随机巨址通信中基于LDPC结构的可纠错多址码的构造与传输理论

随机巨址接入是近年来通信和信息领域的前沿热点，其希望在给定信噪比下，容纳更多的用户与此同时保证通信质量。我们提出的基于低密度奇偶校验码(LDPC)结构的可纠错多址接入码具有两大优势：存在大量适合多用户传输的可用码字集合；具有纠错能力可以改善系统传输质量。我们首先基于非二进制准循环LDPC的泰讷图结构，通过代数法设计基矩阵和替代矩阵集合，建立有限域矢量空间和多址叠加信号复数域矢量空间的映射关系，构造可纠错多址接入码(LDPC-UDC)，并使其具有双循环结构特征。然后，根据有限域哈达玛变换理论，结合消息传递算法思想设计多用户检测方案。最后，提出基于LDPC-UDC多维码本的随机多址接入系统，分析系统的信道容量，确定相应的接收机检测方案并进行性能分析。我们提出的LDPC-UDC将信道编码与多址接入有机融合，具有理论研究意义；与此同时易于工程转化，具有现实意义；为随机巨址接入提供有效技术解决方案。

Currently, massive random access is an appealing and hot research topic in both communication and information theory. In general, its target is to support massive users with acceptable BER (bit error rate) for a given SNR (signal-to-noise power ratio). To realize this purpose, we propose error correction multiple-access codes, which is also named as uniquely-decodable codes (UDC). Applying UDC in massive access communications is an attractive idea, since it has two major features. One is that there are a large number of codebooks for various users, and the other is that it can correct errors and provide better BER performances. Therefore, this project mainly focuses on three aspects. First of all, the base matrix and replacement sets of our proposed UDC are constructed by algebra method, referring to the idea of non-binary quasi-cyclic low-density parity-check codes (NB-QC-LDPC). Thus, our proposed UDC can be named as LDPC-UDC. One of the core issues is to find the relationship between the finite field and complex superimposed signals’ space. Secondly, essential and applicable multiple-user detection algorithms are presented for our proposed LDPC-UDC. Fast Hadamard transform (FHT) is taken into consideration to reduce the decoding complexity. Moreover, it is also interesting to present doubly cyclic LDPC-UDC. Thirdly, we propose multiple dimension LDPC-UDC systems for massive access communications; and do researches on its channel capacity, codebook design, detection algorithms, and performance analysis. Our proposed LDPC-UDC is a combination of channel codes and multiple-access, bringing lots of attractive research topics. Moreover, LDPC-UDC can be realized by hardware, and it is a valuable solution for the future massive access communications.