# LDPC Coded Massive MIMO Systems
## 6 Conclusions  
In this study, we designed the LDPC coded massive MIMO system equipped with an iterative JDD algorithm using the low-complexity FG-GAI BP detection and the sum-product decoding. We defined a factor graph representation of the LDPC coded massive MIMO system and defined updating rules for messages flowing in the JDD process. We proposed a 3-D EXIT analysis as an engineering tool for investigating the behavior of iterative JDD algorithm of coded massive MIMO receiver. Based on the EXIT analysis, we designed jointly irregular LDPC codes through the optimization of degree distributions and the JDD strategy to achieve the lowest BER with a given amount of computational complexity. The proposed 3-D EXIT analysis enables the efficient design of LDPC codes and JDD strategy for coded massive MIMO system in a joint manner. We observed that the JDD strategy and corresponding LDPC codes designed appropriately by using the proposed EXIT analysis shows a faster convergence rate than a conventional JDD algorithm. Thus, the proposed scheme results in the improved BER performance over the conventional one with the equivalent amount of computational complexity. This result is meaningful especially when the computational complexity of coded massive MIMO receiver is constrained to finite amount, which is a practical situation.  
In addition to the results presented in this paper, we plan to work on the following issues as future works.  
* We will perform 3-D EXIT analysis for coded massive MIMO system equipped with various kinds of MIMO detectors. Based on this, we plan to optimize the JDD strategy for each SISO MIMO detector under consideration and correspondingly design LDPC codes. Then, we will compare BER performances of coded massive MIMO systems using different MIMO detectors.
* We will study and analyze the influence of imperfect channel estimation on the performance of LDPC coded massive MIMO system. It is hard to obtain the perfect channel estimation in practice, so we need to investigate this issue thoroughly to utilize the proposed scheme in practical communication systems.  
Figure 10: BER performances of coded massive MIMO systems with the proposed LDPC codes and JDD strategy and with the conventional LDPC codes and GIO JDD, where \(R=0.75\) and \(N=2048\) over \(16\times 16\) and \(256\times 256\) channels were considered.  
* We will work on the finite-length analysis of LDPC coded massive MIMO system. It is well known that using channel codes with short to medium blocklength results in a gentle waterfall in the BER curve [42; 43; 44; 45]. Since practical communication systems use finite-length channel codes, we need to study this issue as a future work for the practical application of the coded massive MIMO technology.  
Conceptualization, J.W.L., I.H. and H.J.P.; software, I.H. and H.J.P.; investigation, J.W.L.; writing, J.W.L. and I.H.; project administration, J.W.L.; funding acquisition, J.W.L.  
This research was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (NRF-2016R1D1A1B03933174).  
The authors declare no conflict of interest.