A Universal Parallel Two-Pass MDL Context Tree Compression Algorithm

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.Comment: Accepted to Journal of Selected Topics in Signal Processing special issue on Signal Processing for Big Data (expected publication date June 2015). 10 pages double column, 6 figures, and 2 tables. arXiv admin note: substantial text overlap with arXiv:1405.6322. Version: Mar 2015: Corrected a typ

A Novel Rate Control Algorithm for Onboard Predictive Coding of Multispectral and Hyperspectral Images

Predictive coding is attractive for compression onboard of spacecrafts thanks to its low computational complexity, modest memory requirements and the ability to accurately control quality on a pixel-by-pixel basis. Traditionally, predictive compression focused on the lossless and near-lossless modes of operation where the maximum error can be bounded but the rate of the compressed image is variable. Rate control is considered a challenging problem for predictive encoders due to the dependencies between quantization and prediction in the feedback loop, and the lack of a signal representation that packs the signal's energy into few coefficients. In this paper, we show that it is possible to design a rate control scheme intended for onboard implementation. In particular, we propose a general framework to select quantizers in each spatial and spectral region of an image so as to achieve the desired target rate while minimizing distortion. The rate control algorithm allows to achieve lossy, near-lossless compression, and any in-between type of compression, e.g., lossy compression with a near-lossless constraint. While this framework is independent of the specific predictor used, in order to show its performance, in this paper we tailor it to the predictor adopted by the CCSDS-123 lossless compression standard, obtaining an extension that allows to perform lossless, near-lossless and lossy compression in a single package. We show that the rate controller has excellent performance in terms of accuracy in the output rate, rate-distortion characteristics and is extremely competitive with respect to state-of-the-art transform coding

Algorithmic Complexity of Financial Motions

We survey the main applications of algorithmic (Kolmogorov) complexity to the problem of price dynamics in financial markets. We stress the differences between these works and put forward a general algorithmic framework in order to highlight its potential for financial data analysis. This framework is “general" in the sense that it is not constructed on the common assumption that price variations are predominantly stochastic in nature.algorithmic information theory; Kolmogorov complexity; financial returns; market efficiency; compression algorithms; information theory; randomness; price movements; algorithmic probability