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Coding schemes for the binary memoryless -user adder channel are investigated in this paper. First upper and lower bounds on the capacity sum, which are asymptotically tight with increasing , are derived for the noiseless case. Second, a class of -user uniquely decodable codes with rates, asymptotically in , equal to the maximal achievable values is constructed. A decoding algorithm for these codes is also presented. Next, a class of error-correcting codes for the noisy -user adder channel is constructed. It is shown that these codes can he used to construct multilevel codes suitable for use on the additive white Gaussian noise channel.