Compute-forward multiple access (CFMA) is a transmission strategy which allows the receiver in a multiple access channel (MAC) to first decode linear combinations of the transmitted signals and then solve for individual messages. Compared to existing MAC strategies such as joint decoding or successive interference cancellation (SIC), CFMA was shown to achieve the MAC capacity region for fixed channels under certain signal-to-noise (SNR) conditions without time-sharing using only single-user decoders. This paper studies the CFMA scheme for a two-user Gaussian fast fading MAC with channel state information only available at the receiver (CSIR). We develop appropriate lattice decoding schemes for the fading MAC and derive the achievable rate pairs for decoding linear combinations of codewords with any integer coefficients. We give a sufficient and necessary condition under which the proposed scheme can achieve the ergodic sum capacity. Furthermore, we investigate the impact of channel statistics on the capacity achievability of the CFMA scheme. In general, the sum capacity is achievable if the channel variance is small compared to the mean value of the channel strengths. Various numerical results are presented to illustrate the theoretical findings.

翻译：计算前向多址接入（CFMA）是一种传输策略，它允许多址接入信道（MAC）中的接收器首先解码传输信号的线性组合，然后求解各个消息。与现有MAC策略（如联合解码或连续干扰消除（SIC））相比，CFMA被证明能在特定信噪比（SNR）条件下，无需时分复用，仅使用单用户解码器即可实现固定信道的MAC容量区域。本文研究了两用户高斯快衰落MAC下的CFMA方案，其中信道状态信息仅在接收端可用（CSIR）。我们为衰落MAC开发了适当的格形解码方案，并推导了使用任意整数系数解码码字线性组合的可达速率对。我们给出了所提方案实现遍历和容量的充分必要条件。此外，我们研究了信道统计特性对CFMA方案容量可达性的影响。通常，当信道方差相对于信道强度均值较小时，和容量可达。最后，通过多种数值结果说明理论发现。