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Cooperative relay transmission is an effective way to combat multi-path fading. With proper coding scheme, the diversity and coding gains can be obtained. A two-hop decode- and-forward relay protocol using distributed linear dispersion code (LDC) is introduced and analyzed in terms of capacity gains over the system with the traditional uniform power allocation. To optimize the capacity of the system subjected to a total transmit power constraint, an optimal power allocation scheme based on genetic algorithm is explored, which distributes resource appropriately to each hop according to the channel state information (CSI) and some characteristics of distributed LDC. Theoretical analysis and numerical results indicate that with optimal power allocation, the proposed coded cooperative system will outperform the one with traditional uniform power allocation.