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Homomorphic permutation is fundamental to privacy-preserving computations based on batch-encoding homomorphic encryption. It underpins nearly all homomorphic matrix operations and predominantly influences their complexity. Permutation…
We present a new variable-length computation-friendly encoding scheme, named SFDC (Succinct Format with Direct aCcesibility), that supports direct and fast accessibility to any element of the compressed sequence and achieves compression…
Huffman encoding is often improved by using block codes, for example a 3-block would be an alphabet consisting of each possible combination of three characters. We take the approach of starting with a base alphabet and expanding it to…
The emerging semantic compression has been receiving increasing research efforts most recently, capable of achieving high fidelity restoration during compression, even at extremely low bitrates. However, existing semantic compression…
In the recent years, heterogeneous machine learning accelerators have become of significant interest in science, engineering and industry. The major processing speed bottlenecks in these platforms come from (a) an electronic data…
This paper sheds light on universal coding with respect to classes of memoryless sources over a countable alphabet defined by an envelope function with finite and non-decreasing hazard rate. We prove that the auto-censuring AC code…
A new incremental algorithm for data compression is presented. For a sequence of input symbols algorithm incrementally constructs a p-adic integer number as an output. Decoding process starts with less significant part of a p-adic integer…
Grammar compression represents a string as a context free grammar. Achieving compression requires encoding such grammar as a binary string; there are a few commonly used encodings. We bound the size of practically used encodings for several…
Recent semantic communication methods explore effective ways to expand the communication paradigm and improve the system performance of the communication systems. Nonetheless, the common problem of these methods is that the essence of…
Many information systems employ lossy compression as a crucial intermediate stage among other processing components. While the important distortion is defined by the system's input and output signals, the compression usually ignores the…
We present a new data structure called the \emph{Compressed Random Access Memory} (CRAM) that can store a dynamic string $T$ of characters, e.g., representing the memory of a computer, in compressed form while achieving asymptotically…
Canonical Huffman code is an optimal prefix-free compression code whose codewords enumerated in the lexicographical order form a list of binary words in non-decreasing lengths. Gagie et al. (2015) gave a representation of this coding…
Data compression has been widely applied in many data processing areas. Compression methods use variable-size codes with the shorter codes assigned to symbols or groups of symbols that appear in the data frequently. Fibonacci coding, as a…
Constrained counting and sampling are two fundamental problems in Computer Science with numerous applications, including network reliability, privacy, probabilistic reasoning, and constrained-random verification. In constrained counting,…
We perform several numerical studies for our recently published adaptive compressive tomography scheme [D. Ahn et al. Phys. Rev. Lett. 122, 100404 (2019)], which significantly reduces the number of measurement settings to unambiguously…
The bits-back argument suggests that latent variable models can be turned into lossless compression schemes. Translating the bits-back argument into efficient and practical lossless compression schemes for general latent variable models,…
We present a novel, practical approach to speed up sparse matrix-vector multiplication (SpMVM) on GPUs. The novel key idea is to apply lossless entropy coding to further compress the sparse matrix when stored in one of the commonly…
Arithmetic Coding is an efficient lossless compression scheme applied for many multimedia standards such as JPEG, JPEG2000, H.263, H.264 and H.265. Due to nonlinearity, high error propagation and high error sensitivity of arithmetic coders,…
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…
This paper presents new lower and upper bounds for the compression rate of binary prefix codes optimized over memoryless sources according to various nonlinear codeword length objectives. Like the most well-known redundancy bounds for…