Simple Coding Techniques for Many-Hop Relaying

TL;DR

This paper presents a simple, efficient protocol for many-hop binary relaying that achieves positive information velocity and characterizes its scaling laws, improving over complex existing methods.

Contribution

It introduces a new deterministic protocol for binary relaying that is simpler and achieves positive information velocity, along with scaling law characterizations and multi-bit extension.

Findings

Protocol attains positive information velocity with small error probability.

Characterization of low-noise and high-noise scaling laws.

Extension to transmit multiple bits efficiently over many hops.

Abstract

In this paper, we study the problem of relaying a single bit of information across a series of binary symmetric channels, and the associated trade-off between the number of hops $m$, the transmission time $n$, and the error probability. We introduce a simple, efficient, and deterministic protocol that attains positive information velocity (i.e., a non-vanishing ratio $\frac{m}{n}$ and small error probability) and is significantly simpler than existing protocols that do so. In addition, we characterize the optimal low-noise and high-noise scaling laws of the information velocity, and we adapt our 1-bit protocol to transmit $k$ bits over $m$ hops with $O(m+k)$ transmission time.