A fast realization of new Mersenne number transformation and its applications

Hua, Jingyu; Liu, Fei; Xu, Zhijiang; Feng, Li; Wang, Dongming

doi:10.1002/cta.2614

Cited by 4 publications

(5 citation statements)

References 15 publications

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“…To fully clarify the proposed algorithm, we apply (18) separately for each stage as follows: For stage one (i=0) (21) Following the same procedure for stage four (i=3). Therefore, it is feasible to calculate transformations using the matrices provided in (18) using the butterfly structure, as illustrated in Figure 1.…”

Section: Applications Of the Developed Algorithmmentioning

confidence: 99%

New fast Walsh–Hadamard–Hartley transform algorithm

Mardan

Hamood

2023

IJECE

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<span lang="EN-US">This paper presents an efficient fast Walsh–Hadamard–Hartley transform (FWHT) algorithm that incorporates the computation of the Walsh-Hadamard transform (WHT) with the discrete Hartley transform (DHT) into an orthogonal, unitary single fast transform possesses the block diagonal structure. The proposed algorithm is implemented in an integrated butterfly structure utilizing the sparse matrices factorization approach and the Kronecker (tensor) product technique, which proved a valuable and fast tool for developing and analyzing the proposed algorithm. The proposed approach was distinguished by ease of implementation and reduced computational complexity compared to previous algorithms, which were based on the concatenation of WHT and FHT by saving up to 3N-4 of real multiplication and 7.5N-10 of real addition.</span>

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Section: Applications Of the Developed Algorithmmentioning

confidence: 99%

New fast Walsh–Hadamard–Hartley transform algorithm

Mardan

Hamood

2023

IJECE

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“…The following two sequences, where l = 0, 1, 2 and 3, can be defined: 12) and ( 13) into (11), and rearranging and applying re-indexing l of β 1 2k+1 2 l and β 2 2k+1 2 l from (11) according to the bit reverse order, yields the following:…”

Section: Derivation Of Radix-2 2 Algorithm For Onmntmentioning

confidence: 99%

“…A detailed discussion on different fast algorithms such as radix-2, radix-4, and split-radix for NMNT and GN-MNT can be found in [9,10]. Hue et al [11] presented a realization of NMNT using the Walsh-Hadamard Transform (WHT) to speed up the calculation. The split-radix algorithm has the lowest arithmetic complexity.…”

Section: Introductionmentioning

confidence: 99%

Radix-22 Algorithm for the Odd New Mersenne Number Transform (ONMNT)

Al-Aali,

Hamood,

Boussakta

2023

Signals

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This paper introduces a new derivation of the radix-22 fast algorithm for the forward odd new Mersenne number transform (ONMNT) and the inverse odd new Mersenne number transform (IONMNT). This involves introducing new equations and functions in finite fields, bringing particular challenges unlike those in other fields. The radix-22 algorithm combines the benefits of the reduced number of operations of the radix-4 algorithm and the simple butterfly structure of the radix-2 algorithm, making it suitable for various applications such as lightweight ciphers, authenticated encryption, hash functions, signal processing, and convolution calculations. The multidimensional linear index mapping technique is the conventional method used to derive the radix-22 algorithm. However, this method does not provide clear insights into the underlying structure and flexibility of the radix-22 approach. This paper addresses this limitation and proposes a derivation based on bit-unscrambling techniques, which reverse the ordering of the output sequence, resulting in efficient calculations with fewer operations. Butterfly and signal flow diagrams are also presented to illustrate the structure of the fast algorithm for both ONMNT and IONMNT. The proposed method should pave the way for efficient and flexible implementation of ONMNT and IONMNT in applications such as lightweight ciphers and signal processing. The algorithm has been implemented in C and is validated with an example.

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“…Number theoretic transformation (NTT) is a mathematical method commonly used in general circuit theory 35,36 . NTT has the talent to process invertible integer domain transformation and can losslessly compress multiple integers into a compact integer and vice versa 37,38 .…”

Section: Introductionmentioning

confidence: 99%

“…15,34 Number theoretic transformation (NTT) is a mathematical method commonly used in general circuit theory. 35,36 NTT has the talent to process invertible integer domain transformation and can losslessly compress multiple integers into a compact integer and vice versa. 37,38 This paper combines JPEG and NTT to propose a lightweight image compression method for IoT devices, called image compression with cascaded NTT and JPEG (ImgCCNJ) method.…”

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confidence: 99%

Enhanced image compression method exploiting NTT for internet of thing

Zhou

Wen

Zou

et al. 2022

Circuit Theory & Apps

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Joint photographic experts group (JPEG) is the common compression technology of image transmission with the Internet of Things (IoT), which probably causes low compression ratio (CR) and increases the requirement for transmission rate. Therefore, a lightweight image compression method combining JPEG and number theoretic transformation (NTT) is proposed to address the above problems. Simulation results show that the proposed method has higher CR than JPEG, embedded zerotree wavelet (EZW), and combining singular value decomposition with wavelet difference reduction (SVD-WDR) compression algorithms, which reduces the requirement of IoT devices for transmission rate. K E Y W O R D Scompression ratio, image compression, internet of thing, number theoretic transformation | INTRODUCTIONAt the dawn of the 5G era, research related to vehicle networking, 1 resource allocation, 2,3 5G Internet of Things (IoT), 4 and multi-access 5 has received extensive attention from industry scholars. Among the research, the deployment of 5G IoT devices is a research hotspot. With efficient resource utilization, manpower saving, and the ability of collecting data, IoT devices are widely used in wireless location, 6 smart city, 7 smart homes, 8 industrial IoT 9,10 and smart healthcare. 11 Under the wide-scale popularity of IoT devices, image transmission based on IoT devices is one of the most widely involved technologies in the above application scenarios. 12-14 Image transmission is essential for underwater imaging, unmanned aerial vehicles (UAV) imaging, and data collection, whereas most IoT devices currently require high transmission rate due to transmitting low CR images. 15 Moreover, IoT devices must fit in with the requirements of limited energy, low computation, and limited storage, whereas low CR images cannot fulfill these requirements. To address these issues, it is important for IoT devices to investigate a lightweight image compression method which has higher CR than the JPEG compression algorithm.JPEG is a widely used lossy image compression algorithm that compresses raw image data to take up only a small amount of transmission bandwidth and storage space by discarding duplicate or unimportant data from the original image and compressing only the important data. 16 It uses a lossy compression mode to remove redundant data from the original image to obtain both high CR and image recovery quality. 17 Moreover, in the early days, the lossless compression algorithms such as Huffman coding and arithmetic coding were widely studied by scholars. 18 Recently,

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A fast realization of new Mersenne number transformation and its applications

Cited by 4 publications

References 15 publications

New fast Walsh–Hadamard–Hartley transform algorithm

New fast Walsh–Hadamard–Hartley transform algorithm

Radix-22 Algorithm for the Odd New Mersenne Number Transform (ONMNT)

Enhanced image compression method exploiting NTT for internet of thing

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