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In this paper, we study the efficacy of a model-based base-calling approach for Illumina's sequencing platforms. In particular, we investigate Genome Analyzer I reads and provide a detailed biochemical model of the sequencing process, incorporating various non-idealities evident in such systems. Parameters of the model are estimated via a supervised learning based on the particle swarm optimization technique. A computationally efficient sequential decoding method is proposed for base-calling. It is demonstrated that the performance of the proposed approach is comparable to Illumina's base-calling method.