标题： 具有幅度约束的公开讨论密钥协议 显示英文标题

标题： Secret-Key Agreement with Public Discussion subject to an Amplitude Constraint

摘要： 本文研究了在信道输入受到峰值功率约束$A$条件下，利用公共讨论实现秘密密钥协商的问题。证明了最优输入分布是具有有限支撑的离散分布。首先通过将秘密密钥信道模型转化为等效的高斯窃听信道（合法接收方具有更好的噪声统计特性），然后利用高斯窃听信道最优分布为离散这一事实，得到了该结论。为了克服寻找最优离散分布时计算量大的问题，提出了一些次优方案，并通过数值结果显示它们的性能接近于容量。此外，给出了秘密密钥容量的上下界，并用其证明当$A$趋于无穷大时，秘密密钥容量收敛到平均功率约束为$A^2$时的秘密密钥容量。最后，当幅度约束 \( A \) 较小时（$A \to 0$），证明了秘密密钥容量渐近等于具有幅度约束 \( A \) 且没有保密约束的合法用户的容量。 显示英文摘要

摘要： This paper 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. The result is obtained by first transforming the secret-key channel model into an equivalent Gaussian wiretap channel with better noise statistics at the legitimate receiver and then using the fact that the optimal distribution of the Gaussian wiretap channel is discrete. 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 ($A \to 0$), 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.