Abstract
Since energy efficiency, high bandwidth, and low transmission delay are challenging issues in mobile networks, due to resource constraints, there is a great importance in designing of new communication methods. In particular, lossless data compression may provide high performance under constrained resources. In this paper we present a novel on-line and entropy adaptive compression scheme for streaming unbounded length inputs. The scheme extends the window dictionary Lempel–Ziv compression and is adaptive and tailored to compress on-line non entropy stationary inputs. Specifically, the window dictionary size is changed in an adaptive manner to fit the current best compression rate for the input. On-line entropy adaptive compression scheme (EAC), introduced and analyzed in this paper, examines all possible sliding window sizes over the next input portion to choose the optimal window size for this portion; a size that implies the best compression ratio. The size found is then used in the actual compression of this portion. We suggest an adaptive encoding scheme, which optimizes the parameters block by block, and base the compression performance on the optimality proof of LZ77 when applied to blocks (Ziv in IEEE Trans Inf Theory 55(5):1941–1944, 2009). This adaptivity can be useful for many communication tasks. In particular, providing efficient utilization of energy consuming wireless devices by data compression. Due to the dynamic and non-uniform structure of multimedia data, adaptive approaches for data processing are of special interest. The EAC scheme was tested on different types of files (docx, ppt, jpeg, xls) and over synthesized files that were generated as segments of homogeneous Markov Chains. Our experiments demonstrate that the EAC scheme typically provides a higher compression ratio than LZ77 does, when examined in the scope of on-line per-block compression of transmitted (or compressed) files. We propose techniques intended to control the adaptive on-line compression process by estimating relative entropy between two sequential blocks of data. This approach may enhance performance of the mobile networks.
Similar content being viewed by others
References
Ziv, J., & Lempel, A. (1977). A universal algorithm for sequential data compression. IEEE Transactions on Information Theory, IT–24, 337–343.
Ziv, J., & Lempel, A. (1978). Compression of individual sequences via variable-rate coding. IEEE Transactions on Information Theory, IT–24, 530–536.
Bender, P. E., & Wolf, J. K. (1991). New asymptotic bounds and improvements on the Lempel–Ziv data compression algorithm. IEEE Transactions on Information Theory, 37(3), 721–729.
Hershkovits, Y., & Ziv, J. (1998). On sliding-window universal data compression with limited memory. IEEE Transactions on Information Theory, 44(1), 66–78.
Wyner, A. D., & Ziv, J. (1994). The sliding-window Lempel–Ziv algorithm is asymptotically optimal. Proceedings of the IEEE, 82(6), 872–877.
Hershkovits, Y., & Ziv, J. (1997). On fixed-database universal data compression with limited memory. IEEE Transactions on Information Theory, 43(6), 1966–1976.
Rao Kosaraju, S., Manzini, G. (1999). Compression of low entropy strings with Lempel–Ziv algorithms. SIAM Journal Computation, 29(3), 893–911.
Ma, T. (2013). A survey of energy-efficient compression and communication techniques for multimedia in resource constrained systems. Communications Surveys and Tutorials, IEEE, 15(3), 963–972.
Dolev, S., Korach, E., & Yukelson, D. (2001). The sound of silence: Guessing games for saving energy in a mobile environment. Journal of Parallel and Distributed Computing, 61, 868–883.
Deng, X., & Yang, Y. (2012). On-line adaptive compression in delay sensitive wireless sensor networks. IEEE Transactions on Computers, 61(10), 1429–1442.
Kolhe, K. R., Devale, P. R., & Shrivastava, P. (2010). High performance multimedia data compression through improved dictionary. International Journal of Computer Applications, 10(1), 29–35.
Shermer, E., Avigal, M., Shapira, D. (2010). Neural Markovian predictive compression: An algorithm for online lossless data compression, DCC, pp. 209–218.
Caire, G., Shamai, S., Shokrollahi, A., & Verdu, S. (2004). Universal variable-length data compression of binary sources using fountain codes, IEEE Information Theory Workshop.
