On Distance Properties of Quasi-Cyclic Protograph-Based LDPC Codes

Details On Distance Properties of Quasi-Cyclic Protograph-Based LDPC Codes On Distance Properties of Quasi-Cyclic Protograph-Based LDPC Codes

2010-04-30

arxiv.org/abs/1004.5429v1

Computer Science

Information Theory

Submitted to IEEE International Symposium on Information Theory, to be held June 2010

Scientific paper

10.1109/ISIT.2010.5513638

Recent work has shown that properly designed protograph-based LDPC codes may have minimum distance linearly increasing with block length. This notion rests on ensemble arguments over all possible expansions of the base protograph. When implementation complexity is considered, the expansion is typically chosen to be quite orderly. For example, protograph expansion by cyclically shifting connections creates a quasi-cyclic (QC) code. Other recent work has provided upper bounds on the minimum distance of QC codes. In this paper, these bounds are expanded upon to cover puncturing and tightened in several specific cases. We then evaluate our upper bounds for the most prominent protograph code thus far, one proposed for deep-space usage in the CCSDS experimental standard, the code known as AR4JA.

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