Parallel 3-dimensional DCT computation on k-ary n-cubes

The three dimensional discrete cosine transform (3D DCT) has been widely used in many applications such as video compression. On the other hand, the k-ary n-cube is one of the most popular interconnection networks used in many recent multicomputers. As direct calculation of 3D DCT is very time consuming, many researchers have been working on developing algorithms and special-purpose architectures for fast computation of 3D DCT. This paper proposes a parallel algorithm for efficient calculation of 3D DCT on the k-ary n-cube multicomputers. The time complexity of the proposed algorithm is of O(N) for an N times N times N input data cube while direct calculation of 3D DCT has a complexity of O(N⁶)