  Protograph-based Raptor-like low-density parity-check codes (PBRL codes) are
a recently proposed family of easily encodable and decodable rate-compatible
LDPC (RC-LDPC) codes. These codes have an excellent iterative decoding
threshold and performance across all design rates. PBRL codes designed thus
far, for both long and short block-lengths, have been based on optimizing the
iterative decoding threshold of the protograph of the RC code family at various
design rates.
  In this work, we propose a design method to obtain better quasi-cyclic (QC)
RC-LDPC codes with PBRL structure for short block-lengths (of a few hundred
bits). We achieve this by maximizing an upper bound on the minimum distance of
any QC-LDPC code that can be obtained from the protograph of a PBRL ensemble.
The obtained codes outperform the original PBRL codes at short block-lengths by
significantly improving the error floor behavior at all design rates.
Furthermore, we identify a reduction in complexity of the design procedure,
facilitated by the general structure of a PBRL ensemble.
