Computer Science – Information Theory
Scientific paper
2012-01-11
Computer Science
Information Theory
11 pages, 6 figures, 6 tables. Submitted to IEEE Transactions on Information Theory
Scientific paper
Recent work by Divsalar et al. has shown that properly designed protograph-based low-density parity-check(LDPC) codes may have minimum distance linearly increasing with block length. This fact rests on ensemble arguments over all possible expansions of the base protograph. However, when implementation complexity is considered, the expansions are frequently selected from a smaller class of orderly expansions. For example, protograph expansion by cyclically shifting connections generates a quasi-cyclic (QC) code. Other recent work by Smarandache and Vontobel 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 these upper bounds for the family of protograph codes known as AR4JA that have been proposed for deep space usage in the CCSDS experimental standard. Finally, we note that at block lengths more than 4400 bits these upper bounds fall below the ensemble statistical lower bounds of Divsalar, generating a new perspective on the minimum distance for the AR4JA codes in the standard.
Butler Brian K.
Siegel Paul H.
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