On Lattice-Code based Multiple Access: Uplink Architecture and Algorithms

This paper studies a lattice-code based multiple-access (LCMA) framework, and develops a package of processing techniques that are essential to its practical implementation. In the uplink, $K$ users encode their messages with the same ring coded modulation of $2^{m}$-PAM signaling. With it, the integer sum of multiple codewords belongs to the $n$-dimension lattice of the base code. Such property enables efficient \textit{algebraic binning} for computing linear combinations of $K$ users' messages. For the receiver, we devise two new algorithms, based on linear physical-layer network coding and linear filtering, to calculate the symbol-wise a posteriori probabilities (APPs) w.r.t. the $K$ streams of linear codeword combinations. The resultant APP streams are forwarded to the $q$-ary belief-propagation decoders, which parallelly compute $K$ streams of linear message combinations. Finally, by multiplying the inverse of the coefficient matrix, all users' messages are recovered. Even with single-stage parallel processing, LCMA is shown to support a remarkably larger number of users and exhibits improved frame error rate (FER) relative to existing NOMA systems such as IDMA and SCMA. Further, we propose a new multi-stage LCMA receiver relying on \emph{generalized matrix inversion}. With it, a near-capacity performance is demonstrated for a wide range of system loads. Numerical results demonstrate that the number of users that LCMA can support is no less than 350\% of the length of the spreading sequence or number of receive antennas. Since LCMA relaxes receiver iteration, off-the-shelf channel codes in standards can be directly utilized, avoiding the compatibility and convergence issue of channel code and detector in IDMA and SCMA.