—Convolutional turbo decoding requires large data access and consumes large memories. To reduce the size of the metrics memory, the traceback MAP decoding is introduced for double-binary convolutional turbo codes without losing the correction performance. The traceback technique reduces the metrics memory size with no other checkers which prolong the decoding latency. Two proposed traceback structures have a tradeoff between the power and operating frequency. The traceback structures can achieve around 20% power reduction of the metrics memory and around 7% power reduction of the decoders for WiMAX standard.