In this paper, we propose and analyze a generalized construction of distributed network codes for a network consisting of $M$ users sending independent 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.

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