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A serial unequal error protection (UEP) code system for use with information sources that contain a mixture of both important and less important data is proposed. To achieve UEP, the proposed scheme uses a form of trellis coded modulation (TCM) which encodes the data by switching between two codes that use different signal constellations. The proposed system uses two ring signal constellations (2RING). No extra information about which code was used is added. The receiver decides which code was used by examining the received signal points. In this paper, a theoretical analysis of the 2RING signal constellation is presented, and the effectiveness of the system for AWGN channels is shown using computer simulations.