Line and Lattice Networks under
Deterministic Interference Models
Jasper Goseling, Michael Gastpar and Jos H. Weber
Capacity bounds are compared for four different deterministic models of wireless networks, representing four
different ways of handling broadcast and superposition in the physical layer. In particular, the transport capacity under
a multiple unicast traffic pattern is studied for a one-dimensional network of regularly spaced nodes on a line and
for a two-dimensional network of nodes placed on a hexagonal lattice. The considered deterministic models are: (i)
P/P, a model with exclusive transmission and reception, (ii) P/M, a model with simultaneous reception of the sum
of the signals transmitted by all nearby nodes, (iii) B/P, a model with simultaneous transmission to all nearby nodes
but exclusive reception, and (iv) B/M, a model with both simultaneous transmission and simultaneous reception. All
four deterministic models are considered under half-duplex constraints. For the one-dimensional scenario, it is found
that the transport capacity under B/M is twice that under P/P. For the two-dimensional scenario, it is found that the
transport capacity under B/M is at least 2.5 times, and no more than six times, the transport capacity under P/P.
The transport capacities under P/M and B/P fall between these bounds.
Capacity, Network Coding, Deterministic Model, Multi-source, Multi-commodity, Computation Codes
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