Title
Errorfree Implementation of the Discrete Cosine Transform: Algorithms and Architectures using Multidimensional Algebraic Intege,Used
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The advancement in multimediabased applications has sustained the need for more efficient ways to encode signals and images. Over the years, the Discrete Cosine Transform (DCT) has emerged as the most popular transform for many image and video coding applications. While implementing the DCT using finiteprecision, approximation of the realvalued transform coefficients is required. It not only results in computational error, but also limits the quality of the reconstruction. An errorfree encoding using algebraic integers has been shown to be an effective way of resolving the issue. The mapping technique ? referred as Algebraic Integer Quantization (AIQ) ? encodes the irrational basis functions using algebraic integers. This research presents novel AIQbased architectures for the fast implementation of several 8x8 2D scaled DCT and Inverse scaled DCTs. A new Integerlike 8x8 2D DCT for H.264 encoder is also presented. Apart from the multiplicationfree nature, the presented scheme eliminates any quantization errors during the transform stage resulting in areaefficient and highspeed designs suitable for realtime image or video compression and HDTV applications.
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