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Multiplication-free 8×8 2D DCT architecture using algebraic integer encoding

Multiplication-free 8×8 2D DCT architecture using algebraic integer encoding

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A novel architecture for a 2D 8×8 discrete cosine transform (DCT) is presented. The architecture uses a new algebraic integer encoding of a 1D radix-8 DCT that allows the separable computation of a 2D 8×8 DCT without any intermediate number representation conversions. This is a considerable improvement on previously introduced algebraic integer encoding techniques. Using this encoding scheme, an entire 8×8 2D DCT-SQ (scalar quantisation) algorithm can be implemented with only 24 adders.

Inspec keywords: graph theory; adders; matrix multiplication; digital arithmetic; algebraic codes; encoding; discrete cosine transforms

Other keywords: adders; scalar quantisation algorithm; discrete cosine transform; algebraic integer encoding; 2D DCT architecture

Subjects: Codes; Logic and switching circuits; Digital arithmetic methods; Logic circuits; Combinatorial mathematics; Combinatorial mathematics; Integral transforms; Integral transforms

References

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      • Dimitrov, V.S., Jullien, G.A., Miller, W.C.: `A new DCT algorithm based on encoding algebraic integers', ICASSP, 1998, Seattle, WA, USA, p. 1377–1380.
    2. 2)
    3. 3)
      • V. Dimitrov , G.A. Jullien . Multidimensional algebraic integer encoding for high performance implementation of the DCT and IDCT. Electron. Lett. , 7 , 602 - 603
    4. 4)
      • Y. Arai , T. Agui , M. Nakajima . A fast DCT-SQ scheme for images. Trans. IEICE , 11 , 1095 - 1097
    5. 5)
      • Shams, A., Pan, W., Chidanandan, A., Bayoumi, M.: `A low power high performance distributed DCT architecture', Proc. ISVLSI, 2002, Pittsburgh, PA, USA, p. 21–27.
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