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Iterative decoding of convolutional turbo code (CTC) has a large memory power consumption. To reduce the power consumption of the state metrics cache (SMC), low-power memory-reduced traceback maximum a posteriori algorithm (MAP) decoding is proposed. Instead of storing all state metrics, the traceback MAP decoding reduces the size of the SMC by accessing difference metrics. The proposed traceback computation requires no complicated reversion checker, path selection, and reversion flag cache. For double-binary (DB) MAP decoding, radix-2times2 and radix-4 traceback structures are introduced to provide a tradeoff between power consumption and operating frequency. These two traceback structures achieve an around 20% power reduction of the SMC, and around 7% power reduction of the DB MAP decoders. In addition, a high-throughput 12-mode WiMAX CTC decoder applying the proposed radix-2times2 traceback structure is implemented by using a 0.13-mum CMOS process in a core area of 7.16 mm2. Based on postlayout simulation results, the proposed decoder achieves a maximum throughput rate of 115.4 Mbps and an energy efficiency of 0.43 nJ/bit per iteration.