text: abstract
  protograph low-density-parity-check (ldpc) are considered to design near-capacity lowrate 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.