Patent Publication Number: US-11641478-B2

Title: Usage of default and user-defined scaling matrices

Description:
CROSS REFERENCE TO RELATED APPLICATIONS 
     This application is a continuation of International Patent Application No. PCT/CN2020/110275, filed on Aug. 20, 2020, which claims the priority to and benefits of International Patent Application No. PCT/CN2019/101555, filed on Aug. 20, 2019. All the aforementioned patent applications are hereby incorporated by reference in their entireties. 
    
    
     TECHNICAL FIELD 
     This patent document relates to video coding techniques, devices and systems. 
     BACKGROUND 
     In spite of the advances in video compression, digital video still accounts for the largest bandwidth use on the internet and other digital communication networks. As the number of connected user devices capable of receiving and displaying video increases, it is expected that the bandwidth demand for digital video usage will continue to grow. 
     SUMMARY 
     Devices, systems and methods related to digital video coding, and specifically, to video coding and decoding that use scaling matrices and/or transform matrices. 
     In an example aspect, a method of video processing is disclosed. The method includes performing a conversion between a video block of a video and a coded representation of the video, wherein the coded representation conforms to a format rule, wherein the format rule specifies that applicability of a transform skip mode to the video block is determined by a coding condition of the video block, wherein the format rule specifies that a syntax element indicative of applicability of the transform skip mode is omitted from the coded representation, and wherein the transform skip mode includes, skipping applying a forward transform to at least some coefficients prior to encoding into the coded representation, or during decoding, skipping applying an inverse transform to at least some coefficients prior to decoding from the coded representation. 
     In another example aspect, a method of video processing is disclosed. The method includes comprises determining, fora conversion between two adjacent video blocks of a video and a coded representation of the video, whether an in-loop filter or a post-reconstruction filter is to be used for the conversion depending on whether forward transform or an inverse transform is used for the conversion, wherein the forward transform includes, skipping applying the forward transform to at least some coefficients prior to encoding into the coded representation, or during decoding, skipping applying the inverse transform to at least some coefficients to decoding from the coded representation; and performing the conversion based on the use of the in-loop filter or the post-reconstruction filter. 
     In another example aspect, a method of video processing is disclosed. The method includes determining, for a conversion between a video block of a video and a coded representation of the video, factors of a scaling tool based on a coding mode of the video block; and performing the conversion using the scaling tool, wherein the use of the scaling tool comprises: scaling at least some coefficients representing the video block during encoding or descaling at least some coefficients from the coded representation during decoding. 
     In another example aspect, a method of video processing is disclosed. The method includes determining, for a conversion between a video block of a video and a coded representation of the video, to disable use of a scaling tool due to a block differential pulse code modulation (BDPCM) coding tool or a quantized residual BDPCM (QR-BDPCM) coding tool for the conversion of the video block; and performing the conversion without using the scaling tool, wherein the use of the scaling tool comprises: scaling at least some coefficients representing the video block during encoding or descaling at least some coefficients from the coded representation during decoding. 
     In another example aspect, a method of video processing is disclosed. The method includes selecting, fora conversion between video blocks of a video and a coded representation of the video, scaling matrices based on a transform matrix selected for the conversion, wherein the scaling matrices are used to scale at least some coefficients of the video blocks, and wherein the transform matrices are used to transform the at least some coefficients of the video blocks during the conversion; and performing the conversion using the scaling matrices. 
     In another example aspect, a method of video processing is disclosed. The method includes determining, according to a rule, whether to apply a scaling matrix based on whether a secondary transform matrix is applied to a portion of a video block of a video, wherein the scaling matrix is used to scale at least some coefficients of the video block, and wherein the secondary transform matrix is used to transform at least some residual coefficients of the portion of the video block during the conversion; and performing a conversion between the video block of the video and a bitstream representation of the video using the selected scaling matrix. 
     In another example aspect, a method of video processing is disclosed. The method includes determining, for a video block that has a non-square shape, a scaling matrix for use in a conversion between the video block of a video and a coded representation of the video, wherein a syntax element in the coded representation signals the scaling matrix, and wherein the scaling matrix is used to scale at least some coefficients of the video blocks during the conversion; and performing the conversion based on the scaling matrix. 
     In another example aspect, a method of video processing is disclosed. The method includes performing a conversion between a video block of a video and a coded representation of the video, wherein the video block comprises a first number of positions at which a scaling matrix is applied during the conversion and a second number of positions at which the scaling matrix is not applied during the conversion based on a rule. 
     In another example aspect, a method of video processing is disclosed. The method includes determining that a scaling matrix is to be applied during a conversion between a video block of a video and a coded representation of the video; and performing the conversion based on the scaling matrix, wherein the coded representation indicates a number of elements of the scaling matrix, and wherein the number depends on whether coefficient zeroing out is applied to coefficients of the video block. 
     In another example aspect, a method of video processing is disclosed. The method includes performing a conversion between a video block of a video and a coded representation of the video according to a rule, wherein the video block is represented in the coded representation after zeroing out all but top-left M×N transform coefficients after applying a K×L transform matrix to transform coefficients of the video block, wherein the coded representation is configured to exclude signaling of elements of a scaling matrix at positions corresponding to the zeroing out, wherein the scaling matrix is used for scaling the transform coefficients. 
     In another example aspect, a method of video processing is disclosed. The method includes determining, during a conversion between a video block of a video and a coded representation of the video, based on a rule whether a single quantization matrix is to be used based on a size of the video block, wherein all video blocks having the size use the single quantization matrix; and performing the conversion using the quantization matrix. 
