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Quantum Key Distribution (QKD) offers unconditional security for symmetric key exchange by leveraging fundamental quantum principles such as the no-cloning theorem and measurement disturbance. In recent years, continuous-variable QKD (CV-QKD) protocols have gained prominence because of their compatibility with standard optical components, higher key rates over short distances, lower cost, and potential for photonic integration. However, their performance deteriorates over long distances due to increased sensitivity to channel loss and noise. To mitigate this, non-binary Low-Density Parity Check (NB-LDPC) codes have emerged as an effective error correction strategy during the reconciliation phase. The Extended Min-Sum (EMS) algorithm is a well-suited decoding technique for NB-LDPC codes over Galois Fields (<tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\text{GF}(q)$</tex>). However, its high computational complexity poses significant challenges for real-time deployment. Forward/backward EMS (FB-EMS), a scheduling-optimized variant of EMS, substantially reduces complexity and improves the feasibility of hardware implementation. This paper presents a flexible High-level Synthesis (HLS)-based implementation of FBEMS, accompanied by a comprehensive design space exploration on the Zynq Ultrascale+ RFSoC <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$4 \times 2$</tex> platform. The proposed architecture, FP-FBEMS, achieves a balance between on-chip resource usage and throughput, providing more than 2.48 Mbps over GF(64) with high scalability. Furthermore, our design achieves up to <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\mathbf{4 2. 0 3} \boldsymbol{\times}$</tex> higher throughput than a software implementation on the Ryzen Threadripper 3960X. Extensive designspace exploration confirms the system's flexibility, robustness, and state-of-the-art performance.