A joint design of sphere decoding and synchronization algorithms for multiple-input–multiple-output (MIMO) orthogonal frequency-division multiplexing (OFDM) systems with progressive parallel inter-carrier interference canceller (PPIC) based on factor graph based soft self-iterative equalization in wireless multipath channels for high speed wireless transmission is proposed. This algorithm can suppress inter-antenna interferences and cancel inter-carrier interferences iteratively and progressively. With a proper designed message passing schedule and random interleaver, the short cycle problem is solved. The proposed PPIC is superior to PIC both in computational complexity and system architecture. It is very suitable for VLSI implementation and it is a potential candidate for data detection/decoding in future high data rate, and high mobility, We consider the performance analysis and design optimization of low density parity check (LDPC) coded multipleinput- multiple-output (MIMO) orthogonal frequency-division multiplexing (OFDM) systems for high speed wireless transmission.