When simultaneous wireless information and power transfer is carried out, a fundamental tradeoff between achievable rate and harvested energy exists because the received power is used for two different purposes. The tradeoff is well characterized by the rate-energy region, and several techniques have been proposed to improve the achievable rate-energy region. However, the existing techniques still have a considerable loss in either energy or rate and thus the known achievable rate-energy regions are far from the ideal one. Deriving tight upper and lower bounds on the rate-energy region of our proposed scheme, we prove that the rate-energy region can be expanded almost to the ideal upper bound. Contrary to the existing techniques, in the proposed scheme, the information decoding circuit not only extracts amplitude and phase information but also combines the extracted information with the amplitude information obtained from the rectified signal. Consequently, the required energy for decoding can be minimized, and thus the proposed scheme achieves a near-optimal rate-energy region, which implies that the fundamental tradeoff in the achievable rate-energy region is nearly eliminated. To practically account for the theoretically achievable rate-energy region, we also present practical examples with an $M$-ary multi-level circular QAM with Gaussian maximum likelihood detection.