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We consider a nonergodic multiple-access Gaussian block-fading channel where a fixed number of independent and identically distributed (i.i.d.) fading coefficients affect each codeword. Variable-rate coding with input power constraint enforced on a per-codeword basis is examined. A centralized power and rate allocation policy is determined as a function of the previous and present fading coefficients. The power control policy that optimizes the expected rates is obtained through dynamic programming and the average capacity region and the average capacity region per unit energy are characterized. Moreover, we study the slope of spectral efficiency curve versus Eb/N0 (dB), and we quantify the penalty incurred by time-division multiple access (TDMA) over superposition coding in the low-power regime.