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Distributed storage systems such as Ceph have been widely adopted, with erasure coding technology being an essential fault-tolerance technique. While ensuring data reliability and security, it significantly reduces the cost of data storage. Due to the computational overhead and encoding latency introduced by the erasure coding process, the data encoding rate is often constrained. To address this issue, an FPGA-accelerated erasure coding encoding scheme in Ceph, based on an efficient layered strategy (FPGA-Accelerated Erasure Coding Encoding in Ceph with an Efficient Layered Strategy, LFEC-Accelerator), is proposed and implemented. This approach takes full advantage of FPGA's parallel computing capabilities to accelerate the erasure coding algorithm at the hardware level. Furthermore, to maximize the utilization of the FPGA controller's resources and ensure that all processing steps are properly managed and scheduled, our approach introduces a hierarchical structure comprising a communication interface layer, task scheduling layer, and hardware acceleration layer. Experimental results indicate that, under the same erasure coding configurations and file sizes, our solution outperforms native Ceph-supported erasure coding libraries such as Jerasure, Clay, Shec and ISA, with an encoding rate improvement of up to 3.04 times. [ABSTRACT FROM AUTHOR]