D-IRA Codes Over Integer Rings for Lattice-Based Multiple Access

We study capacity-approaching irregular repeat accumulate (IRA) codes over integer rings $\mathbb {Z}_{2^{m}}$ for $2^{m}$ -PAM signaling, $m=1,2,\cdots $ . Such codes belong to the ensemble of lattice codes. First, the effect of zero-divisors on the iterative belief-propagation (BP) decoding is analyzed. We show that the symmetric Gaussian approximation is invalid for existing IRA codes over integer rings. Then we propose a new doubly IRA (D-IRA) ring code structure, which consists of irregular multiplier distribution and irregular node-degree distribution. Such structure can restore the symmetry and optimize the BP decoding threshold. Numerical result demonstrates the improved performance of D-IRA codes for AWGN channel. Also, it is demonstrated that the lattice based multiple-access scheme with D-IRA code performs within 3 dB the capacity limit.