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This paper proposes a unified framework for addressing progressive image transmission over noisy channels based on the finite-state Markov channel (FSMC) model. FSMC models are simple yet general enough to model binary symmetric, Gilbert-Elliott, and fading channels. They allow error sequence analysis that facilitates quantifying the statistical characteristics of the embedded bitstreams transmitted over FSMC in closed form. Using a concatenation of rate-compatible puncturing convolutional code and cyclic redundancy check code for error protection, we use a concatenation of rate-compatible punctured convolutional code and cyclic redundancy check code for error protection, which results in an unequal error protection (UEP) system, and find (sub-)optimal rate allocation solutions for our setup. By mapping fading channels to FSMCs, the JSCC problem is thus solved without the burden of simulations using an image-dependent lookup table. Fast algorithms are proposed to search for the optimal UEP. Experiments on embedded image bitstreams over FSMCs confirm our analytical results.