In most modern wireless systems, adaptive modulation and channel coding is applied to achieve a high spectral efficiency. Hence, suitable receivers need to support a large variety of modulation and channel coding schemes (MCS) while maintaining a low complexity. The performance and complexity of a multi-dimensional factor-graph based (MD-GSIR) framework for iterative joint channel estimation and data detection is investigated for the application of adaptive modulation and coding in an LTE environment. Three detection algorithms within the MD-GSIR framework are investigated and a novel tree-based detection is proposed. The versatile structure of the MD-GSIR concept offers a flexible trade-off between computational complexity and performance. Furthermore, the message exchange is adapted to support the irregular training structure which may occur in adaptive environments.