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.

翻译：本文研究了一种基于格码的多址接入（LCMA）框架，并开发了对其实际应用至关重要的一系列处理技术。在上行链路中，$K$个用户采用相同的$2^{m}$-PAM信号环编码调制方案对其消息进行编码。通过该方案，多个码字的整数和属于基础码的$n$维格。这一特性使得能够为计算$K$个用户消息的线性组合实现高效的\textit{代数分箱}。针对接收端，我们基于线性物理层网络编码和线性滤波，设计了两种新算法，用于计算关于$K$个线性码字组合流的符号后验概率。所得的APP流被馈送至$q$元置信传播解码器，该解码器并行计算$K$个线性消息组合流。最后，通过乘以系数矩阵的逆矩阵，所有用户的消息得以恢复。即使采用单级并行处理，LCMA也被证明能够支持显著更多的用户，并且相较于现有的非正交多址接入系统（如IDMA和SCMA），其帧错误率性能得到改善。此外，我们提出了一种基于\emph{广义矩阵求逆}的新型多级LCMA接收机。通过该方案，在广泛的系统负载范围内实现了接近容量的性能。数值结果表明，LCMA能够支持的用户数量不低于扩频序列长度或接收天线数量的350%。由于LCMA放宽了接收机迭代要求，标准中的现成信道编码可直接使用，从而避免了IDMA和SCMA中信道编码与检测器之间的兼容性和收敛性问题。