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To further reduce the size of computers and increase their speed, optical technology has to replace electrical technology for motherboard-level interconnects. This letter presents a new design for motherboard-level interconnects based on the unguided optical interconnection board concept. The design includes chips with optical transceivers that communicate using diffused light through the same shared optical medium. In this letter, we derive a model of bit-error probability (BER) and find the order of the Lambertian reflection that maximizes the BER.