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The partially repeated cooperation system employing Low Density Parity-Check (LDPC) codes achieves space diversity and extra coding gain at the same time. This paper focuses on the power constrained system, in which the total power of the source node and the relay node remains constant. Thus different power allocation schemes result in different repetition lengths at the relay node, and it is interesting to determine the optimal in terms of performance. A modified Gaussian Approximation algorithm is proposed to search for the feasible decoding threshold of the partially repeated regular LDPC codes, with which the outage probability is obtained and used to show the power efficiency of different power allocation schemes. The numerical results show that the partially repeated scheme can achieve a higher power efficiency than the all repeated one. However, the efficiency of the power allocation scheme strongly depends on the channel realizations of the system.