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.

翻译：我们研究有向图上低速率通信问题的误差指数，其中图中的每条边代表一个噪声通信信道，且存在单一源节点和目的节点。我们推导了基于最大流的可达性误差指数上界和逆界，当存在两条消息且所有信道满足称为成对可逆性的对称条件时，这些界是匹配的。更一般地，我们证明上下界相差在4倍以内。我们还证明，在三条消息的情况下，存在基于最大流的误差指数严格次优的情形，从而表明我们的紧致性结果在无额外假设时无法推广到两条消息以上。