I. Introduction
Video CODING equipment has extensively used block transform coding techniques to reduce the data rates with quantization and entropy coding. Among several block transforms, the discrete cosine transform (DCT) [1] has widely been applied to still image and video decoding standards, such as JPEG [2], MPEG-1/2 [3], [4], and MPEG-4 [5]. Distinct from the well-known 88 DCT utilized in the above-mentioned standards, the new multiplierless transform [6], which is called BinDCT, is applied to both lossy and lossless image coding with only shift and add operations, and obtains competitive results, compared with the floating-point DCT. Owing to the low-complexity and effective coding performance of integer transforms, the advanced video coding (AVC) in ITU-T H.264 [7]–[9], which is also known as MPEG-4 part 10, uses integer transform matrices for transform coding. The 44 and 88 transforms in [7] and [9] can be computed exactly in integer arithmetic to avoid inverse transform mismatch problems and are applied to high-resolution video sequences. The VC-1 standard [10], [11], which is developed by Microsoft Corporation and standardized by the Society of Motion Picture and Television Engineers (SMPTE), uses 44 and 88 integer transforms for the video coding. For the audio video coding standard (AVS) in China [12], [13], the video standard uses the 88 integer transform to achieve the high efficiency and can be applied to code HDTV contents. Recently, supporting multiple transform functions in multiple standards has been an important issue in multimedia applications, such as H.264/AVC, VC-1, AVS, JPEG, and MPEG-1/2/4 [14]–[27]. Thus, the cost-effective design of multiple forward and inverse transforms for the multiple video coding has also been an interesting research.