This letter studies the rate-equivocation region of a degraded signal-dependent noise wiretap channel (SDGN-WC), where the noise is Gaussian. This signal-dependent noise occurs in optical wireless communication (OWC) settings based on intensity modulation and direct detection (IM-DD). In this setup, the transmitted signals are nonnegative and are restricted by an average optical power constraint. We consider the rate-equivocation region of the degraded SDGN-WC and through solving a convex optimization problem, we establish that the support set of the optimal distributions must be countably infinite. Our result implies that when the transmitted optical signals are restricted by an average optical power: 1) the secrecy capacity is achieved by a distribution which has a countably infinite support set; 2) the channel capacity (the case with no secrecy constraints) is also achieved by a distribution having a countably infinite support set.

中文翻译：

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降级信号相关噪声窃听通道的速率等效区域的结果

这封信研究了退化的信号相关噪声窃听通道 (SDGN-WC) 的速率模棱两可区域，其中噪声为高斯。这种与信号相关的噪声出现在基于强度调制和直接检测 (IM-DD) 的光无线通信 (OWC) 设置中。在此设置中，传输的信号是非负的，并受平均光功率约束。我们考虑退化的 SDGN-WC 的速率模棱两可区域，并通过解决凸优化问题，我们确定最优分布的支持集必须是可数无限的。我们的结果表明，当传输的光信号受平均光功率限制时：1) 保密容量是通过具有可数无限支持集的分布实现的；