Hosseinigoki Fatemeh, Kosut Oliver
School of Electrical, Computer and Energy Engineering, Arizona State University, Tempe, AZ 85287, USA.
Entropy (Basel). 2019 Jun 7;21(6):575. doi: 10.3390/e21060575.
In this paper, we determine the capacity of the Gaussian arbitrarily-varying channel with a (possibly stochastic) encoder and a deterministic list-decoder under the average probability of error criterion. We assume that both the legitimate and the adversarial signals are restricted by their power constraints. We also assume that there is no path between the adversary and the legitimate user but the adversary knows the legitimate user's code. We show that for any list size , the capacity is equivalent to the capacity of a point-to-point Gaussian channel with noise variance increased by the adversary power, if the adversary has less power than times the transmitter power; otherwise, the capacity is zero. In the converse proof, we show that if the adversary has enough power, then the decoder can be confounded by the adversarial superposition of several codewords while satisfying its power constraint with positive probability. The achievability proof benefits from a novel variant of the Csiszár-Narayan method for the arbitrarily-varying channel.
在本文中，我们在平均错误概率准则下确定了具有（可能是随机的）编码器和确定性列表解码器的高斯任意变化信道的容量。我们假设合法信号和对抗信号都受其功率约束。我们还假设对抗者与合法用户之间没有路径，但对抗者知道合法用户的码。我们表明，对于任何列表大小，如果对抗者的功率小于发射机功率的 倍，则容量等同于噪声方差因对抗者功率而增加的点对点高斯信道的容量；否则，容量为零。在逆命题证明中，我们表明如果对抗者有足够的功率，那么解码器可能会以正概率被几个码字的对抗叠加混淆，同时满足其功率约束。可达性证明受益于用于任意变化信道的Csiszár - Narayan方法的一种新颖变体。
