We consider two users $A$ and $B$ wanting to exchange their messages $M_{A}$ and $M_{B}$ via a relay in a wireless communication network. To this aim, we have two methods: direct forward (DF) and computation and forward (CAF). In the first method, after an orthogonal multiple access (OMA) or non-orthogonal multiple access (NOMA) phase, the receiver decodes the two messages. In the second method, after a NOMA phase, the receiver decodes only the (modulo) sum. In the latter case the capacity region (computation region) is not known. This paper compares the two methods. To such aim, we propose a unified coding framework and identify a lower bound of achievable computation rates. We consider three constellations for the symmetric two-user Gaussian channel with Eisenstein constellation showing highest performance. We also show that a minimum signal-to-noise ratio is required for our CAF method to outperform DF, and we obtain the numerical values of such minimum ratios for the three constellations. Finally, we show achievability of our bounds, which is proved to require affine codes for computation, which has not been proved before. Overall, our results are useful for communication system designers towards practical implementation of multiple access methods in integrated wireless systems.

中文翻译：

---

物理层计算作为集成无线系统的 NOMA

我们考虑两个用户 $A$ 和 $B$ 想要交换他们的消息 $M_{A}$ 和 $M_{B}$ 通过无线通信网络中的中继。为此，我们有两种方法：直接转发（DF）和计算转发（CAF）。在第一种方法中，在正交多址 (OMA) 或非正交多址 (NOMA) 阶段之后，接收器对这两个消息进行解码。在第二种方法中，在 NOMA 阶段之后，接收器仅解码（模）和。在后一种情况下，容量区域（计算区域）未知。本文比较了这两种方法。为此，我们提出了一个统一的编码框架，并确定了可实现的计算率的下限。我们考虑了对称双用户高斯信道的三个星座，其中爱森斯坦星座表现出最高的性能。我们还表明，我们的 CAF 方法需要最小的信噪比才能优于 DF，我们得到了三个星座的最小比率的数值。最后，我们展示了我们的边界的可实现性，这被证明需要仿射代码进行计算，而这在以前从未被证明过。总的来说，我们的结果对于通信系统设计人员在集成无线系统中实际实现多址方法很有用。