@article{krishnan_baron_2015, title={A Universal Parallel Two-Pass MDL Context Tree Compression Algorithm}, volume={9}, ISSN={["1941-0484"]}, DOI={10.1109/jstsp.2015.2403800}, abstractNote={Computing problems that handle large amounts of data necessitate the use of lossless data compression for efficient storage and transmission. We present a novel lossless universal data compression algorithm that uses parallel computational units to increase the throughput. The length-$N$ input sequence is partitioned into $B$ blocks. Processing each block independently of the other blocks can accelerate the computation by a factor of $B$, but degrades the compression quality. Instead, our approach is to first estimate the minimum description length (MDL) context tree source underlying the entire input, and then encode each of the $B$ blocks in parallel based on the MDL source. With this two-pass approach, the compression loss incurred by using more parallel units is insignificant. Our algorithm is work-efficient, i.e., its computational complexity is $O(N/B)$. Its redundancy is approximately $B\log(N/B)$ bits above Rissanen's lower bound on universal compression performance, with respect to any context tree source whose maximal depth is at most $\log(N/B)$. We improve the compression by using different quantizers for states of the context tree based on the number of symbols corresponding to those states. Numerical results from a prototype implementation suggest that our algorithm offers a better trade-off between compression and throughput than competing universal data compression algorithms.}, number={4}, journal={IEEE JOURNAL OF SELECTED TOPICS IN SIGNAL PROCESSING}, author={Krishnan, Nikhil and Baron, Dror}, year={2015}, month={Jun}, pages={741–748} }
@inproceedings{krishnan_baron_mihcak_2014, title={A Parallel two-pass MDL context tree algorithm for universal source coding}, DOI={10.1109/isit.2014.6875156}, abstractNote={We present a novel lossless universal source coding algorithm that uses parallel computational units to increase the throughput. The length-N input sequence is partitioned into B blocks. Processing each block independently of the other blocks can accelerate the computation by a factor of B, but degrades the compression quality. Instead, our approach is to first estimate the minimum description length (MDL) source underlying the entire input, and then encode each of the B blocks in parallel based on the MDL source. With this two-pass approach, the compression loss incurred by using more parallel units is insignificant. Our algorithm is work-efficient, i.e., its computational complexity is O(N/B). Its redundancy is approximately B log(N/B) bits above Rissanen’s lower bound on universal coding performance, with respect to any tree source whose maximal depth is at most log(N/B).}, booktitle={2014 ieee international symposium on information theory (isit)}, author={Krishnan, N. and Baron, Dror and Mihcak, M. K.}, year={2014}, pages={1862–5} }