To address the limitations of traditional over-the-air federated learning (OA-FL) such as limited server coverage and low resource utilization, we propose an OA-FL in MIMO cloud radio access network (MIMO Cloud-RAN) framework, where edge devices upload (or download) model parameters to the cloud server (CS) through access points (APs). Specifically, in every training round, there are three stages: edge aggregation; global aggregation; and model updating and broadcasting. To better utilize the correlation among APs, called inter-AP correlation, we propose modeling the global aggregation stage as a lossy distributed source coding (L-DSC) problem to make analysis from the perspective of rate-distortion theory. We further analyze the performance of the proposed OA-FL in MIMO Cloud-RAN framework. Based on the analysis, we formulate a communication-learning optimization problem to improve the system performance by considering the inter-AP correlation. To solve this problem, we develop an algorithm by using alternating optimization (AO) and majorization-minimization (MM), which effectively improves the FL learning performance. Furthermore, we propose a practical design that demonstrates the utilization of inter-AP correlation. The numerical results show that the proposed practical design effectively leverages inter-AP correlation, and outperforms other baseline schemes.