An accurate fixed-point 8×8 IDCT algorithm based on 2-D algebraic integer representation

Abstract

This paper proposes an algorithm that is based on the application of Algebraic Integer (AI) representation of numbers on the AAN fast Inverse Discrete Cosine Transform (IDCT) algorithm. AI representation allows for maintaining an error-free representation of IDCT until the last step of each 1-D stage of the algorithm, where a reconstruction step from the AI domain to the fixed precision binary domain is required. This delay in introducing the rounding error prevents the accumulation of error throughout the calculations, which leads to the reported high-accuracy results. The proposed algorithm is simple and well suited for hardware implementation due to the absence of computationally extensive multiplications. The obtained results confirm the high accuracy of the proposed algorithm compared to other fixed-point implementations of IDCT.