Understanding how information can efficiently spread in distributed systems under noisy communications is a fundamental question in both biological research and artificial system design. When agents are able to control whom they interact with, noise can often be mitigated through redundancy or other coding techniques, but it may have fundamentally different consequences on well-mixed systems. Specifically, Boczkowski et al. (2018) considered the noisy $\mathcal{PULL}(h)$ model, where each message can be viewed as any other message with probability $\delta$. The authors proved that in this model, the basic task of propagating a bit value from a single source to the whole population requires $\Omega(\frac{n\delta}{h(1-\delta|\Sigma|)^2})$ (parallel) rounds. The current work shows that the aforementioned lower bound is almost tight. In particular, when each agent observes all other agents in each round, which relates to scenarios where each agent senses the system's average tendency, information spreading can reliably be achieved in $\mathcal{O}(\log n)$ time, assuming constant noise. We present two simple and highly efficient protocols, thus suggesting their applicability to real-life scenarios. Notably, they also work in the presence of multiple conflicting sources and efficiently converge to their plurality opinion. The first protocol we present uses 1-bit messages but relies on a simultaneous wake-up assumption. By increasing the message size to 2 bits and removing the speedup in the information spreading time that may result from having multiple sources, we also present a simple and highly efficient self-stabilizing protocol that avoids the simultaneous wake-up requirement. Overall, our results demonstrate how, under stochastic communication, increasing the sample size can compensate for the lack of communication structure by linearly accelerating information spreading time.

翻译：理解信息如何在噪声通信条件下高效传播于分布式系统，既是生物学研究也是人工系统设计中的基础性问题。当智能体能够控制其交互对象时，噪声通常可通过冗余或其他编码技术得到缓解，但在充分混合的系统中可能产生根本性不同的影响。具体而言，Boczkowski等人（2018）研究了噪声$\mathcal{PULL}(h)$模型，其中每条消息以概率$\delta$可能被视作其他任意消息。作者证明在该模型中，将比特值从单个源节点传播至整个群体的基本任务需要$\Omega(\frac{n\delta}{h(1-\delta|\Sigma|)^2})$（并行）轮次。本研究表明上述下界几乎是紧致的。特别地，当每个智能体每轮观测所有其他智能体（对应每个智能体感知系统平均趋势的场景）时，在恒定噪声假设下信息传播可稳定地在$\mathcal{O}(\log n)$时间内实现。我们提出了两种简洁高效的协议，这暗示了其在现实场景中的适用性。值得注意的是，这些协议在存在多个冲突源的情况下依然有效，并能高效收敛至多数意见。我们提出的首个协议使用1比特消息，但依赖于同步唤醒假设。通过将消息大小增至2比特并消除多源可能带来的信息传播加速效应，我们还提出了一种简洁高效的自稳定协议，该协议无需同步唤醒要求。总体而言，我们的结果表明在随机通信条件下，增加样本量可通过线性加速信息传播时间来弥补通信结构的缺失。