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We propose a skew-insensitive frame-by-frame synchronization scheme for Tb/s optoelectronic packet-switch fabrics (PSFs). The proposed scheme employs an instantaneous-frame-reception technique and an automatic-frame-alignment technique. Cable length and transmission delay adjustment in erbium-doped fiber amplifiers and interconnects across shelves and cabinets are no longer necessary. The proposed scheme minimizes the frame header overhead such as a guard-time pattern and maximizes the effective bandwidth of the PSF. A partially installed 2.56-Tb/s PSF testbed, in spite of the presence of cables whose length is not known, demonstrates error-free switching of frames with a guard-time length as short as 3 ns.