带安全参数的通信模型容量区域的研究
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摘要
数据传输的高效性和安全性一直是通信中的两个最基本的研究课题。高效性意味着对于给定的通信系统模型,要设计出尽可能达到信道容量的编码方案,同时该编码方案所对应的译码错误概率要趋近于零。而安全性意味着如果存在窃听者,即使他知道所有的编码方案的细节,他也不能窃听到任何的信息。本文从多用户信息论的角度,对通信网络中数据传输的高效性和安全性进行了详细的研究。
在高效性方面,本文对带信道状态信息的多接入信道模型的容量区域进行了研究(该问题是Gel'fand-Pinsker信道在多接入信道模型中的推广),找到了能达到信道容量的编码和译码方案,同时也求出了该模型下的容量区域的具体数学表达式。该问题属于热点问题,但是以往的工作均只求出了一个容量区域的子区域,所以确定整个容量区域是有着重要的理论指导意义的。
在安全性方面,本文着重研究了窃听信道模型下的安全问题。在该系列模型中,我们假设有一个窃听者能通过一个噪声信道被动窃听主信道传输的信息。我们研究了以下问题：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,我们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,得到整个容量区域。该容量区域是所有可以实现的传输效率和疑惑度的2元组所组成的区域,所有在该区域的二元组都能够具体实现,而所有不在该区域的二元组都不能具体实现。而在因果和有记忆的情况下,我们得到了容量区域的内外界。更进一步,我们刻画了该模型下的安全容量,即在保证窃听者得不到任何信息的情况下,消息传输效率的最大值。第二,我们刻画了当主信道的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,该窃听信道模型的容量区域以及安全容量。第三,众所周知,反馈不能增加离散无记忆信道的信道容量,带着这个疑问,我们研究了反馈能不能增加窃听信道的容量区域的问题,答案是惊喜的,可以!第四,我们进一步研究了非降阶的窃听信道带反馈的模型,并且得到了它的容量区域和安全容量。目前反馈在安全上的研究非常少,本文系统研究了反馈在安全模型中的作用。
最后,我们离开窃听信道模型,去研究广播信道模型的安全问题。具体来讲,我们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。
在安全性的研究上,降阶广播信道模型是窃听信道模型的扩展。总体来说我们是研究了窃听信道及其扩展模型在考虑了信道状态信息和反馈的情况下的容量区域问题,这里的容量区域实际上是包含了所有可达的安全参数和传输效率的区域。以上问题的研究均为理论成果,我们从数学上刻画和解释了系统安全和传输效率的关系。更为重要的是,我们提出了很多有趣的编码方案来达到上述各种模型的容量区域,这在现实中有着十分重要的指导作用。另外一个非常有趣的结论产生在带反馈的非降阶的窃听信道模型中,在该模型下,我们假设窃听者的信道噪声比合法用户的信道噪声还要小。这在一般的窃听信道模型中是不可能保证系统安全的,因为窃听者知道所有编码方案的细节且能比合法用户还要更容易译码。但是通过反馈,我们证明并设计了编码方案,使得在带反馈的非降阶的窃听信道模型下,仍然能够保证系统安全,因为我们可以把反馈当作一个密钥共享的手段。这个把反馈当作密钥共享的手段的思想被广泛应用于其他带反馈模型的分析中。
The most important issues in communication are reliability and security. The reliabilityquantifies the maximum rate achievable with small probability of error. Security is an impor-tant issue when the transmitted information is confidential and needs to be kept as secret aspossible from wiretapper. In this thesis, we investigate the reliability and security problemsin multi-user information theory.
For the reliability, we investigate the situation that the multiple-access channel (MAC)is controlled by a channel state information sequence, and meanwhile it is available to thechannel encoders in a causal or noncausal manner. This new model can be viewed as aMAC extension of Shannon’s model and Gel’fand-Pinsker’s model. The capacity region isdetermined for the new model in both causal and noncausal manners, and an example abouthow to calculate the capacity region is given.
For the security, firstly, we investigate the wiretap channel with memoryless side in-formation. In the new model, the conditional transition probability distribution of the mainchannel depends on a channel state information, which is available at the joint source-channelencoder in a memoryless manner. The capacity region considering transmission rate andequivocation, is determined for the new model. For the causal and noncausal manners, wederive the inner and outer bounds on the capacity region. Furthermore, the secrecy capacityof the new model is described and bounded, which provides the best transmission rate withperfect secrecy.
