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Optical processing of optical labels at high-bit rate is expected in broadband photonic label routers. So far, a variety of optical waveguide circuits and systems to recognize optical BPSK and QPSK coded labels have been studied. In this paper, we propose optical waveguide circuits to recognize optical 16QAM codes. The circuits consist of multi-stage connection of previously proposed circuit for QPSK code recognition. The recognition characteristics for 16QAM codes are theoretically analyzed. To confirm the recognition principle, FD-BPM simulation is performed with a two-dimensional model. Scaled circuits for recognition of 2-symbol 16QAM coded labels and 64QAM codes are also discussed.