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In this work, we propose and analyze a generalized construction ofdistributed network codes for a network consisting of M users sending differentinformation to a common base station through independent block fading channels.The aim is to increase the diversity order of the system without reducing itscode rate. The proposed scheme, called generalized dynamic network codes(GDNC), is a generalization of the dynamic network codes (DNC) recentlyproposed by Xiao and Skoglund. The design of the network codes that maximizesthe diversity order is recognized as equivalent to the design of linear blockcodes over a nonbinary finite field under the Hamming metric. The proposedscheme offers a much better tradeoff between rate and diversity order. Anoutage probability analysis showing the improved performance is carried out,and computer simulations results are shown to agree with the analyticalresults.

Generalized Distributed Network Coding Based on Nonbinary Linear Block Codes for Multi-User Cooperative Communications