     In another example aspect, a method of video processing is disclosed. The method includes determining, for a conversion between a coded representation of a video block of a video and the video block, based on a coded mode information, whether a transform skip mode is enabled for the conversion; and performing the conversion based on the determining; wherein, in the transform skip mode, application of a transform to at least some coefficients representing the video block is skipped during the conversion. 
     In another example aspect, another method of video processing is disclosed. The method includes determining to use a scaling matrix for a conversion between a coded representation of a video block and the video block due to a use of a block differential pulse code modulation (BDPCM) or a quantized residual BDPCM (QR-BDPCM) mode for the conversion; and performing the conversion using the scaling matrix; wherein the scaling matrix is used to scale at least some coefficients representing the video block during the conversion. 
     In another example aspect, another method of video processing is disclosed. The method includes determining to disable use of a scaling matrix for a conversion between a coded representation of a video block and the video block due to a use of a block differential pulse code modulation (BDPCM) or a quantized residual BDPCM (QR-BDPCM) mode for the conversion; and performing the conversion using the scaling matrix; wherein the scaling matrix is used to scale at least some coefficients representing the video block during the conversion. 
     In another example aspect, another method of video processing is disclosed. The method includes determining, fora conversion between a coded representation of a video block of a video and the video block, an applicability of an in-loop filter depending on whether a transform skip mode is enabled for the conversion; and performing the conversion based on the applicability of the in-loop filter, wherein, in the transform skip mode, application of a transform to at least some coefficients representing the video block is skipped during the conversion. 
     In another example aspect, another method of video processing is disclosed. The method includes selecting a scaling matrix for a conversion between video blocks of a video and a coded representation of the video blocks such that a same scaling matrix is selected for inter coding and intra block copy coding based conversion, and performing the conversion using the selected scaling matrix, wherein the scaling matrix is used to scale at least some coefficients of the video blocks. 
     In another example aspect, another method of video processing is disclosed. The method includes selecting a scaling matrix for a conversion between video blocks of a video and a coded representation of the video blocks based on a transform matrix selected for the conversion, and performing the conversion using the selected scaling matrix, wherein the scaling matrix is used to scale at least some coefficients of the video blocks and wherein the transform matrix is used to transform at least some coefficients of the video block during the conversion. 
     In another example aspect, another method of video processing is disclosed. The method includes selecting a scaling matrix for a conversion between video blocks of a video and a coded representation of the video blocks based on a secondary transform matrix selected for the conversion, and performing the conversion using the selected scaling matrix, wherein the scaling matrix is used to scale at least some coefficients of the video blocks and wherein the secondary transform matrix is used to transform at least some residual coefficients of the video block during the conversion. 
     In another example aspect, another method of video processing is disclosed. The method includes determining, fora video block that has a non-square shape, a scaling matrix for use in a conversion between the video block and a coded representation of the video block, wherein a syntax element in the coded representation signals the scaling matrix; and performing the conversion based on the scaling matrix, wherein the scaling matrix is used to scale at least some coefficients of the video blocks during the conversion. 
     In another example aspect, another method of video processing is disclosed. The method includes determining that a scaling matrix is to be applied partially during a conversion between a coded representation of a video block and the video block; and performing the conversion based by partially applying the scaling matrix such that the scaling matrix is applied in a first set of positions and disabled at remaining positions in the video block. 
     In another example aspect, another method of video processing is disclosed. The method includes determining that a scaling matrix is to be applied during a conversion between a coded representation of a video block and the video block; and performing the conversion based on the scaling matrix; wherein the coded representation signals a number of elements of the scaling matrix, wherein the number depends on application of coefficient zeroing out in the conversion. 
     In another example aspect, another method of video processing is disclosed. The method includes determining, during a conversion between a video block and a coded representation of the video block, a single quantization matrix to use based on a size of the video block being of a specific type; and performing the conversion using the quantization matrix. 
     In yet another representative aspect, the above-described method is embodied in the form of processor-executable code and stored in a computer-readable program medium. 
     In yet another representative aspect, a device that is configured or operable to perform the above-described method is disclosed. The device may include a processor that is programmed to implement this method. 
     In yet another representative aspect, a video decoder apparatus may implement a method as described herein. 
     The above and other aspects and features of the disclosed technology are described in greater detail in the drawings, the description and the claims. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG.  1    is a block diagram of an example video encoder implementation. 
         FIG.  2    shows an example of a secondary transform. 
         FIG.  3    shows an example of a reduced secondary transform (RST). 
         FIG.  4    is an illustration of the two scalar quantizers used in the proposed approach of dependent quantization. 
         FIG.  5    shows an example of state transition and quantizer selection for the proposed dependent quantization. 
         FIGS.  6 A- 6 B  show examples of diagonal scan orders. 
         FIG.  7    shows an example of selected positions for QM signaling (32×32 transform size). 
         FIG.  8    shows an example of selected positions for QM signaling (64×64 transform size). 
         FIG.  9    shows an example of applying zeroing out to coefficients. 
         FIG.  10    shows an example of only selected elements in the dashed region (e.g., the M×N region) are signaled. 
         FIG.  11    is a block diagram of an example of a video processing hardware platform. 
         FIG.  12    is a flowchart of an example method of video processing. 
         FIG.  13    is a block diagram illustrating an example of video decoder. 
         FIG.  14    is a block diagram showing an example video processing system in which various techniques disclosed herein may be implemented. 
         FIG.  15    is a block diagram that illustrates an example video coding system that may utilize the techniques of this disclosure. 
         FIG.  16    is a block diagram illustrating an example of video encoder. 
         FIGS.  17 - 27    are flowcharts of example methods of video processing. 
     
