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This correspondence analyzes the bit-error rate (BER) performance of coded synchronous code-division multiple-access (CDMA) systems assuming perfect channel state information (CSI) and optimal joint multiuser detection/decoding (OJMUDD). Our analysis is conducted in the same framework as that of uncoded systems. First, we derive the precise probability of an error event, then we provide an upper bound on the BER based on the sum of pairwise error probabilities, and, finally, we tighten the upper bound by considering decomposable error events. Many new concepts unique to coded systems are introduced. We propose to use quasi parity checks for identifying permissible error events, introduce the concept of compatible probability of error matrices, extend the list of conditions for identifying decomposable error events, and introduce the concept of conjugate sets to explore the symmetry among indecomposable error events. Simulation results are given along with theoretical predictions.