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A new method is proposed to analyze the cutoff rate of a variable-bit-rate (VBR) optical fast frequency hopping code division multiple access system (OFFH-CDMA) using fiber Bragg gratings and direct detection. This approach exploits the linear structure of passive optical CDMA systems and the nominal time required to accomplish the encoding-decoding operations in such systems. A system model is presented and analyzed based on a newly introduced bit-overlap procedure. An expression for the cutoff rate of a VBR OFFH-CDMA system is derived. It is shown that for a required quality of service (QoS) guarantee, the system's data rate can be increased beyond the nominal limit imposed by the physical constraint of the encoder-decoder set.