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Abstract:
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We derive new cut-set bounds on the achievable rates in a general
multi-terminal network with finite number of states. Multiple
states are common in communication networks in the form of
multiple channel and nodes' states. Our results are broadly
applicable and provide much tighter upper bounds than the known
single state min-cut max-flow theorem, and hence form an important
new tool to bound the performance of multi-node networks.
Two examples are presented to illustrate the tightness and
the utility of the new bounds. In each of the example
applications, the known single-state max-flow min-cut theorem
provides a bound strictly looser than the new cut-set bounds. The
first illustrative example is single-user compound channels, where
both the transmitter and receiver have channel state information.
The example of compound channels represents the smallest possible
network with only two nodes, but has multiple states due to
channel variations. The upper bound derived using the proposed
bounds turns out to be the capacity of the compound channel, which
implies that the bound is tight in this case. The second example
is from a contemporary network problem. Here, we demonstrate the
application of new bounds to characterize the limits on rate of
information transfer in `cheap' relay networks, where the relay
nodes can either transmit or receive, but not both simultaneously.
In this case, each constituent channel has a single state but
relay nodes can be in one of the two states, transmit or receive
mode, giving rise to multiple network states. Here, again, the
upper bound coincide with the capacity of the channel if the relay
channel is degraded. |
