针对在线对手的代码
Codes against Online Adversaries
摘要：
在这项工作中，我们考虑的信息通信中存在的在线对抗干扰。在所研究的设置中，发送方希望通过发送码字x=x_1，.，x_n在通信信道上逐符号地传输。对抗性干扰机可以一次一个地查看所发送的符号x_i，并且可以改变它们的p分数。然而，干扰机的决定必须以在线或因果的方式做出。更一般地，对于延迟参数0<d<1，我们研究干扰机关于x_i的损坏的决策必须仅取决于x_j（j <i-dn）的场景。在这项工作中，我们开始研究代码的在线对手，并提出了一个严格的表征的信息量可以在0延迟，更一般地说，d-延迟在线设置。我们证明了严格的结果添加剂和覆盖干扰时，传输的符号被假定为在一个足够大的字段F。最后，我们将我们的结果扩展到一个干扰或监听在线模型，在那里的在线对手可以干扰一个符号或窃听它。我们再次提供了一个严格的表征，这个模型的几个变种的可实现的速率。我们证明每个模型的速率区域在本质上是信息理论的，并且适用于计算上无界的对手。速率区域由p和d的“简单”分段线性函数表征。我们构造的代码，以达到最佳的速率为每种情况下的计算效率。
英文摘要：
In this work we consider the communication of information in the presence of an online adversarial jammer. In the setting under study, a sender wishes to communicate a message to a receiver by transmitting a codeword x=x_1,...,x_n symbol-by-symbol over a communication channel. The adversarial jammer can view the transmitted symbols x_i one at a time, and can change up to a p-fraction of them. However, the decisions of the jammer must be made in an online or causal manner. More generally, for a delay parameter 0<d<1, we study the scenario in which the jammer's decision on the corruption of x_i must depend solely on x_j for j < i - dn. In this work, we initiate the study of codes for online adversaries, and present a tight characterization of the amount of information one can transmit in both the 0-delay and, more generally, the d-delay online setting. We prove tight results for both additive and overwrite jammers when the transmitted symbols are assumed to be over a sufficiently large field F. Finally, we extend our results to a jam-or-listen online model, where the online adversary can either jam a symbol or eavesdrop on it. We again provide a tight characterization of the achievable rate for several variants of this model. The rate-regions we prove for each model are informational-theoretic in nature and hold for computationally unbounded adversaries. The rate regions are characterized by "simple" piecewise linear functions of p and d. The codes we construct to attain the optimal rate for each scenario are computationally efficient.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
