We design a low-density parity-check (LDPC) coded multi-user (MU) massive multipleinput multiple-output (MIMO) system with an iterative joint detection and decoding (JDD) algorithm. As a low-complexity MU detection scheme, we consider a factor graph based belief propagation detection with Gaussian approximation of interference, called a FG-GAI BP detection. We introduce a factor graph representation of LDPC coded MU massive MIMO system and define the message updating rule in the JDD process. We devise a design tool for analyzing extrinsic information transfer (EXIT) characteristics of messages exchanged in JDD, based on which degree distribution of LDPC codes and a JDD strategy are efficiently designed for coded MU massive MIMO systems. A JDD strategy and LDPC codes are designed such that a fast convergence of JDD and a low bit error probability are attained. It is observed that the coded MU massive MIMO system equipped with LDPC codes and the JDD strategy designed by the proposed method shows a lower bit error rate than conventional ones with a given number of iterations.