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We focus on applications of low-rate Gallager (1963) (low-density parity-check) codes in code-division multiple-access schemes. The codes that we present here achieve good performance with relatively short frame-lengths in additive white Gaussian noise channels and, perhaps more importantly, in fading channels. These codes can be decoded with low complexity by using iterative decoding procedures. We present a construction that yields good short frame-length Gallager codes. Bounds on the frame-error probability for a maximum-likelihood decoder are obtained.