Simple Coding Techniques for Many-Hop Relaying

Yan Hao Ling; Jonathan Scarlett

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arXiv · 2112.07120

Simple Coding Techniques for Many-Hop Relaying

Yan Hao Ling·Jonathan Scarlett

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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.

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Yan Hao Ling, Jonathan Scarlett. 2021-12-14. Simple Coding Techniques for Many-Hop Relaying. https://arxiv.org/abs/2112.07120

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