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access icon free Short-critical-path and structurally orthogonal scaled CORDIC-based approximations of the eight-point discrete cosine transform

A family of multiplierless transforms is presented that approximate the eight-point type-II discrete cosine transform (DCT) as accurately as the state-of-the-art scaled DCT schemes, but having 14–17% shorter critical paths (1/6 or 1/7 less adders). Compared to the existing solutions that use the coordinate rotation digital computer (CORDIC) algorithm, the advantage of higher throughput is accompanied by saving additions. Only some lifting-based BinDCT schemes require less adders in total, in spite of longer critical paths. The transforms have been derived from the fast Loeffler's algorithm by replacing the rotation stage with unfolded CORDIC iterations, which have been arranged so that two rotation approximations use the same scaling. This is equivalent to imposing structural orthogonality (losslessness) on a system, from which the scaling can then be extracted so as to shorten the critical path. Supporting ideas are a notation for more conveniently describing CORDIC circuits, and an angle conversion that allows rotations to be approximated using an extended set of CORDIC circuits. The research results have been validated by field programmable gate array-based hardware design experiments and by usability tests based on a software JPEG codec.

References

    1. 1)
      • 9. Wu, Z., Sha, J., Wang, Z., Li, L., Gao, M.: ‘An improved scaled DCT architecture’, IEEE Trans. Consum. Electron., 2009, 55, (2), pp. 685689 (doi: 10.1109/TCE.2009.5174440).
    2. 2)
      • 7. Parfieniuk, M.: ‘Shortening the critical path in CORDIC-based approximations of the eight-point DCT’. Proc. Int. Conf. Signals Electronic Systems (ICSES), Cracow, Poland, 14–17 September 2008, pp. 405408.
    3. 3)
      • 15. Jeong, H., Kim, J., Cho, W.-k.: ‘Low-power multiplierless DCT architecture using image data correlation’, IEEE Trans. Consum. Electron., 2004, 50, (1), pp. 262267 (doi: 10.1109/TCE.2004.1277872).
    4. 4)
      • 4. Liang, J., Tran, T.D.: ‘Fast multiplierless approximations of the DCT with the lifting scheme’, IEEE Trans. Signal Process., 2001, 49, (12), pp. 30323044 (doi: 10.1109/78.969511).
    5. 5)
      • 2. Loeffler, C., Lightenberg, A., Moschytz, G.: ‘Practical fast 1-D DCT algorithms with 11 multiplications’. Proc. IEEE Int. Conf. Acoustic, Speech, Signal Processing (ICASSP), Glasgow, Scotland, 23–26 May 1989, vol. 2, pp. 988991.
    6. 6)
      • 11. Calderbank, A.R., Daubechies, I., Sweldens, W., Yeo, B.-L.: ‘Wavelet transforms that map integers to integers’, Appl. Comput. Harmon. Anal., 1998, 5, (3), pp. 332369 (doi: 10.1006/acha.1997.0238).
    7. 7)
      • 12. Britanak, V.: ‘New universal rotation-based fast computational structures for an efficient implementation of the DCT-iv/DST-iv and analysis/synthesis MDCT/MDST filter banks’, Signal Process., 2009, 89, (11), pp. 22132232 (doi: 10.1016/j.sigpro.2009.04.041).
    8. 8)
      • 13. Krishna, G., Sridhar, T., Kumar, K.: ‘Design and implementation of low power fast DCT architecture using modified FGA algorithm’, Int. J. Syst., Algorith. Appl., 2012, 2, pp. 7376.
    9. 9)
      • 18. Wu, A.Y., Wu, C.S.: ‘A unified view for vector rotational CORDIC algorithms and architectures based on angle quantization approach’, IEEE Trans. Circuits Syst. I, 2002, 49, (10), pp. 14421456 (doi: 10.1109/TCSI.2002.803363).