    
    
     DETAILED DESCRIPTION 
     Embodiments of the disclosed technology may be applied to existing video coding standards (e.g., HEVC, H.265) and future standards to improve compression performance. Section headings are used in the present document to improve readability of the description and do not in any way limit the discussion or the embodiments (and/or implementations) to the respective sections only. 
     1. Summary 
     This document is related to image/video coding technologies. Specifically, it is related to quantization matrix in image/video coding. It may be applied to the existing video coding standard like HEVC, or the standard (Versatile Video Coding) to be finalized. It may be also applicable to future video coding standards or video codec. 
     2. Background 
     Video coding standards have evolved primarily through the development of the well-known ITU-T and ISO/IEC standards. The ITU-T produced H.261 and H.263, ISO/IEC produced MPEG-1 and MPEG-4 Visual, and the two organizations jointly produced the H.262/MPEG-2 Video and H.264/MPEG-4 Advanced Video Coding (AVC) and H.265/HEVC standards. Since H.262, the video coding standards are based on the hybrid video coding structure wherein temporal prediction plus transform coding are utilized. To explore the future video coding technologies beyond HEVC, Joint Video Exploration Team (JVET) was founded by VCEG and MPEG jointly in 2015. Since then, many new methods have been adopted by JVET and put into the reference software named Joint Exploration Model (JEM). In April 2018, the Joint Video Expert Team (JVET) between VCEG (Q6/16) and ISO/IEC JTC1 SC29/WG11 (MPEG) was created to work on the VVC standard targeting at 50% bitrate reduction compared to HEVC. 
     The latest version of VVC draft, i.e., Versatile Video Coding (Draft 5) could be found at: 
     http://phenix.it-sudparis.eu/jvet/doc_end_user/current_document.php?id=6640 
     The latest reference software of VVC, named VTM, could be found at: 
     https://vcgit.hhi.fraunhofer.de/jvet/VVCSoftware_VTM/tags/VTM-4.0 
     2.1. Colorspace and Chrome Subsampling 
     Color space, also known as the color model (or color system), is an abstract mathematical model which simply describes the range of colors as tuples of numbers, typically as 3 or 4 values or color components (e.g. RGB). Basically speaking, color space is an elaboration of the coordinate system and sub-space. 
     For video compression, the most frequently used color spaces are YCbCr and RGB. 
     YCbCr, Y′CbCr, or Y Pb/Cb Pr/Cr, also written as YCBCR or Y′CBCR, is a family of color spaces used as a part of the color image pipeline in video and digital photography systems. Y′ is the luma component and CB and CR are the blue-difference and red-difference chroma components. Y′ (with prime) is distinguished from Y, which is luminance, meaning that light intensity is nonlinearly encoded based on gamma corrected RGB primaries. 
     Chroma subsampling is the practice of encoding images by implementing less resolution for chroma information than for luma information, taking advantage of the human visual system&#39;s lower acuity for color differences than for luminance. 
     2.1.1. 4:4:4 
     Each of the three Y′CbCr components have the same sample rate, thus there is no chroma subsampling. This scheme is sometimes used in high-end film scanners and cinematic post production. 
     2.1.2. 4:2:2 
     The two chroma components are sampled at half the sample rate of luma: the horizontal chroma resolution is halved. This reduces the bandwidth of an uncompressed video signal by one-third with little to no visual difference 
     2.1.3. 4:2:0 
     In 4:2:0, the horizontal sampling is doubled compared to 4:1:1, but as the Cb and Cr channels are only sampled on each alternate line in this scheme, the vertical resolution is halved. The data rate is thus the same. Cb and Cr are each subsampled at a factor of 2 both horizontally and vertically. There are three variants of 4:2:0 schemes, having different horizontal and vertical siting.
         In MPEG-2, Cb and Cr are cosited horizontally. Cb and Cr are sited between pixels in the vertical direction (sited interstitially).   In JPEG/JFIF, H.261, and MPEG-1, Cb and Cr are sited interstitially, halfway between alternate luma samples.   In 4:2:0 DV, Cb and Cr are co-sited in the horizontal direction. In the vertical direction, they are co-sited on alternating lines.
 
