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A theory for pulse amplification and saturation in quantum dot (QD) semiconductor optical amplifiers (SOAs) is developed. In particular, the maximum bit rate at which a data stream of pulses can be amplified without significant patterning effects is investigated. Simple expressions are derived that clearly show the dependence of the maximum bit rate on material and device parameters. A comparative analysis of QD, quantum well (QW), and bulk SOAs shows that QD SOAs may have superior properties; calculations predict patterning-free amplification up to bit rates of ∼150-200 Gb/s with pulse output energies of ∼0.2-0.4 pJ. The superiority of QD SOAs is based on: 1) the faster achievement of the regime of maximum gain in QD SOAs compared to QW and bulk SOAs and 2) the lower effective cross section of photon-carrier interaction in QDs.