It is shown that Csiszar and Korner's (1978) characterization of a discrete memoryless channel (DMC)X/spl rarr/Y as being less noisy than the DMC X/spl rarr/Z is equivalent to the condition that the mutual-information difference I(X;Y)-I(X;Z) be a convex-/spl cap/ function of the probability distribution for X. This result is used to obtain a simple determination of the capacity region of the broadcast channel with confidential messages (BCC), which is a DMC X/spl rarr/(Y,Z), when the DMC X/spl rarr/Y to the legitimate receiver is less noisy than the DMC X/spl rarr/Z to the enemy cryptanalyst and there is a probability distribution for X having strictly positive components that achieves capacity on both these channels. In particular, when these DMC's are both symmetric, then the secrecy capacity of the BCC is the difference of their capacities. It is shown further that the less-noisy condition in this result cannot be weakened to the condition that the DMC X/spl rarr/Y be more capable than the DMC X/spl rarr/Z in the sense of Csiszar and Korner.
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机译：结果表明，Csiszar和Korner（1978）将离散无记忆通道（DMC）X / spl rarr / Y的噪声比DMC X / spl rarr / Z的噪声小等同于互信息差I （X; Y）-I（X; Z）是X的概率分布的凸/ spl上限/函数。此结果用于获得带有机密消息（BCC）的广播信道容量区域的简单确定），即DMC X / spl rarr /（Y，Z），当发给合法接收方的DMC X / spl rarr / Y的噪声小于对敌方密码分析员发给DMC X / spl rarr / Z的噪声时，具有严格正分量的X的概率分布，在这两个通道上均实现了容量。特别地，当这些DMC都是对称的时，则BCC的保密容量就是它们容量的差。进一步表明，在Csiszar和Korner的意义上，该结果中的低噪条件不能减弱为DMC X / spl rarr / Y比DMC X / spl rarr / Z更强大的条件。
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