Li, Z., Wang, C., Ni, P. (2003). A report on impact of data compression on energy consumption of wireless-networked hand held devices, Technical Report no. 03-003, Purdue e-Pubs, Department of Computer Science, Purdue University .
Dolev, S., Frenkel, S., Kopeetsky, M., & Zbarski, D. (2014). Implementation of entropy adaptive online compression, Technical Report 11–03. Department of Computer Science: Ben Gurion University of the Negev.
Rice, J. A. (1995). Mathematical statistics and data analysis. North Scituate: Duxbury Press.
Ziv, J. (2009). The universal LZ77 compression algorithm is essentially optimal for individual finite-length N-blocks. IEEE Transactions on Information Theory, 55(5), 1941–1944.
Reif, J. H., & Storer, J. A. (2001). Optimal lossless compression of a class of dynamic sources. Information Sciences Journal, 135, 87–105. Elseiver.
Knuth, D. E. (1985). Dynamic Huffman coding. Journal of Algorithms, 6, 163–180.
Vitter, J. S. (1987). Design and analysis of dynamic Huffman codes. Journal of the Association for Computing Machinery, 34(4), 825–845.
Yang, L., & Dick, R. P. (2010). On-line memory compression for embedded systems. ACM Transactions on Embedded Computing Systems (TECS), 9(3), 1–30.
Wyner, A. D., Ziv, J., & Wyner, A. J. (1998). On the role of pattern matching in information theory. IEEE Transactions on Information Theory, 44(6), 2045–2056.
Potapov, V. N. (2004). Redundancy estimates for the Lempel–Ziv algorithm of data compression. Discrete Applied Mathematics, 135, 245–254.
Verdu, S., & Han, T. S. (1997). The role of the asymptotic equipartition property in noiseless source coding. IEEE Transactions on Information Theory, 43(3), 847–857.
Hankerson, D., Harris, G. A., & Johnson, P. D. (2003). Introduction to information theory and data compression (2nd ed.). Boca Raton: Chapman and Hall/CRC.
Bell, T., & Kulp, D. (1993). Longest-match string searching for Lempel–Ziv compression. Software-Practice and Experience Journal, 23(7), 757–771.
Baronchelli, A., Caglioti, E., & Loreto, V. (2006). Measuring complexity with zippers, in ArxiVe.
Puglisi, A., Caglioti, E., Loreto, V., & Vulpiani, A. (2003). Data compression and learning in time sequences analysis. Physica D: Non Linear Phenomena, 180(1–2), 92–107.
Goto, K., Bannai, H. (2013). Simpler and faster Lempel–Ziv factorization, arXiv:1211.3642v2.
Savari, S. A. (1977). Redundancy of the Lempel–Ziv incremental parsing rule. IEEE Transactions on Information Theory, 43(1), 9–21.
Shanmugasundaram, S., & Lourdusamy, R. (2011). A comparative study of text compression algorithms. International Journal of Wisdom Based Computing, 1(3), 68–76.
Acknowledgments
We thank Asaf Cohen for useful remarks and discussions. We thank Dmitry Zbarski for implementing and testing our Entropy Adaptive Compression scheme. We thank the Editor and the manuscript reviewers for their invaluable suggestions and comments.
Author information
Authors and Affiliations
Corresponding author
Additional information
Partially supported by Deutsche Telekom, Rita Altura Trust Chair in Computer Sciences, Israeli Internet Association, Israeli Ministry of Science, Lynne and William Frankel Center and Israel Science Foundation (Grant number 428/11). The second author has been partially supported by the Russian Foundation for Basic Research under grant RFBR 15-07-05316. The third author has been partially supported by the internal research program of the Shamoon College of Engineering. An extended abstract of this work was presented at IEEE NCA 2014.
Rights and permissions
About this article
Cite this article
Dolev, S., Frenkel, S., Kopeetsky, M. et al. Improving of entropy adaptive on-line compression. Wireless Netw 23, 2521–2532 (2017). https://doi.org/10.1007/s11276-016-1289-9
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11276-016-1289-9