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Shannon's information theory deliberately excludes message semantics. This paper develops a rigorous framework for semantic communication that integrates formal proof systems with Shannon-theoretic tools. We introduce an axiomatic…
The quality of image encryption is commonly measured by the Shannon entropy over the ciphertext image. However, this measurement does not consider to the randomness of local image blocks and is inappropriate for scrambling based image…
Sorted data is usually easier to compress than unsorted permutations of the same data. This motivates a simple compression scheme: specify the sorted permutation of the data along with a representation of the sorted data compressed…
In the classic wiretap model, Alice wishes to reliably communicate to Bob without being overheard by Eve who is eavesdropping over a degraded channel. Systems for achieving that physical layer security often rely on an error correction code…
Today's HPC applications are producing extremely large amounts of data, such that data storage and analysis are becoming more challenging for scientific research. In this work, we design a new error-controlled lossy compression algorithm…
The Shannon entropy is a fundamental measure for quantifying diversity and model complexity in fields such as information theory, ecology, and genetics. However, many existing studies assume that the number of species is known, an…
Superdense Coding is a cornerstone in secure quantum communication, exploiting pre-shared entanglement to encode two classical bits within a single qubit. However, noise and decoherence deteriorate entanglement quality, restricting both…
In this paper, we consider contention resolution algorithms that are augmented with predictions about the network. We begin by studying the natural setup in which the algorithm is provided a distribution defined over the possible network…
We consider the lossless compression bound of any individual data sequence. If we fit the data by a parametric model, the entropy quantity $nH({\hat \theta}_n)$ obtained by plugging in the maximum likelihood estimate is an underestimate of…
This research note suggests a new way to realize a high speed direct encryption based on quantum detection theory. The conventional cipher is designed by a mathematical algorithm and its security is evaluated by the complexity of the…
In this thesis we present several results in coding theory, concerning error-correcting codes and the Shannon capacity. 1. We give a general symmetry reduction of matrices occuring in semidefinite programs in coding theory. 2. We apply the…
Measuring similarity between incomplete data is a fundamental challenge in web mining, recommendation systems, and user behavior analysis. Traditional approaches either discard incomplete data or perform imputation as a preprocessing step,…
Suppose A is a finite set equipped with a probability measure P and let M be a ``mass'' function on A. We give a probabilistic characterization of the most efficient way in which A^n can be almost-covered using spheres of a fixed radius. An…
Driven by the ``scale-is-everything'' paradigm, modern machine learning increasingly demands ever-larger datasets and models, yielding prohibitive computational and storage requirements. Dataset distillation mitigates this by compressing an…
Conformal prediction constructs a set of labels instead of a single point prediction, while providing a probabilistic coverage guarantee. Beyond the coverage guarantee, adaptiveness to example difficulty is an important property. It means…
This paper studies the performance of sparse regression codes for lossy compression with the squared-error distortion criterion. In a sparse regression code, codewords are linear combinations of subsets of columns of a design matrix. It is…
A new line of research uses compression methods to measure the similarity between signals. Two signals are considered similar if one can be compressed significantly when the information of the other is known. The existing compression-based…
We study a quantity called discrete layered entropy, which approximates the Shannon entropy within a logarithmic gap. Compared to the Shannon entropy, the discrete layered entropy is piecewise linear, approximates the expected length of the…
Most of the world's digital data is currently encoded in a sequential form, and compression methods for sequences have been studied extensively. However, there are many types of non-sequential data for which good compression techniques are…
Recent advancements in neural compression have surpassed traditional codecs in PSNR and MS-SSIM measurements. However, at low bit-rates, these methods can introduce visually displeasing artifacts, such as blurring, color shifting, and…