On compatibility of order-8 integer cosine transforms and the discrete cosine transform

The author shows that integer cosine transforms (ICTs) are functionally compatible with discrete cosine transforms (DCTs) that are used in image coding. It is provided that the w-bit ICT can inversely transform exactly represented DCT coefficients with less mean-square-error than the w-bit DCT for w equal to 4, 3 and 2 and scaling factors of ICTs implemented using 8 bits. Conversely, an exactly represented DCT can inversely transform the coefficients from the w-bit ICT with less mean-square-error than the w-bit DCT. Therefore, the ICTs can be said to be compatible with the DCT. These ICTs, while being considered as new transforms, can also be regarded as alternative and better ways to implement the DCT when the number of bits for representing kernel components are restricted to 4, 3, and 2