We consider communication over the Gaussian multiple-access channel in the regime where the number of users grows linearly with the codelength. We investigate coded CDMA schemes where each user's information is encoded via a linear code before being modulated with a signature sequence. We propose an efficient approximate message passing (AMP) decoder that can be tailored to the structure of the linear code, and provide an exact asymptotic characterization of its performance. Based on this result, we consider a decoder that integrates AMP and belief propagation and characterize the tradeoff between spectral efficiency and signal-to-noise ratio, for a given target error rate. Simulation results are provided to demonstrate the benefits of the concatenated scheme at finite lengths.

翻译：我们考虑在高斯多址接入信道中通信的情形，此时用户数量随码长线性增长。我们研究编码码分多址方案，其中每个用户的信息在通过签名序列调制之前，先使用线性码进行编码。我们提出了一种高效的近似消息传递（AMP）解码器，该解码器可根据线性码的结构进行定制，并对其性能给出了精确的渐近刻画。基于这一结果，我们考虑一种融合AMP与置信传播的解码器，并针对给定目标误码率，刻画了频谱效率与信噪比之间的权衡关系。仿真结果验证了所提出的级联方案在有限码长下的优势。