  Protograph low-density-parity-check (LDPC) are considered to design
near-capacity low-rate codes over the binary erasure channel (BEC) and binary
additive white Gaussian noise (BIAWGN) channel. For protographs with degree-one
variable nodes and doubly-generalized LDPC (DGLDPC) codes, conditions are
derived to ensure 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.
