  In this work, we propose and analyze a generalized construction of
distributed network codes for a network consisting of $M$ users sending
different information to a common base station through independent block fading
channels. The aim is to increase the diversity order of the system without
reducing its throughput. The proposed scheme, called generalized
dynamic-network codes (GDNC), is a generalization of the dynamic-network codes
(DNC) recently proposed by Xiao and Skoglund. The design of the network codes
that maximize the diversity order is recognized as equivalent to the design of
linear block codes over a nonbinary finite field under the Hamming metric. We
prove that adopting a systematic generator matrix of a maximum distance
separable block code over a sufficiently large finite field as the network
transfer matrix is a sufficient condition for full diversity order under link
failure model. The proposed generalization offers a much better tradeoff
between rate and diversity order compared to the DNC. An outage probability
analysis showing the improved performance is carried out, and computer
simulations results are shown to agree with the analytical results.
