In this work, we investigate the problem of secure broadcasting over block-fading wiretap channels with limited channel knowledge at the transmitter. More particularly, we analyze the effect of having a finite rate feedback on the throughput of multi-user broadcast wiretap channels. We consider that the transmitter is only provided by a $b$ -bits feedback of the main channel state information (CSI) sent by each legitimate receiver, at the beginning of each fading block, over error-free public links with limited capacity. Also, we assume that the transmitter is aware of the statistics of the eavesdropper’s CSI but not of its channel’s realizations. Under these assumptions of CSI uncertainty, we characterize the ergodic secrecy capacity of the system when a common message is broadcasted to all legitimate receivers, the ergodic secrecy sum-capacity when multiple independent messages are transmitted, and the ergodic secrecy capacity region for the broadcast channel with confidential messages (BCCM). In all three scenarios, we show that as long as the transmitter has some knowledge of the main CSI, obtained even through a 1-bit CSI feedback, a non-zero secrecy rate can still be achieved. The impact of having the feedback sent over a binary erasure channel (BEC) is also investigated for the BCCM case. Here again, and even with the possibility of having the feedback bits erased, a positive secrecy rate can still be achieved as long as the erasure event is not a probability-one event. An asymptotic analysis of the obtained results is provided for the high SNR regime, and the scaling law of the system, when the number of legitimate receivers is large, is also presented.

中文翻译：

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使用有限 CSI 反馈保护多用户广播窃听通道

在这项工作中，我们研究了在发送方信道知识有限的块衰落窃听信道上的安全广播问题。更具体地说，我们分析了有限速率反馈对多用户广播窃听信道吞吐量的影响。我们认为发送器仅由每个合法接收器在每个衰落块开始时通过容量有限的无差错公共链路发送的主信道状态信息 (CSI) 的 $b$ 位反馈提供。此外，我们假设发射机知道窃听者的 CSI 的统计信息，但不知道其信道的实现。在 CSI 不确定性的这些假设下，我们描述了当一个公共消息被广播到所有合法接收者时系统的遍历保密能力，传输多个独立消息时的遍历保密和容量，以及带有保密消息的广播信道（BCCM）的遍历保密容量区域。在所有三个场景中，我们表明只要发射机对主 CSI 有一些了解，即使通过 1 位 CSI 反馈获得，仍然可以实现非零保密率。对于 BCCM 情况，还研究了通过二进制擦除信道 (BEC) 发送反馈的影响。同样，即使有可能擦除反馈位，只要擦除事件不是概率为一的事件，仍然可以实现正保密率。当合法接收器的数量很大时，对高信噪比机制和系统的标度律提供了对所得结果的渐近分析，