We investigate the spectral efficiency achievable by random synchronous code-division multiple access (CDMA) with quaternary phase-shift keying (QPSK) modulation and binary error-control codes, in the large system limit where the number of users, the spreading factor, and the code block length go to infinity. For given codes, we maximize spectral efficiency assuming a minimum mean-square error (MMSE) successive stripping decoder for the cases of equal rate and equal power users. In both cases, the maximization of spectral efficiency can be formulated as a linear program and admits a simple closed-form solution that can be readily interpreted in terms of power and rate control. We provide examples of the proposed optimization methods based on off-the-shelf low-density parity-check (LDPC) codes and we investigate by simulation the performance of practical systems with finite code block length.

We optimize the random-like ensemble of irregular repeat-accumulate (IRA) codes for binary-input symmetric channels in the large block-length limit. Our optimization technique is based on approximating the evolution of the densities (DE) of the messages exchanged by the belief-propagation (BP) message-passing decoder by a one-dimensional dynamical system. In this way, the code ensemble optimization can be solved by linear programming. We propose four such DE approximation methods, and compare the performance of the obtained code ensembles over the binary-symmetric channel (BSC) and the binary-antipodal input additive white Gaussian noise channel (BIAWGNC). Our results clearly identify the best among the proposed methods and show that the IRA codes obtained by these methods are competitive with respect to the best known irregular low-density parity-check (LDPC) codes. In view of this and the very simple encoding structure of IRA codes, they emerge as attractive design choices.