Rounding Error Reduction of Integer DCT utilizing Structure of Permutation Groups on Order and Sign of Signals

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  • OTAKE Wataru
    Nagaoka University of technology, Department of Electrical Engineering
  • IWAHASHI Masahiro
    Nagaoka University of technology, Department of Electrical Engineering

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Other Title
  • 信号置換と符号置換による整数DCTの丸め誤差低減法(画像符号化,通信・ストリーム技術、一般)
  • 信号置換と符号置換による整数DCTの丸め誤差低減法
  • シンゴウ チカン ト フゴウ チカン ニ ヨル セイスウ DCT ノ マルメ ゴサ テイゲンポウ

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Abstract

In case of a two point rotation transform (RT), which is a component of the discrete cosine transform (DCT), is implemented in lifting structure, its multiplier coefficient has a singular point. Therefore, the coefficient value becomes close to infinity near the singular point depending on its rotation angle. As a result, rounding errors inside the transform are extremely amplified by such coefficients. In this report, we introduce permutation of order and sign of input and output signals of RT to shift the singular point. In this case, RT can be implemented with one of some candidates. Therefore, there exists the best combination of the candidates such that the error of the DCT becomes the minimum. We determine it utilizing structure of group of the permutations, comprehensively and efficiently. We confirmed that the error was reduced in Chen's DCT.

Journal

  • ITE Technical Report

    ITE Technical Report 33.55 (0), 59-63, 2009

    The Institute of Image Information and Television Engineers

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