  Motivated by applications of distributed storage systems to key-value stores,
the multi-version coding problem was formulated to efficiently store frequently
updated data in asynchronous decentralized storage systems. Inspired by
consistency requirements in distributed systems, the main goal in the
multi-version coding problem is to ensure that the latest possible version of
the data is decodable, even if the data updates have not reached some servers
in the system. In this paper, we study the storage cost of ensuring consistency
for the case where the data versions are correlated, in contrast to previous
work where data versions were treated as being independent. We provide
multi-version code constructions that show that the storage cost can be
significantly smaller than the previous constructions depending on the degree
of correlation, despite the asynchrony and the decentralized nature. Our
achievability results are based on Reed-Solomon codes and random binning.
Through an information-theoretic converse, we show that our multi-version codes
are nearly-optimal, within a factor of $2$, in certain interesting regimes.
