Information velocity (IV) is a recently proposed notion to capture the speed of reliable information dissemination over a large-scale network. It is the speed at which reliable end-to-end communication over $k$ hops can be achieved within $t$ time instances, and is defined formally as the asymptotic ratio $k/t$ as $k$ tends to infinity subject to vanishing error probability. To date, even for a tandem of binary erasure channels without feedback, the optimal IV for disseminating multiple (say $m$) bits remains unknown. We make progress on this open problem by characterizing the optimal IV for the regime where the message size $m = o(k^{1/2})$. The main contribution lies in achievability, where we propose a simple bit-separation scheme that pipelines message bits in an orderly fashion with carefully designed temporal spacing so that the flows of different bits do not collide with one another with high probability. This is in sharp contrast to previous attempts in the literature where schemes involve coding over time and across nodes. To go beyond the regime $m = o(k^{1/2})$, we further investigate the setting where every node in the network has strictly causal access to the state information of the BEC links in the entire network. For such a setting with global state information (GSI), we develop an enhanced scheme and characterize the optimal IV for the regime where the message size $m = o(k)$. Interestingly, for the regime $m = o(k^{1/2})$, GSI does not improve the information velocity.

翻译：信息速度(Information Velocity, IV)是近期提出的概念，用于刻画大规模网络中可靠信息传播的速度。它衡量在$k$跳网络中经过$t$个时间实例实现可靠端到端通信的速度，形式上定义为当$k$趋于无穷大且错误概率趋于零时的渐近比值$k/t$。迄今为止，即使对于无反馈的二元擦除信道串联链，传输多个（如$m$个）比特的最优IV仍未知。我们通过刻画消息长度$m = o(k^{1/2})$场景下的最优IV，在该开放问题上取得进展。主要贡献在于可达性：我们提出一种简单的比特分离方案，通过精心设计的时空间隔有序流水化传输消息比特，使得不同比特的流以高概率互不冲突。这与现有文献中采用跨时间跨节点编码的方案形成鲜明对比。为突破$m = o(k^{1/2})$场景限制，我们进一步研究网络中每个节点可严格因果获取全网BEC链路状态信息的情况。针对这种具有全局状态信息(GSI)的场景，我们提出增强方案并刻画消息长度$m = o(k)$时的最优IV。有趣的是，对于$m = o(k^{1/2})$场景，GSI无法提升信息速度。