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This paper proposes a new method for contention resolution in random-access wireless networks. Using orthogonal complementary codes to design access-request packets, users can reserve channel access successfully, even in severe contentions. Collisions among access-request packets can be resolved and exploited, whereas collisions among data packets are avoided. System throughput and delay performance can be enhanced, because random-access contention becomes transparent. Specifically, system throughput approaches the offered load up to the maximum value one with improved average packet delay performance. A joint layer design approach is proposed with both the physical layer signal-detection algorithm and the medium access-control layer random-access protocol. The performance is analyzed with the consideration of signal detection errors. Simulations are performed to demonstrate its superior performance.