In this paper, we study the problem of storing an archive of versioned data in a reliable and efficient manner in distributed storage systems. We propose a new storage technique called differential erasure coding (DEC) where the differences (deltas) between subsequent versions are stored rather than the whole objects, akin to a typical delta encoding technique. However, unlike delta encoding techniques, DEC opportunistically exploits the sparsity (i.e., when the differences between two successive versions have few non-zero entries) in the updates to store the deltas using compressed sensing techniques applied with erasure coding. We first show that DEC provides significant savings in the storage size for versioned data whenever the update patterns are characterized by in-place alterations. Subsequently, we propose a practical DEC framework so as to reap storage size benefits against not just in-place alterations but also real-world update patterns such as insertions and deletions that alter the overall data sizes. We conduct experiments with several synthetic workloads to demonstrate that the practical variant of DEC provides significant reductions in storage overhead (up to 60\% depending on the workload) compared to baseline storage system which incorporates concepts from Rsync, a delta encoding technique to store and synchronize data across a network.