  Many applications require data processing to be performed on individual
pieces of data which are of finite sizes, e.g., files in cloud storage units
and packets in data networks. However, traditional universal compression
solutions would not perform well over the finite-length sequences. Recently, we
proposed a framework called memory-assisted universal compression that holds a
significant promise for reducing the amount of redundant data from the
finite-length sequences. The proposed compression scheme is based on the
observation that it is possible to learn source statistics (by memorizing
previous sequences from the source) at some intermediate entities and then
leverage the memorized context to reduce redundancy of the universal
compression of finite-length sequences. We first present the fundamental gain
of the proposed memory-assisted universal source coding over conventional
universal compression (without memorization) for a single parametric source.
Then, we extend and investigate the benefits of the memory-assisted universal
source coding when the data sequences are generated by a compound source which
is a mixture of parametric sources. We further develop a clustering technique
within the memory-assisted compression framework to better utilize the memory
by classifying the observed data sequences from a mixture of parametric
sources. Finally, we demonstrate through computer simulations that the proposed
joint memorization and clustering technique can achieve up to 6-fold
improvement over the traditional universal compression technique when a mixture
of non-binary Markov sources is considered.
