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Achieving the Secrecy Capacity of Wiretap Channels Using Polar Codes

机译：使用极性代码实现窃听通道的保密容量

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摘要

Suppose that Alice wishes to send messages to Bob through a communication channel $C_{1}$, but her transmissions also reach an eavesdropper Eve through another channel $C_{2}$. This is the wiretap channel model introduced by Wyner in 1975. The goal is to design a coding scheme that makes it possible for Alice to communicate both reliably and securely. Reliability is measured in terms of Bob's probability of error in recovering the message, while security is measured in terms of the mutual information between the message and Eve's observations. Wyner showed that the situation is characterized by a single constant ${cal C}_{s}$, called the secrecy capacity, which has the following meaning: for all $varepsilon !! > !! 0$ , there exist coding schemes of rate $R! geqslant {cal C}_{s} ! ! - ! varepsilon$ that asymptotically achieve the reliability and security objectives. However, his proof of this result is based upon a random-coding argument. To date, despite considerable research effort, the only case where we know how to construct coding schemes that achieve secrecy capacity is when Eve's channel $C_{2}$ is an erasure channel, or a combinatorial variation thereof.
机译：假设爱丽丝希望通过通信信道$ C_ {1} $向鲍勃发送消息，但她的传输也通过另一个信道$ C_ {2} $到达窃听者夏娃。这是Wyner在1975年引入的窃听通道模型。目标是设计一种编码方案，以使Alice能够可靠而安全地进行通信。可靠性是根据鲍勃在恢复消息时出错的概率来衡量的，而安全性是根据消息与夏娃的观察之间的相互信息来衡量的。威纳（Wyner）表明，这种情况的特征是单个常数$ {cal C} _ {s} $，称为保密能力，其含义如下：对于所有$ varepsilon！ >！ 0 $，存在速率为$ R！的编码方案！ geqslant {cal C} _ {s}！ ！ -！渐近地达到可靠性和安全性目标的变量。但是，他对此结果的证明是基于随机编码参数的。迄今为止，尽管进行了大量的研究工作，但我们唯一知道如何构造实现保密能力的编码方案的情况是，夏娃的信道$ C_ {2} $是一个擦除信道或其组合变体。

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