We consider communication over the Gaussian multiple-access channel in the regime where the number of users grows linearly with the codelength. In this regime, schemes based on sparse superposition coding can achieve a near-optimal tradeoff between spectral efficiency and signal-to-noise ratio. However, these schemes are feasible only for small values of user payload. This paper investigates efficient schemes for larger user payloads, focusing on 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 its tradeoff between spectral efficiency and signal-to-noise ratio, for a given target error rate. Simulation results show that the decoder achieves state-of-the-art performance at finite lengths, with a coded CDMA scheme defined using LDPC codes and a spatially coupled matrix of signature sequences.

翻译：本文研究高斯多址接入信道中的通信问题，重点关注用户数量与码长呈线性增长的系统场景。在此场景下，基于稀疏叠加编码的方案能够实现频谱效率与信噪比之间的近似最优权衡。然而，这些方案仅适用于较小用户载荷的情况。本文针对较大用户载荷场景，研究以编码CDMA方案为核心的高效通信方案，其中每个用户的信息先通过线性码编码，再使用特征序列进行调制。我们提出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表征。基于此结果，我们研究了一种融合AMP与置信传播的解码器，并在给定目标误码率条件下，刻画了其频谱效率与信噪比之间的权衡关系。仿真结果表明：采用LDPC码与特征序列空间耦合矩阵定义的编码CDMA方案，该解码器在有限码长条件下能够达到当前最优性能。