Error-free Implementation of the Discrete Cosine Transform

The advancement in multimedia-based 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 finite-precision, approximation of the real-valued transform coefficients is required. It not only results in computational error, but also limits the quality of the reconstruction. An error-free 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 AIQ-based architectures for the fast implementation of several 8x8 2-D scaled DCT and Inverse scaled DCTs. A new Integer-like 8x8 2-D DCT for H.264 encoder is also presented. Apart from the multiplication-free nature, the presented scheme eliminates any quantization errors during the transform stage resulting in area-efficient and high-speed designs suitable for real-time image or video compression and HDTV applications.