Secondly, the model of wiretap channel has been reconsidered for the case that the mainchannel is controlled by channel state information (side information), and it is available at thetransmitter in a causal case (termed here causal side information) or noncausal case (termedhere noncausal side information). Moreover, there is a noiseless feedback from the legitimatereceiver to the transmitter, and it helps them share a secret key, which enlarges the wiretap-per’s uncertainty about the transmitted message. Measuring the uncertainty by equivocation(conditional entropy), the capacity region considering transmission rate and equivocation, isdetermined for the new model of wiretap channel with causal side information and noiselessfeedback. Furthermore, the secrecy capacity is formulated and bounded.
Thirdly, we study the model of wiretap channel with noiseless feedback, and the capac-ity region considering transmission rate and equivocation, is determined. Furthermore, thesecrecy capacity of this model is formulated, which provides the best transmission rate withperfect secrecy. Although the traditional channel capacity is kept in the wiretap channel withnoiseless feedback, the secrecy capacity is larger than that of the model of wiretap channel(without feedback).
Fourthly, we study the non-degraded wiretap channel with noiseless feedback, and it isfirst investigated by R. Ahlswede and N. Cai, where a lower and upper bound on the secrecycapacity is provided in their work. However, the capacity region considering transmissionrate and the equivocation to the wiretapper, has not been determined yet. In this article, thecapacity region is determined for the non-degraded wiretap channel with noiseless feedback.Furthermore, the secrecy capacity of this model is formulated.
Finally, we investigate the model of degraded broadcast channel with side informa-tion, confidential messages and noiseless feedback. This work is from Steinberg’s work onthe degraded broadcast channel with causal and noncausal side information, and Csisz′arand Ko¨rner’s work on broadcast channel with confidential messages. In this new model,the transmitter sends a confidential message to the non-degraded receiver, and meanwhilesends a common message to both the degraded and non-degraded receivers. Moreover, thechannel for the non-degraded receiver is controlled by channel state information (side infor-mation), and it is available to the transmitter in a causal manner (termed here causal sideinformation) or 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 thedegraded receiver’s uncertainty about the confidential message. Measuring the uncertaintyby equivocation (a conditional entropy), the capacity region composed of all achievable rates-equivocation triples is determined for this new model in both causal and noncausal manners.Furthermore, the secrecy capacity in both manners is formulated.
在高效性方面,本文对带信道状态信息的多接入信道模型的容量区域进行了研究(该问题是Gel'fand-Pinsker信道在多接入信道模型中的推广),找到了能达到信道容量的编码和译码方案,同时也求出了该模型下的容量区域的具体数学表达式。该问题属于热点问题,但是以往的工作均只求出了一个容量区域的子区域,所以确定整个容量区域是有着重要的理论指导意义的。
在安全性方面,本文着重研究了窃听信道模型下的安全问题。在该系列模型中,我们假设有一个窃听者能通过一个噪声信道被动窃听主信道传输的信息。我们研究了以下问题：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,我们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,得到整个容量区域。该容量区域是所有可以实现的传输效率和疑惑度的2元组所组成的区域,所有在该区域的二元组都能够具体实现,而所有不在该区域的二元组都不能具体实现。而在因果和有记忆的情况下,我们得到了容量区域的内外界。更进一步,我们刻画了该模型下的安全容量,即在保证窃听者得不到任何信息的情况下,消息传输效率的最大值。第二,我们刻画了当主信道的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,该窃听信道模型的容量区域以及安全容量。第三,众所周知,反馈不能增加离散无记忆信道的信道容量,带着这个疑问,我们研究了反馈能不能增加窃听信道的容量区域的问题,答案是惊喜的,可以!第四,我们进一步研究了非降阶的窃听信道带反馈的模型,并且得到了它的容量区域和安全容量。目前反馈在安全上的研究非常少,本文系统研究了反馈在安全模型中的作用。
最后,我们离开窃听信道模型,去研究广播信道模型的安全问题。具体来讲,我们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。
在安全性的研究上,降阶广播信道模型是窃听信道模型的扩展。总体来说我们是研究了窃听信道及其扩展模型在考虑了信道状态信息和反馈的情况下的容量区域问题,这里的容量区域实际上是包含了所有可达的安全参数和传输效率的区域。以上问题的研究均为理论成果,我们从数学上刻画和解释了系统安全和传输效率的关系。更为重要的是,我们提出了很多有趣的编码方案来达到上述各种模型的容量区域,这在现实中有着十分重要的指导作用。另外一个非常有趣的结论产生在带反馈的非降阶的窃听信道模型中,在该模型下,我们假设窃听者的信道噪声比合法用户的信道噪声还要小。这在一般的窃听信道模型中是不可能保证系统安全的,因为窃听者知道所有编码方案的细节且能比合法用户还要更容易译码。但是通过反馈,我们证明并设计了编码方案,使得在带反馈的非降阶的窃听信道模型下,仍然能够保证系统安全,因为我们可以把反馈当作一个密钥共享的手段。这个把反馈当作密钥共享的手段的思想被广泛应用于其他带反馈模型的分析中。
The most important issues in communication are reliability and security. The reliabilityquantifies the maximum rate achievable with small probability of error. Security is an impor-tant issue when the transmitted information is confidential and needs to be kept as secret aspossible from wiretapper. In this thesis, we investigate the reliability and security problemsin multi-user information theory.
