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This paper presents a simple yet effective method for designing nested families of LDPC codes. Rate compatible codes are essential for many communication applications, e.g. hybrid automatic repeat request (HARQ) systems, and their design is nontrivial due to the difficulty of simultaneously guaranteeing the quality of several related codes. Puncturing can be used to generate rate-compatible LDPC codes, but it produces a gap to capacity that, in practice, often significantly exceeds the gap of the mother code. We propose an alternative method based on successively extending a high-rate protograph. The resulting codes not only inherit the advantages of protograph codes, namely low encoding complexity and efficient decoding algorithms, but also cover a wide range of rates and have very good performance with iterative decoding thresholds that are within 0.2 dB of their capacity limits.