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In this paper, exact analytical expressions for the bit error rates (BERs) in a multiple-access chaos-based digital communication system are derived. Comparisons are made with those obtained using traditional approximation methods which assume a Gaussian distribution for the conditional decision parameter. The obtained results are compared to the results of brute-force (BF) numerical simulations. It is found that the exact analytical BERs are in perfect agreement with BF simulations and hence provide better prediction of the BER performance than those given by traditional Gaussian-approximation-based methods.