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 efficient, constant rate schemes that successfully conduct any computation with high probability as long as the adversary corrupts at most $\varepsilon /m$ fraction of the total communication, where $m$ is the number of links in the network and $\varepsilon$ is a small constant. This scheme assumes the parties share a random string to which the adversarial noise is oblivious. We can remove this assumption at the price of being resilient to $\varepsilon / (m\log m)$ adversarial error. 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.
翻译:在互动编码领域,两个或两个以上当事方希望对可能吵闹的通信网络进行分布式计算。最终目标是制定高效的编码计划,能够容忍高水平的噪音,同时只增加一个恒定因素(即恒定速度)。在这项工作中,我们考虑在一个任意的地形学上同步通信网络,在强大的对抗性插入式删除噪音模型中。也就是说,吵闹的频道可能会对任何传输符号的内容进行对抗性改变,或者完全删除传送的符号或向频道注入一个新的符号。我们提供高效的固定费率计划,只要对手腐败者最多能容忍高水平的噪音,同时只增加通信总量的一小部分(即恒定速度)。我们考虑的是,在网络中连接的数量是美元,而美元是小的固定。这个计划假定各方拥有一个随机的绳子,而对抗性噪音是模糊的。我们可以取消这一假设,价格是能够适应美元/模型/(m=log m)的任何计算都是高概率的,只要敌方腐败分子在双度递合制中选择,我们最具有弹性的压式的汇率计划就是确定我们最有弹性的汇率的汇率。之前的工作是确定我们最有弹性的联盟的汇率的汇率的汇率。我们的最佳选择。考虑的是,我们最有弹性的策略,我们最有弹性的保守的汇率。在两个插入式的汇率。