In the field of interactive coding, two or more parties wish to carry out a distributed computation over a communication network that may be noisy. The ultimate goal is to develop efficient coding schemes that can tolerate a high level of noise while increasing the communication by only a constant factor (i.e., constant rate). In this work we consider synchronous communication networks over an arbitrary topology, in the powerful adversarial insertion-deletion noise model. Namely, the noisy channel may adversarially alter the content of any transmitted symbol, as well as completely remove a transmitted symbol or inject a new symbol into the channel. We provide an efficient, constant rate scheme that conducts any computation on any arbitrary network, and succeeds with high probability as long as an oblivious adversary corrupts at most $\frac { \varepsilon }{m}$ fraction of the total communication, where $m$ is the number of links in the network and $\varepsilon $ is a small constant. In this work (the first part), our scheme assumes that the parties share a random string to which the adversarial noise is oblivious. While previous work considered the insertion-deletion noise model in the two-party setting, to the best of our knowledge, our scheme is the first multiparty scheme that is resilient to insertions and deletions. Furthermore, our scheme is the first computationally efficient scheme in the multiparty setting that is resilient to adversarial noise.

中文翻译：

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高效的多方交互式编码-第一部分：明显的插入，删除和替换

在交互式编码领域，两个或两个以上的参与者希望在可能有噪声的通信网络上进行分布式计算。最终目标是开发一种有效的编码方案，该方案可以容忍高水平的噪声，同时仅以恒定因子（即恒定速率）增加通信量。在这项工作中，我们在强大的对抗插入删除噪声模型中考虑了任意拓扑上的同步通信网络。即，有噪声的信道可以对抗性地改变任何被发送的符号的内容，以及完全去除被发送的符号或向该信道注入新的符号。我们提供了一种高效，恒定速率的方案，该方案可以在任意网络上进行任何计算，并且只要被遗忘的对手最多破坏，其成功率就很高。 $ \ frac {\ varepsilon} {m} $ 占总沟通的比例，其中 $ m $ 是网络中的链接数，并且 $ \ varepsilon $ 是一个小常数。在这项工作（第一部分）中，我们的方案假定双方共享随机字符串，而对抗性噪声却被忽略。尽我们所知，虽然先前的工作在两方环境中考虑了插入删除噪声模型，但据我们所知，我们的方案是第一个对插入和删除具有弹性的多方方案。此外，我们的计划是第一个计算效率高 多方设置中的方案可适应 对抗的 噪音。