Optimal modeling for complex system design

The article begins with a brief introduction to the theory describing optimal data compression systems and their performance. A brief outline is then given of a representative algorithm that employs these lessons for optimal data compression system design. The implications of rate-distortion theory for practical data compression system design is then described, followed by a description of the tensions between theoretical optimality and system practicality and a discussion of common tools used in current algorithms to resolve these tensions. Next, the generalization of rate-distortion principles to the design of optimal collections of models is presented. The discussion focuses initially on data compression systems, but later widens to describe how rate-distortion theory principles generalize to model design for a wide variety of modeling applications. The article ends with a discussion of the performance benefits to be achieved using the multiple-model design algorithms

Universal Source Polarization and an Application to a Multi-User Problem

We propose a scheme that universally achieves the smallest possible compression rate for a class of sources with side information, and develop an application of this result for a joint source channel coding problem over a broadcast channel.Comment: to be presented at Allerton 201

Universal Lossless Compression with Unknown Alphabets - The Average Case

Universal compression of patterns of sequences generated by independently identically distributed (i.i.d.) sources with unknown, possibly large, alphabets is investigated. A pattern is a sequence of indices that contains all consecutive indices in increasing order of first occurrence. If the alphabet of a source that generated a sequence is unknown, the inevitable cost of coding the unknown alphabet symbols can be exploited to create the pattern of the sequence. This pattern can in turn be compressed by itself. It is shown that if the alphabet size $k$ is essentially small, then the average minimax and maximin redundancies as well as the redundancy of every code for almost every source, when compressing a pattern, consist of at least 0.5 log(n/k^3) bits per each unknown probability parameter, and if all alphabet letters are likely to occur, there exist codes whose redundancy is at most 0.5 log(n/k^2) bits per each unknown probability parameter, where n is the length of the data sequences. Otherwise, if the alphabet is large, these redundancies are essentially at least O(n^{-2/3}) bits per symbol, and there exist codes that achieve redundancy of essentially O(n^{-1/2}) bits per symbol. Two sub-optimal low-complexity sequential algorithms for compression of patterns are presented and their description lengths analyzed, also pointing out that the pattern average universal description length can decrease below the underlying i.i.d.\ entropy for large enough alphabets.Comment: Revised for IEEE Transactions on Information Theor

Adaptive edge-based prediction for lossless image compression

Many lossless image compression methods have been suggested with established results hard to surpass. However there are some aspects that can be considered to improve the performance further. This research focuses on two-phase prediction-encoding method, separately studying each and suggesting new techniques.;In the prediction module, proposed Edge-Based-Predictor (EBP) and Least-Squares-Edge-Based-Predictor (LS-EBP) emphasizes on image edges and make predictions accordingly. EBP is a gradient based nonlinear adaptive predictor. EBP switches between prediction-rules based on few threshold parameters automatically determined by a pre-analysis procedure, which makes a first pass. The LS-EBP also uses these parameters, but optimizes the prediction for each pre-analysis assigned edge location, thus applying least-square approach only at the edge points.;For encoding module: a novel Burrows Wheeler Transform (BWT) inspired method is suggested, which performs better than applying the BWT directly on the images. We also present a context-based adaptive error modeling and encoding scheme. When coupled with the above-mentioned prediction schemes, the result is the best-known compression performance in the genre of compression schemes with same time and space complexity