Maxflow-Based Bounds for Low-Rate Information Propagation over Noisy Networks

Yan Hao Ling; Jonathan Scarlett

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arXiv · 2304.02226

Maxflow-Based Bounds for Low-Rate Information Propagation over Noisy Networks

Yan Hao Ling·Jonathan Scarlett

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Abstract

We study error exponents for the problem of low-rate communication over a directed graph, where each edge in the graph represents a noisy communication channel, and there is a single source and destination. We derive maxflow-based achievability and converse bounds on the error exponent that match when there are two messages and all channels satisfy a symmetry condition called pairwise reversibility. More generally, we show that the upper and lower bounds match to within a factor of 4. We also show that with three messages there are cases where the maxflow-based error exponent is strictly suboptimal, thus showing that our tightness result cannot be extended beyond two messages without further assumptions.

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Yan Hao Ling, Jonathan Scarlett. 2023-04-05. Maxflow-Based Bounds for Low-Rate Information Propagation over Noisy Networks. https://arxiv.org/abs/2304.02226

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