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In this paper, we introduce multiple-access half-degraded relay channel (MAHDRC), an important model in cooperative uplink of cellular communications, and obtain an achievable rate region for it, using superposition coding, message splitting-partitionning and jointly decoding strategy. According to the possible states for unknown relay channels, also we introduce other types of multiple-access relay channels (MARC). For all of these special MARCs, we obtain the achievable rate regions. Then, we extend the obtained results to the Gaussian case and illustrate the results numerically.