Storage systems have a strong need for substantially improving their error correction capabilities, especially for long-term storage where the accumulating errors can exceed the decoding threshold of error-correcting codes (ECCs). In this work, a new scheme is presented that uses deep learning to perform soft decoding for noisy files based on their natural redundancy. The soft decoding result is then combined with ECCs for substantially better error correction performance. The scheme is representation-oblivious: it requires no prior knowledge on how data are represented (e.g., mapped from symbols to bits, compressed, and combined with meta data) in different types of files, which makes the solution more convenient to use for storage systems. Experimental results confirm that the scheme can substantially improve the ability to recover data for different types of files even when the bit error rates in the files have significantly exceeded the decoding threshold of the ECC.