    10. 10)
      • 22. Kok, C.W., Nguyen, T.Q.: ‘Multirate filter banks and transform coding gain’, IEEE Trans. Signal Process., 1998, 46, (7), pp. 20412044 (doi: 10.1109/78.700978).
    11. 11)
      • 24. Independent JPEG Group (IJG): ‘JPEG image compression software’. Available at http://www.ijg.org.
    12. 12)
      • 16. Yu, S., Swartzlander, E.E.: ‘A scaled DCT architecture with the CORDIC algorithm’, IEEE Trans. Signal Process., 2002, 50, (1), pp. 160167 (doi: 10.1109/78.972492).
    13. 13)
      • 10. Vaidyanathan, P.P., Doğanata, Z.: ‘The role of lossless systems in modern digital signal processing: a tutorial’, IEEE Trans. Educ., 1989, 32, (3), pp. 181197 (doi: 10.1109/13.34150).
    14. 14)
      • 6. Sun, C.-C., Ruan, S.-J., Heyne, B., Goetze, J.: ‘Low-power and high-quality CORDIC-based Loeffler DCT for signal processing’, IET Circuits Devices Syst., 2007, 1, (6), pp. 453461 (doi: 10.1049/iet-cds:20060289).
    15. 15)
      • 3. Chen, W., Smith, C.H., Fralick, S.C.: ‘A fast computational algorithm for the discrete cosine transform’, IEEE Trans. Commun., 1977, 25, (9), pp. 10041009 (doi: 10.1109/TCOM.1977.1093941).
    16. 16)
      • 19. Wu, C.S., Wu, A.Y., Lin, C.H.: ‘A high-performance/low-latency vector rotational CORDIC architecture based on extended elementary angle set and trellis-based searching schemes’, IEEE Trans. Circuits Syst. II, 2003, 50, (9), pp. 589601 (doi: 10.1109/TCSII.2003.816923).
    17. 17)
      • 14. Hsiao, S.-F., Hu, Y.H., Juang, T.-B., Lee, C.-H.: ‘Efficient VLSI implementations of fast multiplierless approximated DCT using parameterized hardware modules for silicon intellectual property design’, IEEE Trans. Circuits Syst. I, 2005, 52, (8), pp. 15681579 (doi: 10.1109/TCSI.2005.851709).
    18. 18)
      • 21. Moulin, P.: ‘A multiscale relaxation algorithm for SNR maximization in nonorthogonal subband coding’, IEEE Trans. Image Process., 1995, 4, (9), pp. 12691281 (doi: 10.1109/83.413171).
    19. 19)
      • 23. Madanayake, A., Cintra, R., Onen, D., et al: ‘A row-parallel 8 × 8 2-D DCT architecture using algebraic integer-based exact computation’, IEEE Trans. Circuits Syst. Video Technol., 2012, 22, (6), pp. 915929 (doi: 10.1109/TCSVT.2011.2181232).
    20. 20)
      • 8. Fox, T.W., Turner, L.E.: ‘Rapid prototyping of field programmable gate array-based discrete cosine transform approximations’, EURASIP J. Appl. Signal Process., 2003, 2003, (6), pp. 543554 (doi: 10.1155/S1110865703301027).
    21. 21)
      • 1. Britanak, V., Yip, P.C., Rao, K.R.: ‘Discrete cosine and sine transforms: general properties, fast algorithms and integer approximations’ (Elsevier/Academic Press, Amsterdam, 2007).
    22. 22)
      • 5. Parfieniuk, M., Petrovsky, A.: ‘Structurally orthogonal finite precision implementation of the eight point DCT’. Proc. IEEE Int. Conf. Acoust., Speech, Signal Process. (ICASSP), Toulouse, France, 14–19 May 2006, vol. 3, pp. 936939.
    23. 23)
      • 17. Meher, P., Valls, J., Juang, T.-B., Sridharan, K., Maharatna, K.: ‘50 years of CORDIC: algorithms, architectures, and applications’, IEEE Trans. Circuits Syst. I, 2009, 56, (9), pp. 18931907 (doi: 10.1109/TCSI.2009.2025803).
    24. 24)
      • 20. Rieder, P., Götze, J., Nossek, J.A., Burrus, C.S.: ‘Parameterization of orthogonal wavelet transforms and their implementation’, IEEE Trans. Circuits Syst. II, 1998, 45, (2), pp. 217226 (doi: 10.1109/82.661654).
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