This paper addresses network code design for robust transmission of sources
over an orthogonal two-hop wireless network with a broadcasting relay. The
network consists of multiple sources and destinations in which each
destination, benefiting the relay signal, intends to decode a subset of the
sources. Two special instances of this network are orthogonal broadcast relay
channel and the orthogonal multiple access relay channel. The focus is on
complexity constrained scenarios, e.g., for wireless sensor networks, where
channel coding is practically imperfect. Taking a source-channel and network
coding approach, we design the network code (mapping) at the relay such that
the average reconstruction distortion at the destinations is minimized. To this
end, by decomposing the distortion into its components, an efficient design
algorithm is proposed. The resulting network code is nonlinear and
substantially outperforms the best performing linear network code. A motivating
formulation of a family of structured nonlinear network codes is also
presented. Numerical results and comparison with linear network coding at the
relay and the corresponding distortion-power bound demonstrate the
effectiveness of the proposed schemes and a promising research direction.Comment: 27 pages, 9 figures, Submited to IEEE Transaction on Communicatio