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

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 code rate. 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 maximizes the diversity order is recognized as equivalent to the design of linear block codes over a nonbinary finite field under the Hamming metric. The proposed scheme offers a much better tradeoff between rate and diversity order. An outage probability analysis showing the improved performance is carried out, and computer simulations results are shown to agree with the analytical results.