  In this work, we develop a pair of rate-diverse encoder and decoder for a
two-user Gaussian multiple access channel (GMAC). The proposed scheme enables
the users to transmit with the same codeword length but different coding rates
under diverse user channel conditions. First, we propose the row-combining (RC)
method and row-extending (RE) method to design practical low-density
parity-check (LDPC) channel codes for rate-diverse GMAC. Second, we develop an
iterative rate-diverse joint user messages decoding (RDJD) algorithm for GMAC,
where all user messages are decoded with a single parity-check matrix. In
contrast to the conventional network-coded multiple access (NCMA) and
compute-forward multiple access (CFMA) schemes that first recover a linear
combination of the transmitted codewords and then decode both user messages,
this work can decode both the user messages simultaneously. Extrinsic
information transfer (EXIT) chart analysis and simulation results indicate that
RDJD can achieve gains up to 1.0 dB over NCMA and CFMA in the two-user GMAC. In
particular, we show that there exists an optimal rate allocation for the two
users to achieve the best decoding performance given the channel conditions and
sum rate.
