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... The worst-case complexity can be reduced to O(log K) by a logarithmic search, see Algorithm 3. In a recently published preprint, this method is called 'bisection search', [12]. Each comparison with an interval boundary halves the number of remaining comparisons. ...

There is a class of entropy-coding methods which do not substitute symbols by code words (such as Huffman coding), but operate on intervals or ranges. This class includes three prominent members: conventional arithmetic coding, range coding, and coding based on asymmetric numeral systems. To determine the correct symbol in the decoder, each of these methods requires the comparison of a state variable with subinterval boundaries. In adaptive operation, considering varying symbol statistics, an array of interval boundaries must additionally be kept up to date. The larger the symbol alphabet, the more time-consuming both the search for the correct subinterval and the updating of interval borders become. Detailed pseudo-code is used to discuss different approaches to speed up the symbol search in the decoder and the adaptation of the array of interval borders, both depending on the chosen alphabet size. It is shown that reducing the $\mathcal{O}$-complexity does not lead to an acceleration in practical implementations if the alphabet size is too small. In adaptive compression mode, the binary indexing method proves to be superior when considering the overall processing time. Although the symbol search (in the decoder) takes longer than with other algorithms, the faster updating of the array of interval borders more than compensates for this disadvantage. A variant of the binary indexing method is proposed, which is more flexible and has a partially lower complexity than the original approach.

... Corresponding results for both antenna arrays are presented in Fig. 15. In addition to non-linear quantizers, arithmetic coding [36] presents an alternative approach to achieving uniform distributions. Arithmetic coding is a lossless data compression technique that employs intervals within the [0,1] range of a distribution function, representing probabilities of the original alphabet. ...

Physical-layer secret key generation (PSKG) stands as a promising privacy protection technique, establishing shared encryption keys through the analysis of highly correlated wireless channel measurements. This approach relies on exploiting reciprocal channel characteristics between uplink and downlink transmissions. Nonetheless, the distinct carrier frequencies employed for uplink and downlink in frequency-division duplexing (FDD) systems pose a challenge in identifying common features. This paper presents a novel approach that exploits the inherent reciprocity between scattering parameters of passive two-port networks within same frequency ranges to overcome this obstacle. By capitalizing this reciprocity and considering closely situated FDD bands, a seamless continuity is anticipated in phase differences extracted form the corresponding S-parameters, between neighboring antennas of an antenna array from both uplink and downlink directions. This continuity, thereby ensures consistency in the generated keys from both transmission ends. Furthermore, a two-stage pre-processing method is proposed to enhance performance effectively. Additionally, the paper suggests the utilization of polynomial curve-fitting through measurement data to improve reciprocity and proposes a non-linear framework for quantizing the merging points of the two FDD bands. A statistical analysis employing multiple linear regression is provided to determine the error probability associated with the generated keys. Empirical results validate the feasibility and effectiveness of the proposed key generation scheme, affirming its attributes in terms of randomness, efficiency, key distribution uniformity, and key disagreement ratio (KDR).

... In the PSR, we developed base-4 arithmetic coding to adapt to the nucleotide space, which was a variant of conventional base-2 arithmetic coding [39][40]. Onedimensional probability space was used when we compressed one-dimensional sequences (e.g., text). ...

DNA has been pursued as a compelling medium for digital data storage during the past decade. While large-scale data storage and random access have been achieved in artificial DNA, the synthesis cost keeps hindering DNA data storage from popularizing into daily life. In this study, we proposed a more efficient paradigm for digital data compressing to DNA, while excluding arbitrary sequence constraints. Both standalone neural networks and pre-trained language models were used to extract the intrinsic patterns of data, and generated probabilistic portrayal, which was then transformed into constraint-free nucleotide sequences with a hierarchical finite state machine. Utilizing these methods, a 12%-26% improvement of compression ratio was realized for various data, which directly translated to up to 26% reduction in DNA synthesis cost. Combined with the progress in DNA synthesis, our methods are expected to facilitate the realization of practical DNA data storage.

... The CABAC technique, developed after year 2000, represents the state-of-the-art of entropy compression of video data [12]. This technique implements very advanced mechanisms of arithmetic coding [13][14][15][16][17][18][19][20], combined with proper pre-processing of syntax elements data. From the point of view of data compression efficiency, the CABAC technique outclasses other entropy coding methods that have been proposed in the context of video data compression [12]. ...

Hybrid video compression plays an invaluable role in digital video transmission and storage services and systems. It performs several-hundred-fold reduction in the amount of video data, which makes these systems much more efficient. An important element of hybrid video compression is entropy coding of the data. The state-of-the-art in this field is the newest variant of the Context-based Adaptive Binary Arithmetic Coding (CABAC) entropy compression algorithm which recently became part of the new Versatile Video Coding (VVC) technology. This work is a part of research that is currently underway to further improve the CABAC technique. This paper provides analysis of the potential for further improvement of the CABAC by more accurate calculation of probabilities of data symbols. The CABAC technique calculates those probabilities by the use of idea of the two-parameters hypothesis. For the needs of analysis presented in this paper, an extension of the aforementioned idea was proposed which consists of three- and four-parameters hypothesis. In addition, the paper shows the importance of proper calibration of parameter values of the method on efficiency of data compression. Results of experiments show that for the considered in the paper variants of the algorithm improvement the possible efficiency gain is at levels 0.11% and 0.167%, for the three- and four-parameter hypothesis, respectively.

