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Ambient backscatter technology has attracted much attention recently, because it enables battery-free devices, such as tags or sensors, to communicate through wireless energy harvesting and radio backscattering. Existing studies about ambient backscatter assume that the tags have only two states: backscatter or non-backscatter. Actually, some references have shown that the tags can readily realize three states: positive and negative phase backscatter, and non-backscatter. In this paper, we propose a new coding scheme for these tags with three states to improve the throughput of the ambient backscatter communication system. We then design a maximum a posteriori (MAP) detector for the reader to extract binary information from ternary coded signals. We also analyze the detection performance in terms of closed-form bit error rate (BER) expressions. It is found that the proposed coding scheme can improve the throughput of an ambient backscatter system, and there exists an error floor for the BER curve. Finally, simulation results are provided to corroborate our theoretical studies.