Design and performance of selected classes of Tanner codes

We study the design of structured Tanner codes with low error-rate floors on the binary additive white Gaussian noise channel (BAWGNC) and the binary erasure channel (BEC). The design technique involves the “doping" of standard LDPC protographs, meaning Hamming or recursive systematic convolutional (RSC) code constraints are used together with singleparity-check (SPC) constraints to construct a code’s protograph. We show that the doping of a “good" graph with Hamming or RSC codes is a pragmatic approach that frequently results in a code with a good threshold and very low error-rate floor. We focus on low-rate Tanner codes, in part because the design of low-rate, low-floor LDPC codes is particularly difficult.

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