In this article, we propose a new fully distributed cell-free multiple-input and multiple-output (MIMO) architecture that enables independent deployment of access points (APs) without any infrastructure such as a central processing unit (CPU). In the proposed architecture, all baseband processing is distributively executed by homogeneous APs without any CPU, thanks to the fully distributed functional split structure. Since the proposed architecture only consists of APs, we expect that a 5G/6G-based private network with a cell-free MIMO capability can easily be built for Industrial Internet of Things (IIoT) applications without the help of mobile network operators (MNOs). We also propose a novel precoding algorithm for orthogonal frequency division multiplexing (OFDM)-based cell-free MIMO systems. In the proposed precoding algorithm, the APs in a user-centric cluster cooperatively maximize the capacity of the target user equipment (UE) while minimizing the interference to nearby UEs. The proposed precoding algorithm solves the OFDM power allocation problem to allocate power on a per-subcarrier basis under the per- AP power constraints, which has not been addressed in previous works. We have built a full-fledged and real-time cell-free MIMO testbed that implements the proposed cell-free MIMO architecture and precoding algorithm. The validity of the proposed architecture and precoding algorithm is verified by experiments and simulations.