Prefix Codes for Power Laws with Countable Support

In prefix coding over an infinite alphabet, methods that consider specific distributions generally consider those that decline more quickly than a power law (e.g., Golomb coding). Particular power-law distributions, however, model many random variables encountered in practice. For such random variables, compression performance is judged via estimates of expected bits per input symbol. This correspondence introduces a family of prefix codes with an eye towards near-optimal coding of known distributions. Compression performance is precisely estimated for well-known probability distributions using these codes and using previously known prefix codes. One application of these near-optimal codes is an improved representation of rational numbers.Comment: 5 pages, 2 tables, submitted to Transactions on Information Theor

Rapid preconditioning of data for accelerating convex hull algorithms

Given a dataset of two-dimensional points in the plane with integer coordinates, the method proposed reduces a set of n points down to a set of s points s ≤ n, such that the convex hull on the set of s points is the same as the convex hull of the original set of n points. The method is O(n). It helps any convex hull algorithm run faster. The empirical analysis of a practical case shows a percentage reduction in points of over 98%, that is reflected as a faster computation with a speedup factor of at least 4

Compressing Sets and Multisets of Sequences

This is the accepted manuscript for a paper published in IEEE Transactions on Information Theory, Vol. 61, No. 3, March 2015, doi: 10.1109/TIT.2015.2392093. © 2015 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.This paper describes lossless compression algorithms for multisets of sequences, taking advantage of the multiset’s unordered structure. Multisets are a generalization of sets, where members are allowed to occur multiple times. A multiset can be encoded naïvely by simply storing its elements in some sequential order, but then information is wasted on the ordering. We propose a technique that transforms the multiset into an order-invariant tree representation, and derive an arithmetic code that optimally compresses the tree. Our method achieves compression even if the sequences in the multiset are individually incompressible (such as cryptographic hash sums). The algorithm is demonstrated practically by compressing collections of SHA-1 hash sums, and multisets of arbitrary, individually encodable objects.This work was supported in part by the Engineering and Physical Sciences Research Council under Grant EP/I036575 and in part by a Google Research Award. This paper was presented at the 2014 Data Compression Conferenc

Semantic Face Compression for Metaverse: A Compact 3D Descriptor Based Approach

In this letter, we envision a new metaverse communication paradigm for virtual avatar faces, and develop the semantic face compression with compact 3D facial descriptors. The fundamental principle is that the communication of virtual avatar faces primarily emphasizes the conveyance of semantic information. In light of this, the proposed scheme offers the advantages of being highly flexible, efficient and semantically meaningful. The semantic face compression, which allows the communication of the descriptors for artificial intelligence based understanding, could facilitate numerous applications without the involvement of humans in metaverse. The promise of the proposed paradigm is also demonstrated by performance comparisons with the state-of-the-art video coding standard, Versatile Video Coding. A significant improvement in terms of rate-accuracy performance has been achieved. The proposed scheme is expected to enable numerous applications, such as digital human communication based on machine analysis, and to form the cornerstone of interaction and communication in the metaverse.Comment: 5 pages, 3 figure

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

Efficient Differential Pixel Value Coding in CABAC for H.264/AVC Lossless Video Compression

Abstract Since context-based adaptive binary arithmetic coding (CABAC) as the entropy coding method in H.264/AVC was originally designed for lossy video compression, it is inappropriate for lossless video compression. Based on the fact that there are statistical differences of residual data between lossy and lossless video compression, we propose an efficient differential pixel value coding method in CABAC for H.264/AVC lossless video compression. Considering the observed statistical properties of the differential pixel value in lossless coding, we modified the CABAC encoding mechanism with the newly designed binarization table and the context-modeling method. Experimental results show that the proposed method achieves an approximately 12% bit saving, compared to the original CABAC method in the H.264/AVC standard

Multi-dimensional data stream compression for embedded systems

The rise of embedded systems and wireless technologies led to the emergence of the Internet of Things (IoT). Connected objects in IoT communicate with each other by transferring data streams over the network. For instance, in Wireless Sensor Networks (WSNs), sensor-equipped devices use sensors to capture properties, such as temperature or accelerometer, and send 1D or nD data streams to a host system. Power consumption is a critical problem for connected objects that have to work for a long time without being recharged, as it greatly affects their lifetime and usability. Data summarization is key for energy-constrained connected devices, as transmitting fewer data can reduce energy usage during transmission. Data compression, in particular, can compress the data stream while preserving information to a great extent. Many compression methods have been proposed in previous research. However, most of them are either not applicable to connected objects, due to resource limitation, or only handle one-dimensional streams while data acquired in connected objects are often multi-dimensional. Lightweight Temporal Compression (LTC) is among the lossy stream compression methods that provide the highest compression rate for the lowest CPU and memory consumption. In this thesis, we investigate the extension of LTC to multi-dimensional streams. First, we provide a formulation of the algorithm in an arbitrary vectorial space of dimension n. Then, we implement the algorithm for the infinity and Euclidean norms, in spaces of dimension 2D+t and 3D+t. We evaluate our implementation on 3D acceleration streams of human activities, on Neblina, a module integrating multiple sensors developed by our partner Motsai. Results show that the 3D implementation of LTC can save up to 20% in energy consumption for slow-paced activities, with a memory usage of about 100 B. Finally, we compare our method with polynomial regression compression methods in different dimensions. Our results show that our extension of LTC gives a higher compression ratio than the polynomial regression method, while using less memory and CPU