K $K$ -user cyclic shift-aided serial concatenated code for Gaussian multiple access channel

A $K$-user cyclic shift-aided serial concatenated code (SCC) is proposed over a Gaussian multiple access channel (MAC). In this code, a cyclic shift-aided SCC, which integrates a regular repeat-accumulate code with rate-$1/q$ and cyclic shift spreading (CSS), is employed for each user. Here, CSS consists of a length-$L$ bit spreading, a same chip-level interleaver and a user-specific cyclic shifter. This change avoids repeated complex interleaver generation operation and the main objective is to replace the random interleaver. At the receiver, iterative decoding is considered. For the design and optimization of the proposed code, a fixed point analysis (FPA) is developed to obtain the optimal $q^{\ast }$ and $L^{\ast }$ that achieves the maximum sum rate. Then, an analytic expression of collision probability is derived as a function of $q$ and $L$. Finally, the advantage is analysed by comparing the generation time of interleaver. Moreover, FPA provides lower computation complexity in optimizing system parameters than the traditional EXIT chart method. Numerical results show that the design and optimization of the proposed code is more accurate, and support distinguishing between the users. The proposed code not only outperforms the traditional IDMA scheme in the bit error rate performance, but also provides much lower generation time of interleaver, especially for multiuser scenarios.