Related papers: Applications of Universal Source Coding to Statist…
We propose two types of universal codes that are suited to two asymptotic regimes when the output alphabet is possibly continuous. The first class has the property that the error probability decays exponentially fast and we identify an…
We simply construct a quantum universal variable-length source code in which, independent of information source, both of the average error and the probability that the coding rate is greater than the entropy rate $H(rho_p)$, tend to 0. If…
Many multivariate data such as social and biological data exhibit complex dependencies that are best characterized by graphs. Unlike sequential data, graphs are, in general, unordered structures. This means we can no longer use classic,…
For a collection of distributions over a countable support set, the worst case universal compression formulation by Shtarkov attempts to assign a universal distribution over the support set. The formulation aims to ensure that the universal…
Measuring the complexity of tree structures can be beneficial in areas that use tree data structures for storage, communication, and processing purposes. This complexity can then be used to compress tree data structures to their…
Assessing whether two datasets are distributionally consistent is central to modern scientific analysis, particularly as generative artificial intelligence produces synthetic data whose fidelity must be validated against real observations…
Optimal encoding of classical data for statistical inference using quantum computing is investigated. A universal encoder is sought that is optimal for a wide array of statistical inference tasks. Accuracy of any statistical inference is…
We consider universal variable-to-fixed length compression of memoryless sources with a fidelity criterion. We design a dictionary codebook over the reproduction alphabet which is used to parse the source stream. Once a source subsequence…
The problem of the universal compression of a sequence from a library of several small to moderate length sequences from similar context arises in many practical scenarios, such as the compression of the storage data and the Internet…
Consider universal data compression: the length $l(x^n)$ of sequence $x^n\in A^n$ with finite alphabet $A$ and length $n$ satisfies Kraft's inequality over $A^n$, and $-\frac{1}{n}\log \frac{P^n(x^n)}{Q^n(x^n)}$ almost surely converges to…
Graphical data arises naturally in several modern applications, including but not limited to internet graphs, social networks, genomics and proteomics. The typically large size of graphical data argues for the importance of designing…
This thesis concerns sequential-access data compression, i.e., by algorithms that read the input one or more times from beginning to end. In one chapter we consider adaptive prefix coding, for which we must read the input character by…
This paper considers lossy source coding of $n$-dimensional memoryless sources and shows an explicit approximation to the minimum source coding rate required to sustain the probability of exceeding distortion $d$ no greater than $\epsilon$,…
This paper describes universal lossless coding strategies for compressing sources on countably infinite alphabets. Classes of memoryless sources defined by an envelope condition on the marginal distribution provide benchmarks for coding…
Consider the set of source distributions within a fixed maximum relative entropy with respect to a given nominal distribution. Lossless source coding over this relative entropy ball can be approached in more than one way. A problem…
A general method of source coding over expansion is proposed in this paper, which enables one to reduce the problem of compressing an analog (continuous-valued source) to a set of much simpler problems, compressing discrete sources.…
We frame the problem of selecting an optimal audio encoding scheme as a supervised learning task. Through uniform convergence theory, we guarantee approximately optimal codec selection while controlling for selection bias. We present…
Time series account for a large proportion of the data stored in financial, medical and scientific databases. The efficient storage of time series is important in practical applications. In this paper, we propose a novel compression scheme…
We present a new lossy compressor for discrete sources. For coding a source sequence $x^n$, the encoder starts by assigning a certain cost to each reconstruction sequence. It then finds the reconstruction that minimizes this cost and…
We study the universal coding under side-channel attacks posed and investigated by Oohama and Santoso (2022). They proposed a theoretical security model for Shannon cipher system under side-channel attacks, where the adversary is not only…