Forward error correction (FEC) is a critical component in communication systems as the errors induced by noisy channels can be corrected using the redundancy in the coded message. This paper introduces a novel multi-mode FEC decoder accelerator that can decode Turbo, LDPC, and Polar codes using a unified architecture. The proposed design explores the similarities in these codes to enable energy efficient decoding with minimal overhead in the total area of the unified architecture. Moreover, the proposed design is highly reconfigurable to support various existing and future FEC standards including 3GPP LTE/5G, and IEEE 802.11n WiFi. Implemented in GF 12nm FinFET technology, the design occupies 8.47mm2 of chip area attaining 25% logic and 49% memory area savings compared to a collection of single-mode designs. Running at 250MHz and 0.8V, the decoder achieves per-iteration throughput and energy efficiency of 690Mb/s and 44pJ/b for Turbo; 740Mb/s and 27.4pJ/b for LDPC; and 950Mb/s and 45.8pJ/b for Polar.