740 research outputs found
Computation in Multicast Networks: Function Alignment and Converse Theorems
The classical problem in network coding theory considers communication over
multicast networks. Multiple transmitters send independent messages to multiple
receivers which decode the same set of messages. In this work, computation over
multicast networks is considered: each receiver decodes an identical function
of the original messages. For a countably infinite class of two-transmitter
two-receiver single-hop linear deterministic networks, the computing capacity
is characterized for a linear function (modulo-2 sum) of Bernoulli sources.
Inspired by the geometric concept of interference alignment in networks, a new
achievable coding scheme called function alignment is introduced. A new
converse theorem is established that is tighter than cut-set based and
genie-aided bounds. Computation (vs. communication) over multicast networks
requires additional analysis to account for multiple receivers sharing a
network's computational resources. We also develop a network decomposition
theorem which identifies elementary parallel subnetworks that can constitute an
original network without loss of optimality. The decomposition theorem provides
a conceptually-simpler algebraic proof of achievability that generalizes to
-transmitter -receiver networks.Comment: to appear in the IEEE Transactions on Information Theor
- …