... To simplify the notation we ignore implementation details like conversions to integer-valued cumulative sums for AC [13,14]. It is assumed that R and AC precision are chosen to obtain compression very close to entropy. ...

Neural-based image and video codecs are significantly more power-efficient when weights and activations are quantized to low-precision integers. While there are general-purpose techniques for reducing quantization effects, large losses can occur when specific entropy coding properties are not considered. This work analyzes how entropy coding is affected by parameter quantizations, and provides a method to minimize losses. It is shown that, by using a certain type of coding parameters to be learned, uniform quantization becomes practically optimal, also simplifying the minimization of code memory requirements. The mathematical properties of the new representation are presented, and its effectiveness is demonstrated by coding experiments, showing that good results can be obtained with precision as low as 4~bits per network output, and practically no loss with 8~bits.

... The general idea behind an AC process is to manipulate the variables Low and Range to encode the incoming symbols into a reduced bitstream according to their probabilities of appearance. The concept that symbols with the Step-by-step arithmetic encoding process based on [34]. ...

With the increasing demand for video transmission through the Internet, video coding has become a key technology to allow this market's growth at a reduced cost. Moreover, with the inception of higher video resolutions (e.g., 4K, 8K) and their impact on video size, new video coding standards must tackle this issue to reduce video traffic demand on the global internet infrastructure. The AV1, a recently released royalties-free video coding format created by the Alliance for Open Media (AOMedia), reaches great compression rates but cannot accomplish real-time execution on software-only implementations due to its high complexity. This paper presents and analyzes AE-AV1, a high-performance 4-stage pipelined architecture to accelerate the AV1 arithmetic encoding process (part of the entropy encoder block) and make it capable of real-time execution. For the analysis, this work aims to rely on fully open-source Electronic Design Automation (EDA) tools and Package Design Kits (PDKs).

We study the problem of data integration from sources that contain probabilistic uncertain information. Data is modeled by possible-worlds with probability distribution, compactly represented in the probabilistic relation model. Integration is achieved efficiently using the extended probabilistic relation model. We study the problem of determining the probability distribution of the integration result. It has been shown that, in general, only probability ranges can be determined for the result of integration. We show that under intuitive and reasonable assumptions we can determine the exact probability distribution of the result of integration. Our methodologies are presented in possible-worlds as well as probabilistic-relation frameworks.

The embedded *erotree wavelet algorithm (EZVV) is :s simple, yet remarkably effective, image compression algo{reversed not sign}rithm, having the property thai the bits in the bit stream are generated in order of Importance, yielding a fully embedded code- The embedded code represents a sequence of binary de{reversed not sign}cisions that distinguish an image from Ihe "null" image. Using an embedded coding algorithm, an encoder can terminate Ihe encoding at any point thereby allowing a target rate or target distortion metric to he met exactly. Also, given a bit slream, the decoder can cease decoding at any point in Ihe hit stream and still produce exactly the same image that would have been encoded at the bit rate corresponding tn the truncated hit stream. In addition to producing a fully embedded bit slream, EZW consistenlly produces compression results that are com{reversed not sign}petitive with virtually all known compression algorithms on standard test images. Yet this performance is achieved with a technique that requires absolutely no training, no pre-slored lables or codebooks, and requires no prior knowledge of the image source. The EZW algorithm is based on four key concepts: 1) a dis{reversed not sign}crete wavelet transform or hierarchical subband decomposi{reversed not sign}tion, 2) prediction of the absence of significant information across scales by exploiting Ihe self-similarity inherent in im{reversed not sign}ages, .1) entropy-coded successive-approximation quantization, and 4} universal lossless data compression which is achieved via adaptive arithmetic coding.

There is no better way to quantize a single vector than to use VQ with a codebook that is optimal for the probability distribution describing the random vector. However, direct use of VQ suffers from a serious complexity barrier that greatly limits its practical use as a complete and self-contained coding technique

The authors present an accessible implementation of arithmetic coding and by detailing its performance characteristics. The presentation is motivated by the fact that although arithmetic coding is superior in most respects to the better-known Huffman method many authors and practitioners seem unaware of the technique. The authors start by briefly reviewing basic concepts of data compression and introducing the model-based approach that underlies most modern techniques. They then outline the idea of arithmetic coding using a simple example, and present programs for both encoding and decoding. In these programs the model occupies a separate module so that different models can easily be used. Next they discuss the construction of fixed and adaptive models and detail the compression efficiency and execution time of the programs, including the effect of different arithmetic word lengths on compression efficiency. Finally, they outline a few applications where arithmetic coding is appropriate.

Arithmetic coding is a data compression technique that encodes data (the data string) by creating a code string which represents a fractional value on the number line between 0 and 1. The coding algorithm is symbolwise recursive; i.e., it operates upon and encodes (decodes) one data symbol per iteration or recursion. On each recursion, the algorithm successively partitions an interval of the number line between 0 and 1, and retains one of the partitions as the new interval. Thus, the algorithm successively deals with smaller intervals, and the code string, viewed as a magnitude, lies in each of the nested intervals. The data string is recovered by using magnitude comparisons on the code string to recreate how the encoder must have successively partitioned and retained each nested subinterval. Arithmetic coding differs considerably from the more familiar compression coding techniques, such as prefix (Huffman) codes. Also, it should not be confused with error control coding, whose object is to detect and correct errors in computer operations. This paper presents the key notions of arithmetic compression coding by means of simple examples.