Error-free computation of 8×8 2D DCT and IDCT using two-dimensional algebraic integer quantization

This paper presents a novel error-free (infinite-precision) architecture for the fast implementation of both 8×8 2D discrete cosine transform and inverse DCT. The architecture uses a new algebraic integer quantization 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 to compute both DCT and IDCT which eliminates the requirements to approximate the transformation matrix elements by obtaining their exact representations and hence mapping the transcendental functions without any errors. Using this encoding scheme, an entire 8×8 1D DCT-SQ (scalar quantization) algorithm can be implemented with only 24 adders. Apart from the multiplication-free nature, this new mapping scheme fits to this algorithm, eliminating any computational or quantization errors and resulting short-word-length and high-speed-design.