We study reliable communication over point-to-point adversarial channels in which the adversary can observe the transmitted codeword via some function that takes the $n$-bit codeword as input and computes an $rn$-bit output for some given $r \in [0,1]$. We consider the scenario where the $rn$-bit observation is computationally bounded -- the adversary is free to choose an arbitrary observation function as long as the function can be computed using a polynomial amount of computational resources. This observation-based restriction differs from conventional channel-based computational limitations, where in the later case, the resource limitation applies to the computation of the (adversarial) channel error. For all $r \in [0,1-H(p)]$ where $H(\cdot)$ is the binary entropy function and $p$ is the adversary's error budget, we characterize the capacity of the above channel. For this range of $r$, we find that the capacity is identical to the completely obvious setting ($r=0$). This result can be viewed as a generalization of known results on myopic adversaries and channels with active eavesdroppers for which the observation process depends on a fixed distribution and fixed-linear structure, respectively, that cannot be chosen arbitrarily by the adversary.

翻译：我们研究了点对点对抗信道中的可靠通信问题，其中对手可通过某个函数观测传输的码字：该函数以$n$比特码字为输入，对给定参数$r \in [0,1]$输出$rn$比特。我们考虑$rn$比特观测受计算能力限制的场景——允许对手自由选择任意观测函数，仅要求该函数可通过多项式时间计算资源实现。这种基于观测的限制与传统基于信道的计算限制不同：后者将资源限制施加于（对抗性）信道误差的计算过程。对于所有$r \in [0,1-H(p)]$（其中$H(\cdot)$为二进制熵函数，$p$为对手的误差预算），我们刻画了上述信道的容量。在该$r$取值范围内，我们发现容量等同于完全公开场景（$r=0$）下的容量。该结果可被视为已知关于近视对手及主动窃听信道结论的推广，此前研究中观测过程分别依赖固定分布或固定线性结构，且对手无法任意选择这些结构。