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“…Basically, the clock ticks n times and node u can transmit X u,i after clock tick i − 1 and before clock tick i. Node u receives Y u,i at clock tick i. Hence, X u,i can be any function of its own messages and its past channel outputs [27,102,167,180].…”

confidence: 99%

“…Basically, the clock ticks n times and node u can transmit X u,i after clock tick i − 1 and before clock tick i. Node u receives Y u,i at clock tick i. Hence, X u,i can be any function of its own messages and its past channel outputs [27,102,167,180].…”

confidence: 99%

“…We associate sources with input nodes ui and sinks with output nodes uo. Such line networks are special cases of discrete memoryless networks (DMNs) and we use the capacity definition from [1] (Section III.D). The capacity region was recently established in [2].…”

confidence: 99%

“…The edges (ui, uo) are the usual links with capacity C u . Such line networks are again special cases DMNs and we use the capacity definition from [1] (Section III.D). …”

confidence: 99%

“…where the definition of directed information I(X n → Y n ) is given in Section II and p(x n ||y n−1 ) = n i=1 p(x i |x i−1 , y i−1 ) is the causal conditioning notation streamlined by Kramer [2]. This upper bound is tight for a certain class of ergodic channels [3]- [5], paving the road to a computable characterization of feedback capacity; see [6]- [8] for examples.…”

confidence: 99%

“…Directed information and its variants also characterize (via multi-letter expressions) the capacity of two-way channels and multiple access channels with feedback [2], [9], and the rate distortion function with feedforward [10], [11]. In another context, directed information also captures the difference in growth rates of wealth in horse race gambling due to causal side information [12].…”

confidence: 99%