Computation of 2D 8x8 DCT Based on the Loeffler Factorization Using Algebraic Integer Encoding

Diego Coelho Sushmabhargavi Nimmalapalli Vassil Dimitrov Arjuna Madanayake Renato Cintra Arnaud Tisserand 1
1 Lab-STICC_UBS_CACS_MOCS
Lab-STICC - Laboratoire des sciences et techniques de l'information, de la communication et de la connaissance
Abstract : This paper proposes a computational method for 2D 8×8 DCT based on algebraic integers. The proposed algorithm is based on the Loeffler 1D DCT algorithm, and is shown to operate with exact computation—i.e., error-free arithmetic—up to the final reconstruction step (FRS). The proposed algebraic integer architecture maintains error-free computations until an entire block of DCT coefficients having size 8×8 is computed, unlike algorithms in the literature which claim to be error-free but in fact introduce arithmetic errors between the column-and row-wise 1D DCT stages in a 2D DCT operation. Fast algorithms are proposed for the final reconstruction step employing two approaches, namely, the expansion factor and dyadic approximation. A digital architecture is also proposed for a particular FRS algorithm, and is implemented on an FPGA platform for on-chip verification. The FPGA implementation operates at 360 MHz, and is capable of a real-time throughput of 3.6 · 10 8 2D DCTs of size 8×8 every second, with corresponding pixel rate of 2.3 · 10 10 pixels per second. The digital architecture is synthesized using 180 nm CMOS standard cells and shows a chip area of 7.41 mm 2. The CMOS design is predicted to operate at 893 MHz clock frequency, at a dynamic power consumption 13.22 mW/MHz · V 2 sup .
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IEEE Transactions on Computers, Institute of Electrical and Electronics Engineers, In press, 〈10.1109/TC.2018.2837755〉
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Soumis le : mercredi 23 mai 2018 - 08:37:43
Dernière modification le : jeudi 7 juin 2018 - 01:03:18

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Diego Coelho, Sushmabhargavi Nimmalapalli, Vassil Dimitrov, Arjuna Madanayake, Renato Cintra, et al.. Computation of 2D 8x8 DCT Based on the Loeffler Factorization Using Algebraic Integer Encoding. IEEE Transactions on Computers, Institute of Electrical and Electronics Engineers, In press, 〈10.1109/TC.2018.2837755〉. 〈hal-01797957〉

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