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Strong Converses Are Just Edge Removal Properties. (arXiv:1706.08172v1 [cs.IT])
来源于:arXiv
This paper explores the relationship between two ideas in network information
theory: edge removal and strong converses. Edge removal properties state that
if an edge of small capacity is removed from a network, the capacity region
does not change too much. Strong converses state that, for rates outside the
capacity region, the probability of error converges to 1. Various notions of
edge removal and strong converse are defined, depending on how edge capacity
and residual error probability scale with blocklength, and relations between
them are proved. In particular, each class of strong converse implies a
specific class of edge removal. The opposite directions are proved for
deterministic networks. Furthermore, a technique based on a novel causal
version of the blowing-up lemma is used to prove that for discrete memoryless
stationary networks, the weak edge removal property---that the capacity region
changes continuously as the capacity of an edge vanishes---is equivalent to the
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