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Like its wireless counterpart, optical code-division multiple access (optical CDMA) offers greater scalability than other optical multiplexing schemes and provides flexible quality of service, physical layer privacy and asynchronous access. However, unlike wireless CDMA, high bit-rate optical CDMA networks use much higher bandwidth, which cannot be effectively processed with modern electronics rendering many earlier developed detection schemes inapplicable. In this paper we show both theoretically and experimentally that conventional electronics-based detection is inefficient in optical CDMA networks and limits the total network throughput by the bandwidth of the photodetector used. As a solution, we show that network performance can be greatly improved using ultrafast all-optical signal processing for signal detection. Recently developed all-optical thresholding devices performing cubic transformation allow for more than seven times increase in throughput for typical network parameters. A comprehensive comparison of different detection methods for optical CDMA including optimized electronics-based and all-optical signal processing-based is given for the first time.