In this work, we propose the integration of GLDPC codes with short polar-like component codes, termed GLDPC codes with polar component codes (GLDPC-PC). This approach leverages the good distance properties of polar-like codes and mitigates their high decoding latency in long block lengths. A recently proposed soft-input soft-output decoder for polar-like codes enables effective iterative belief propagation decoding for GLDPC-PC, ensuring a low error floor under additive white Gaussian noise channels. Simulation results demonstrate that GLDPC-PC codes achieve significant performance improvements in multiple-input multiple-output systems with iterative detection and decoding (IDD). The proposed GLDPC-PC codes and the IDD scheme can be applied to various scenarios.