Multiple Access Channels with Adversarial Users
Multiple Access Channels with Adversarial Users
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DOI：
10.1109/isit.2019.8849729
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发表时间：
2019-07
期刊：
影响因子：
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通讯作者：
Neha Sangwan;Mayank Bakshi;B. Dey;V. Prabhakaran
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文献类型：
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作者：
Neha Sangwan;Mayank Bakshi;B. Dey;V. Prabhakaran
我们研究了两用户多访问通道（MAC）上的身份验证通信，其中一个用户可能是敌对的。当两个用户的行为都是非对抗性的，我们希望他们的消息能够被可靠地解码。然而，我们还希望确保敌对用户不会对其他（诚实）用户的消息造成未被检测到的错误。我们证明了以下三阶段方案是速率最优的：首先使用标准MAC代码来实现未经身份验证的通信；接下来是两个身份验证阶段，其中每个用户将其他用户视为可能的攻击者，对其消息进行身份验证。我们展示了身份验证阶段可以非常短，因为这种形式的身份验证本身，在可能的情况下，可以实现大小以块长度成倍增长的消息集。这导致我们的结果是，离散无内存MAC的认证通信容量区域为零或（未经认证的）MAC容量区域本身。可以说，这也解释了Kosut和Kliewer最近发现的离散无记忆点对点对抗性信道的认证通信能力的类似性质（ITW, 2018）。对于加性高斯噪声信道，我们也得到了类似的结果。
We study authenticated communication over two-user multiple access channels (MAC) where one of the users is possibly adversarial. When both users behave non-adversarially, we want their messages to be decoded reliably. However, we also want to ensure that an adversarial user cannot cause an undetected error on the other (honest) user’s message. We show that the following three-phase scheme is rate-optimal: a standard MAC code is first used to achieve unauthenticated communication; this is followed by two authentication phases where each user authenticates their message treating the other user as a possible adversary. We show that the authentication phases can be very short since this form of authentication itself, when possible, can be achieved for message sets whose size grow doubly exponentially in blocklength. This leads to our result that the authenticated communication capacity region of a discrete memoryless MAC is either zero or the (unauthenticated) MAC capacity region itself. This also, arguably, explains the similar nature of authenticated communication capacity of a discrete memoryless point-to-point adversarial channel recently found by Kosut and Kliewer (ITW, 2018). We also obtain analogous results for additive Gaussian noise channels.