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The original design of standard digital fountain codes assumes that the coded information symbols are equally important. In many applications, some source symbols are more important than others, and they must be recovered prior to the rest. Unequal error protection (UEP) designs are attractive solutions for such source transmissions. In this paper, we introduce a more generalized design for the first universal fountain code design, Luby transform (LT) codes, that make it particularly suited for progressive bit stream transmissions. We apply the generalized LT codes to a progressive source and show that it has better UEP properties than other published results in the literature. For example, using the proposed generalization, we obtained up to 1.7-dB peak signal to noise ratio gain in a progressive image transmission scenario over the two major UEP fountain code designs.