Any interactive protocol between a pair of parties can be reliably simulated in the presence of noise with a multiplicative overhead on the number of rounds (Schulman 1996). The reciprocal of the best (least) overhead is called the interactive capacity of the noisy channel. In this work, we present lower bounds on the interactive capacity of the binary erasure channel. Our lower bound improves the best known bound due to Ben-Yishai et al. 2021 by roughly a factor of 1.75. The improvement is due to a tighter analysis of the correctness of the simulation protocol using error pattern analysis. More precisely, instead of using the well-known technique of bounding the least number of erasures needed to make the simulation fail, we identify and bound the probability of specific erasure patterns causing simulation failure. We remark that error pattern analysis can be useful in solving other problems involving stochastic noise, such as bounding the interactive capacity of different channels.

翻译：任意两方之间的交互协议都可以在存在噪声的情况下可靠地模拟，且轮次数量具有乘法开销（Schulman 1996）。最佳（最小）开销的倒数称为噪声信道的交互容量。本文提出了二进制擦除信道交互容量的下界。我们的下界相比Ben-Yishai等人2021年提出的最佳已知界提升了约1.75倍。这一改进源于利用错误模式分析对模拟协议正确性进行更严密的论证。具体而言，我们没有采用传统的通过界定使模拟失败所需的最小擦除次数的方法，而是识别并量化了导致模拟失败的特定擦除模式的概率。我们指出，错误模式分析还可用于解决其他涉及随机噪声的问题，例如不同信道交互容量的界定。