Executing discrete orthogonal transformations based on computations on the Galois field in the FPGA architecture

Zakharov, V. M.; Shalagin, S. V.

doi:10.1109/sibcon.2016.7491652

Cited by 10 publications

(2 citation statements)

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“…At present, intensive studies are carried out in the following areas of DSP algorithm efficiency increase. The first one is the development of the applied theory of DOT in the direction of the development of algorithms that are computationally effective (fast algorithms, the algorithms with reduced computational complexity, balanced computational complexity algorithms), and hardware algorithms oriented to the implementation in the form of specialized computing devices [13,14]. It should be noted that a wide application during the solution of a number of DSP problems are found by DOT in various ordered systems of discrete Walsh functions [4][5][6][7].…”

Section: Introductionmentioning

confidence: 99%

“…The second direction is related to the implementation of computationally time-consuming operations, such as multiplication by a constant, based on operations for Galois field [14]. It was shown in [15,16] that the set of operations of multiplication (OY) on a constant is realizable at the use of distributed computations, namely, the system of nonlinear polynomial functions (NPF) from many variables in respect of Galois field of the form…”

Section: Introductionmentioning

confidence: 99%

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General method of synthesis by PLIC/FPGA digital devices to perform discrete orthogonal transformations

Ismagilov

Khasanova

Zakharov

et al. 2018

J. Fundam and Appl Sci.

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A general method is proposed to synthesize digital devices in order to perform discrete orthogonal transformations (DOT) on programmable logic integrated circuits (PLIC) of FPGA class. The basic and the most "slow" operation during DOT performance is the operation of multiplying by a constant factor (constant)-OMC. To perform DOT digital devices are implemented at the use of the same type of IP-cores, which allow to realize OMC. According to the proposed method, OMC is determined on the basis of picturing set over the elements of the Galois field. Due to the distributed computing of nonlinear polynomial function systems defined over the Galois field in PLIC/FPGA architecture, the reduction in the estimates of time complexity concerning OMC performance is achieved. Each non-linear polynomial function, like OMC, is realized on the basis of the same type of IP-cores according to one of the structural schemes in accordance with the requirements for the device to perform DOT. The use of IP cores significantly reduces the cost of designing a device that implements DOT in the PLIC/FPGA architecture.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%