In this paper, we derive an exact upper bound (UB) on bit error rate (BER) of the decode-and-forward (DF) cooperation protocol. The destination uses the maximum a posterior (MAP) decoder to estimate the data sent from the source. The MAP decoder is optimal in the sense that it minimizes the the end-to-end error probability. The complexity of derivation comes from the fact that however the source generates data with equal probability, the data received at the destination does not have the same a priori probability. That is because of the error that occurs in the source-to-relay link. Hence, the MAP decoding rule can not be simplified to the maximum likelihood (ML) decoding rule. The results show that the upper bound is very tight. Therefore, the closed form expression of the upper bound can be used to fully study and understand the diversity performance of the DF cooperation protocol.

This study focused on the impact of used engine oil on the compressive strength of concrete. The compressive strengths of concrete cubes soaked in used mineral oil for 6 months were compared with those of oil-free concrete cubes. Five different concrete mixes were adopted to investigate the negative impact of mineral oil on low- and high-strength concrete. Furthermore, this paper describes an investigation into the effect of oil absorption on concrete frame foundations used for large machines at Assiut cement factory, CEMEX, in Egypt. It is concluded that the evaluation of the ggressive effect of mineral oil on concrete by experimentally comparing the strengths of oil-free concrete and oiled concrete at the same age is the most optimal and most reliable of the existing methods. The aggressiveness of oil is very clearly observed for low- and high-strength concrete, and the reductions in compressive strength were observed to be 17% and 11.8%, respectively. Additionally, based on this field study, the degree of oil absorption in concrete is an important determinant of compressive strength.