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Binary LDPC codes built out of protographs constitute a class of high-performance structured codes. In this paper we carefully extend the code construction to the non-binary case. We present a method based on a newly developed EXIT-chart approach to efficiently design non-binary protograph-based LDPC codes with good properties. The results presented here can be particularly useful in the development of coding schemes that can be effectively combined with non-binary modulation in bandwidth-efficient high-speed communication systems.