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Variable length codes (VLCs), used in data compression, are very sensitive to error propagation in the presence of noisy channels. Addressing this problem with joint source-channel turbo techniques has been proposed in the literature and looks quite promising. But to date, most code-related conclusions are based on simulations. This paper states and proves several theoretical results about the robustness of prefix VLCs concatenated with linear error correcting codes (ECC), assuming a maximum likelihood decoder. Especially, an approximate and asymptotically tight distance spectrum of the concatenated code (VLC+ECC) is rigorously developed. Together with the union bound, it provides upper bounds on the symbol and frame/packet error rates.