Abstract
Protograph low-density-parity-check (LDPC) codes are considered to design near-capacity low-rate codes over the binary erasure channel and the binary additive white Gaussian noise channel. For protographs with degree-one variable nodes and doubly-generalized LDPC (DGLDPC) codes, conditions are derived to ensure the equality of bit-error threshold and block-error threshold. Using this condition, low-rate codes with block-error threshold close to capacity are designed and shown to have better error rate performance than other existing codes.
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