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A Method for Estimating the MeanSquared Error of Distributed Arithmetic
Jun TAKEDA Shinichi URAMOTO Masahiko YOSHIMOTO
Publication
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences
Vol.E77A
No.1
pp.272280 Publication Date: 1994/01/25 Online ISSN:
DOI: Print ISSN: 09168508 Type of Manuscript: PAPER Category: Digital Signal Processing Keyword: error analysis, meansquared error, distributed arithmetic, DCT/IDCT,
Full Text: PDF(660.5KB)>>
Summary:
It is important for LSI system designers to estimate computational errors when designing LSI's for numeric computations. Both for the prediction of the errors at an early stage of designing and for the choice of a proper hardware configuration to achieve a target performance, it is desirable that the errors can be estimated in terms of a minimum of parameters. This paper presents a theoretical error analysis of multiplyaccumulation implemented by distributed arithmetic(DA) and proposes a new method for estimating the meansquared error. DA is a method of implementing the multiplyaccumulation that is defined as an inner product of an input vector and a fixed coefficient vector. Using a ROM which stores partial products. DA calculates the output by accumulating the partial products bitserially. As DA uses no parallel multipliers, it needs a smaller chip area than methods using parallel multipliers. Thus DA is effectively utilitzed for the LSI implementation of a digital signal processing system which requires the multiplyaccumulation. It has been known that, if the input data are uniformly distributed, the meansquared error of the multiplyaccumulation implemented by DA is a function of only the word lengths of the input, the output, and the ROM. The proposed method for the error estimation can calculate the meansquared error by using the same parameters even when the input data are not uniformly distributed. The basic idea of the method is to regard the input data as a combination of uniformly distributed partial data with a different word length. Then the meansquared error can be predicted as a weighted sum of the contribution of each partial data, where the weight is the ratio of the partial data to the total input data. Finally, the method is applied to a twodimensional inverse discrete cosine transform (IDCT) and the practicability of the method is confirmed by computer simulations of the IDCT implemented by DA.

