On the Information Velocity over a Tandem of Erasure Channels

2026-04-15

AI Summary

This work resolves the long-standing open problem of determining the maximum information velocity (IV) for reliable multi-bit communication over a cascade of feedback-free binary erasure channels. Focusing on the asymptotic regime where the message length \( m \) is much smaller than the number of hops \( k \), the authors propose a novel bit-separating pipelining scheme that employs precise timing scheduling to avoid bit-stream collisions. By integrating probabilistic analysis with global channel state information, they devise an enhanced transmission strategy. The study fully characterizes the optimal IV when \( m = o(k^{1/2}) \) and establishes that global state information offers no performance gain in this regime. Furthermore, under the assumption of available global state information, the result is extended to the broader asymptotic range \( m = o(k) \).

Technology Category

• Machine Learning: Information Theory
• Planning, Routing, and Scheduling: Scheduling under Uncertainty
• Multiagent Systems: Agent Communication

Application Category

• Security and Privacy: Large-scale security measurements
• Web Mining and Content Analysis: Content-based information diffusion
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems

Abstract

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.

Problem

• information velocity
• erasure channels
• tandem network
• reliable communication
• message size

Innovation

• information velocity
• bit-separation scheme
• binary erasure channel
• global state information
• pipelined transmission