For the reliability, we investigate the situation that the multiple-access channel (MAC)is controlled by a channel state information sequence, and meanwhile it is available to thechannel encoders in a causal or noncausal manner. This new model can be viewed as aMAC extension of Shannon’s model and Gel’fand-Pinsker’s model. The capacity region isdetermined for the new model in both causal and noncausal manners, and an example abouthow to calculate the capacity region is given.
For the security, firstly, we investigate the wiretap channel with memoryless side in-formation. In the new model, the conditional transition probability distribution of the mainchannel depends on a channel state information, which is available at the joint source-channelencoder in a memoryless manner. The capacity region considering transmission rate andequivocation, is determined for the new model. For the causal and noncausal manners, wederive the inner and outer bounds on the capacity region. Furthermore, the secrecy capacityof the new model is described and bounded, which provides the best transmission rate withperfect secrecy.
Secondly, the model of wiretap channel has been reconsidered for the case that the mainchannel is controlled by channel state information (side information), and it is available at thetransmitter in a causal case (termed here causal side information) or noncausal case (termedhere noncausal side information). Moreover, there is a noiseless feedback from the legitimatereceiver to the transmitter, and it helps them share a secret key, which enlarges the wiretap-per’s uncertainty about the transmitted message. Measuring the uncertainty by equivocation(conditional entropy), the capacity region considering transmission rate and equivocation, isdetermined for the new model of wiretap channel with causal side information and noiselessfeedback. Furthermore, the secrecy capacity is formulated and bounded.
Thirdly, we study the model of wiretap channel with noiseless feedback, and the capac-ity region considering transmission rate and equivocation, is determined. Furthermore, thesecrecy capacity of this model is formulated, which provides the best transmission rate withperfect secrecy. Although the traditional channel capacity is kept in the wiretap channel withnoiseless feedback, the secrecy capacity is larger than that of the model of wiretap channel(without feedback).
Fourthly, we study the non-degraded wiretap channel with noiseless feedback, and it isfirst investigated by R. Ahlswede and N. Cai, where a lower and upper bound on the secrecycapacity is provided in their work. However, the capacity region considering transmissionrate and the equivocation to the wiretapper, has not been determined yet. In this article, thecapacity region is determined for the non-degraded wiretap channel with noiseless feedback.Furthermore, the secrecy capacity of this model is formulated.
Finally, we investigate the model of degraded broadcast channel with side informa-tion, confidential messages and noiseless feedback. This work is from Steinberg’s work onthe degraded broadcast channel with causal and noncausal side information, and Csisz′arand Ko¨rner’s work on broadcast channel with confidential messages. In this new model,the transmitter sends a confidential message to the non-degraded receiver, and meanwhilesends a common message to both the degraded and non-degraded receivers. Moreover, thechannel for the non-degraded receiver is controlled by channel state information (side infor-mation), and it is available to the transmitter in a causal manner (termed here causal sideinformation) or 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 thedegraded receiver’s uncertainty about the confidential message. Measuring the uncertaintyby equivocation (a conditional entropy), the capacity region composed of all achievable rates-equivocation triples is determined for this new model in both causal and noncausal manners.Furthermore, the secrecy capacity in both manners is formulated.
引文
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