . An achievable rate from Theorem 3 R = I(x ; yr|sr) − I(x ; y˜e|sr) + H(sr|y˜e) (23) = I(x ; yr|sr) − I(x ; ye, se|sr) + H(sr|se, ye) (24) is less noisy compared to the legitimate receiver’s channel. = 1 1 1 Then the secret-key capacity with sn revealed to both the 8 log(1 + P1) + 2 Eye [H(p(ye), 1 − p(ye))] + 2 , (25)
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Symmetric CSI. Consider the special case where the state sequence s is also revealed to the legitimate receiver. In this case we have a complete characterization of the secret-key capacity.
Symmetric CSI. Numerical Example It can be easily seen that for the dirty paper coding example in section III-B, the secret-key capacity when s is also revealed

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