Data deduplication and erasure coding are two widely used strategies for reducing storage overhead and resisting unexpected failures. However, combining these approaches without careful consideration can potentially diminish fault tolerance and increase access latency. In this paper, we propose DraEC, a decentralized routing algorithm designed specifically for erasure-coded deduplication systems. DraEC encodes data before performing deduplication. It then employs cuckoo hashing to maximize fault tolerance offered by erasure coding without compromising the data deduplication. DraEC further adaptively determines the placement of data and parity blocks to balance the storage load and mitigate access hotspots. Extensive testbed experiments show that DraEC can achieve a 9.2% improvement in write performance, which can increase to 94.1% under intensive write requests. DraEC also achieves a 17.6% improvement in read performance under intensive reads, while introducing less than 1% additional storage overhead.