  A class of rate-adaptive protograph MacKay-Neal (MN) codes is introduced and
analyzed. The code construction employs an outer distribution matcher (DM) to
adapt the rate of the scheme. The DM is coupled with an inner protograph-based
low-density parity-check (LDPC) code, whose base matrix is optimized via
density evolution analysis to approach the Shannon limit of the binary-input
additive white Gaussian noise (biAWGN) channel over a given range of code
rates. The density evolution analysis is complemented by finite-length
simulations, and by a study of the error floor performance.
