信道状态信息和反馈对于一些广播信道容量和安全容量的影响

In recent years, wireless commnication maintains the fast development, the fundamental theory of which is strongly supported by the National Basic Research Program in China. Over the sea, there are also many important programs, for example, the Galileo Programme, the mars odyssey of NASA and so on.One of the big problems is of security. In this project, we focus on the capacity regions (including security parameters) of some broadcast channels affected by outside interference modelled as side information or channel state information,and with anti-interference means 'feedback'..In details, we first consider the model of wiretap channel (degraded broadcast channel) for the case that the main channel is controlled by channel state information (side information), and it is available at the transmitter in a noncausal manner or causal manner. Inner and outer bounds are derived on the capacity regions including security parameters for the noncausal and causal manners, and the secrecy capacity for both manners is also described and bounded, which provides the best transmission rate with perfect secrecy. Moreover, for the special case that the side information is available at the transmitter in a memoryless manner, both the capacity region and the secrecy capacity are determined. Second, the non-degraded wiretap channel (also of broadcast channel) with noiseless feedback is investigated, and the capacity region considering transmission rate and the equivocation to the wiretapper, will be determined. The secrecy capacity of this model is also formulated, which provides the best transmission rate with perfect secrecy. .Third, we investigate the model of degraded broadcast channel with noncausal side information, confidential messages and noiseless feedback, which is from Steinberg's work and Csiszar and K¨orner's work with confidential messages. Here the transmitter sends a confidential message to the non-degraded receiver, and meanwhile sends a common message to the both. Moreover, the channel for the nondegraded receiver is controlled by channel state information (side information), and it is available to the transmitter in a noncausal manner (termed here noncausal side information). In addition, we assume that there is a noiseless feedback from the output of the channel for the non-degraded receiver to the transmitter, and it helps them share a secret key, which enlarges the degraded receiver's uncertainty about the confidential message. Measuring the uncertainty by equivocation (conditional entropy), the capacity region composed of all achievable ratesequivocation triples is determined for this new model. Furthermore, the secrecy capacity is formulated, which provides the best transmission rate with perfect secrecy. In the end, we also investigate a situation that the multiple-access channel (MAC) is controlled by a channel state information sequence, which is available to the channel encoders in a causal or noncausal manner.

近年无线通信技术有了快速发展：在国内，宽带无线移动通信是面向国家重.大战略需求的基础研究内容；在国外，NASA 的火星探测、欧洲的伽利略计划蓬勃发展，而作为现代无线通信的动力与主要源泉之一的Shannon 信息论在国内相对研究较少。从通信环境来讲，无线通信的重要一环是干扰和相应安全问题。干扰可分为外在和内在，内在干扰多为模型内部信道之间的相互影响如干扰信道，外在干扰可以建模为边信息（又称信道状态信息），降低干扰的一种手段是反馈，分别影响编码器、信道物理属性等各个通信环节。另外，从通信目的来讲，多用户信息论中一个最基本的信道就是广播信道，一般广播信道的容量问题及纳入安全因素后的容量问题仍是多用户信息论中的困难问题之一。此次课题申请的主要研究内容为：以带边信息和反馈的一些广播信道安全容量问题或紧的可达区域问题为着眼点，主要使用Shannon信息论来研究相关的信道安全容量理论。

近年信息安全和通信技术有了快速发展，作为国家的两项重大战略需求，其交叉领域的基础研究意义重大。在信息论领域，课题组的主要研究内容包括如下两方面： . 关于从信道状态信息（边信息）和反馈的角度考察信道安全容量，课题组先着重研究了窃听信道模型下：第一，当主信道的信道状态信息能被发送方以无记忆的方式知道时，刻画了窃听者关于发送的消息的疑惑度以及信息传输效率之间的关系。在因果和有记忆的情况下，得到了容量区域的内外界。第二，当这个信道状态信息能以因果或者有记忆的方式被发送方知道，且合法用户接收者的信息能以因果的方式反馈到发送方的情况下，得到该窃听信道模型的容量区域以及安全容量。第三，反馈不能增加离散无记忆信道的信道容量，我们研究了反馈能不能增加窃听信道的容量区域的问题，答案是可以。第四，我们进一步研究了非降阶的窃听信道带反馈的一些模型，并且得到了它的容量区域和安全容量。然后，研究了在带信道状态信息的降阶广播信道模型下，如果发送方能以因果或者有记忆的方式得到信道状态信息，并且非降阶用户的信息能通过反馈而被发送方得到的情况下，该模型的容量区域以及安全容量问题。该模型是基于国际上非常热门的两个模型结合考虑而成。. 第二类窃听信道扩展模型的安全容量问题：第一个通信模型是一类带信源节点和多个信宿节点的特殊的窃听网络。我们求出了在强安全标准条件下的安全容量。第二个通信模型中, 信源消息被编码成随机序列并通过一条离散无记忆信道发送给合法的接收方。窃听者可以窃听主信道输出序列中的一些数据。课题组除了给出强安全标准下的安全容量外,还分析了该编码策略在有限长情况下的性能。第三个通信模型把一系列经典的窃听信道模型包含为它的特例, 如第一类窃听信道, 第二类窃听信道等。但窃听信道不用是主信道的降解形式。我们考虑了主信道为离散无记忆二元对称信道, 窃听信道为无噪的二类窃听信道的条件下, 安全容量不为0的充要条件。

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