For a multiple-input multiple-output (MIMO) system with unknown channel state information (CSI), a novel low-density parity check (LDPC)-coded transmission (LCT) scheme with joint pilot and data channel estimation is proposed. To fine-tune the CSI, a method based on the constraints introduced by the coded data from an LDPC code is designed such that the MIMO detector exploits the fine-tuned CSI. For reducing the computational burden, a coordinate ascent algorithm is employed along with several approximation methods, effectively reducing the required times of MIMO detection and computational complexity to achieve a satisfying performance. Simulation results utilizing WiMAX standard LDPC codes and quadrature phase-shift keying (QPSK) modulation demonstrate gains of up to 1.3 dB at a frame error rate (FER) of $10^{-4}$ compared to pilot-assisted transmission (PAT) over Rayleigh block-fading channels.