  This paper deals with the problem of massive random access for Gaussian
multiple access channel (MAC). We continue to investigate the coding scheme for
Gaussian MAC proposed by A. Vem et al in 2017. The proposed scheme consists of
four parts: (i) the data transmission is partitioned into time slots; (ii) the
data, transmitted in each slot, is split into two parts, the first one set an
interleaver of the low-density parity-check (LDPC) type code and is encoded by
spreading sequence or codewords that are designed to be decoded by compressed
sensing type decoding; (iii) the another part of transmitted data is encoded by
LDPC type code and decoded using a joint message passing decoding algorithm
designed for the T-user binary input Gaussian MAC; (iv) users repeat their
codeword in multiple slots. In this paper we are concentrated on the third part
of considered scheme. We generalized the PEXIT charts to optimize the
protograph of LDPC code for Gaussian MAC. The simulation results, obtained at
the end of the paper, were analyzed and compared with obtained theoretical
bounds and thresholds. Obtained simulation results shows that proposed LDPC
code constructions have better performance under joint decoding algorithm over
Gaussian MAC than LDPC codes considered by A. Vem et al in 2017, that leads to
the better performance of overall transmission system.
