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Broadcast Channels With Privacy Leakage Constraints

机译:具有隐私泄漏限制的广播频道

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The broadcast channel (BC) with one common and two private messages with leakage constraints is studied, where leakage rate refers to the normalized mutual information between a message and a channel symbol string. Each private message is destined for a different user and the leakage rate to the other receiver must satisfy a constraint. This model captures several scenarios concerning secrecy, i.e., when both, either or neither of the private messages are secret. Inner and outer bounds on the leakage-capacity region are derived when the eavesdropper knows the codebook. The inner bound relies on a Marton-like code construction and the likelihood encoder. A uniform approximation lemma is established that states that the marginal distribution induced by the encoder on each of the bins in the Marton codebook is approximately uniform. Without leakage constraints the inner bound recovers Marton’s region and the outer bound reduces to the UVW-outer bound. The bounds match for semi-deterministic (SD) and physically degraded (PD) BCs, as well as for BCs with a degraded message set. The leakage-capacity regions of the SD-BC and the BC with a degraded message set recover past results for different secrecy scenarios. A Blackwell BC example illustrates the results and shows how its leakage-capacity region changes from the capacity region without secrecy to the secrecy-capacity regions for different secrecy scenarios.
机译:研究了具有泄漏约束的一个公共消息和两个私有消息的广播信道(BC),其中泄漏率是指消息和信道符号串之间的归一化互信息。每个私人消息的目的地是不同的用户,并且到另一个接收者的泄漏率必须满足约束条件。该模型捕获了几种与保密有关的情况,即,当两个私人消息中的一个或两个都不为秘密时。当窃听者知道密码本时,就可以得出泄漏容量区域的内部和外部边界。内边界依赖于类似于Marton的代码构造和似然编码器。建立统一的近似引理,该引理指出由编码器在Marton码本中的每个bin上引起的边际分布近似均匀。没有泄漏约束,内边界将恢复Marton的区域,而外边界将减小为UVW的外边界。边界匹配半确定性(SD)和物理退化(PD)BC,以及具有退化消息集的BC。具有降级消息集的SD-BC和BC的泄漏容量区域可恢复不同保密方案的过去结果。一个Blackwell BC示例说明了结果,并显示了其泄漏容量区域如何从不保密的容量区域变为不同保密情况下的保密容量区域。

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