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The number of users that can be supported by frequency-hopped, spread-spectrum multiple-access systems can be increased greatly by using multiuser demodulation and iterative decoding. In the receiver employed hard-decision multiuser demodulation followed by iterative decoding, users exchange decoded information with each other. Additional information from multiuser demodulation in the first decoding iteration is limited by the hard-decision output of the multiuser demodulator. The error-correction used was an errors-and-erasures Reed-Solomon (RS) decoder. We revisit hard-decision demodulation and conventional RS decoding. Hard-decision multiuser demodulation is modified to provide a soft output, which is then given to a nonbinary block turbo code with shortened RS codes as the constituent codes. An iterative multiuser decoding algorithm is developed to do soft multiuser interference cancellation. This soft receiver with soft demodulation and decoding is shown to be more resistant to multiuser interference and channel noise, especially at lower values of signal-to-noise ratio. The results show a great improvement in the ability of the system to support more users (more than three times in some cases), as compared with systems that erase all hits or employ hard-decision multiuser demodulation followed by RS code. We examine the proposed method for synchronous as well as asynchronous frequency-hopped systems in both AWGN and fading channels.