Secret-Key Agreement With Public Discussion Subject to an Amplitude Constraint

This letter considers the problem of secret-key agreement with public discussion subject to a peak power constraint A on the channel input. The optimal input distribution is proved to be discrete with finite support. To overcome the computationally heavy search for the optimal discrete distribution, several suboptimal schemes are proposed and shown numerically to perform close to the capacity. Moreover, lower and upper bounds for the secret-key capacity are provided and used to prove that the secret-key capacity converges for asymptotic high values of A, to the secret-key capacity with an average power constraint A
²
. Finally, when the amplitude constraint A is small (A → 0), the secret-key capacity is proved to be asymptotically equal to the capacity of the legitimate user with an amplitude constraint A and no secrecy constraint.