Compute and Forward for Wireless Networks - Scheduling and Capacity in Heterogenous Networks
The first part of the talk presents high SINR asymptotics for
Compute and Forward Networks (COFN). For this talk, a COFN is
a network with a source node where information (in the form of messages)
is produced, intermediate nodes which acts as relays arranged as $K$ columns,
and after a succession of these, a sink node where the information (messages)
are decoded. The salient characteristic of such networks is that the relay nodes
compute (with arbitrary reliability) functions of the messages which
are inverted at the sink node to obtain the messages which were sent.
The maximum rate at which this can be done, we might call the computational
It is shown that the maximum number of Degrees of Freedom i.e. maximum
capacity (relative to the usual Shannon formula) can be achieved,
through a certain scheme outlined in the talk.
This is shown under the assumption that there is perfect knowledge of
the channel state at each stage of the network. Exploiting
this fact functions of the original messages are encoded as
monomials at each transmitter and then sent on to the next stage, under the
scheme. The scheme is completely impractical but other alternate more
practical schemes are being investigated. These are based on lattice coding.
In the second part of the talk, a definition will be given for Capacity
in Heterogeneous Wireless Networks. It is shown that fixed
schemes can attain this capacity, provided the network is
offered stationary offered traffic.
Adaptive schemes offer the prospect of superior delay performance
and I will discuss two of these. The first supposes that the
so called Cell Range Expansion (CRE)is fixed but then determines
the Almost Blanking Subframe (ABS) fraction according to how
mobiles are distributed amongst the various pico cells and
the macro. The second scheme adapts both the CRE
and the ABS and can be shown to be throughput optimal with
the limit stationary distribution having geometric moments.