二次约束条件下的AVCs
On AVCs with Quadratic Constraints
摘要：
在这项工作中，我们研究了二次功率约束的发射机和一个所谓的“不经意”的干扰（随着额外的AWGN）下的最大概率错误准则的随机变化的信道（AVC），和没有私人之间的随机性的发射机和接收机。这与[1]中考虑的平均错误概率准则下的类似AVC模型以及其中允许共同随机性的模型[2]形成对比-这些区别在下面概述的一些通信场景中是重要的。我们考虑的政权干扰机的功率约束小于发射机的功率约束（在其他政权，它是已知的没有正率是可能的）。对于这种制度，我们表明存在的随机码（发射机和接收机之间没有共同的随机性），使可靠的通信在相同的速率时，干扰机被替换为具有相同的功率约束的AWGN。这与已知的信息理论外边界相匹配。除了是比[1]中更强的结果（能够恢复其中的结果）之外，我们的证明技术也更直接，因此可能是独立的兴趣。
英文摘要：
In this work we study an Arbitrarily Varying Channel (AVC) with quadratic power constraints on the transmitter and a so-called "oblivious" jammer (along with additional AWGN) under a maximum probability of error criterion, and no private randomness between the transmitter and the receiver. This is in contrast to similar AVC models under the average probability of error criterion considered in [1], and models wherein common randomness is allowed [2] -- these distinctions are important in some communication scenarios outlined below. We consider the regime where the jammer's power constraint is smaller than the transmitter's power constraint (in the other regime it is known no positive rate is possible). For this regime we show the existence of stochastic codes (with no common randomness between the transmitter and receiver) that enables reliable communication at the same rate as when the jammer is replaced with AWGN with the same power constraint. This matches known information-theoretic outer bounds. In addition to being a stronger result than that in [1] (enabling recovery of the results therein), our proof techniques are also somewhat more direct, and hence may be of independent interest.
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