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This paper discusses the construction of the Accumulate-Repeat-4-Jagged-Accumulate(AR4JA) codes which is suitable for the deep-space communication based on the protograph. Two-step construction method of designing the AR4JA codes whose minimum distance grows linearly with block size, is proposed. Two-step expansion improves the traditional PEG with adding the ACE algorithm for placing edges in a protograph-based code, which brings down the error floor. Compared to the traditional random expansion and the one step expansion like Progressive Edge-Growth(PEG), the two-step construction algorithm aims at constructing the AR4JA codes with high performance and low complexity.
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