2.2. Coding Flow of a Typical Video Codec
       

       FIG.  1    shows an example of encoder block diagram of VVC, which contains three in-loop filtering blocks: deblocking filter (DF), sample adaptive offset (SAO) and ALF. Unlike DF, which uses predefined filters, SAO and ALF utilize the original samples of the current picture to reduce the mean square errors between the original samples and the reconstructed samples by adding an offset and by applying a finite impulse response (FIR) filter, respectively, with coded side information signaling the offsets and filter coefficients. ALF is located at the last processing stage of each picture and can be regarded as a tool trying to catch and fix artifacts created by the previous stages. 
     2.3. Quantization Matrix 
     The well-known spatial frequency sensitivity of the human visual system (HVS), has been a key driver behind many aspects of the design of modern image and video coding algorithms and standards including JPEG, MPEG2, H.264/AVC High Profile and the HEVC. 
     The quantization matrix used in MPEG2 is an 8×8 matrix. In H.264/AVC, the quantization matrix block size includes both 4×4 and 8×8. These QMs are encoded in SPS (sequence parameter set) and PPS (picture parameters set). The compressed method in H.264/AVC for QM signalling is Differential Pulse Code Modulation (DPCM). 
     In H.264/AVC High Profile, 4×4 block size and 8×8 block size are used. Six QMs for 4×4 block size (i.e. separate matrix for intra/inter coding and Y/Cb/Cr components) and two QMs for 8×8 block size (i.e. separate matrix for intra/inter Y component), so only eight quantization matrices need to be encoded into bitstream. 
     2.4. Transform and Quantization Design in VVC 
     2.4.1. Transform 
     HEVC specifies two-dimensional transforms of various sizes from 4×4 to 32×32 that are finite precision approximations to the discrete cosine transform (DCT). In addition, HEVC also specifies an alternate 4×4 integer transform based on the discrete sine transform (DST) for use with 4×4 luma Intra prediction residual blocks. In addition to that, when certain block sizes, transform skip may be also allowed. 
     The transform matrices cij (i, j=0 . . . nS−1) for nS=4, 8, 16, and 32, DCT-II are defined as follows: 
     nS=4 
     {64, 64, 64, 64} 
     {83, 36, −36, −83} 
     {64, −64, −64, 64} 
     {36, −83, 83, −36} 
     nS=8 
     {64, 64, 64, 64, 64, 64, 64, 64} 
     {89, 75, 50, 18, −18, −50, −75, −89} 
     {83, 36, −36, −83, −83, −36, 36, 83} 
     {75, −18, −89, −50, 50, 89, 18, −75} 
     {64, −64, −64, 64, 64, −64, −64, 64} 
     {50, −89, 18, 75, −75, −18, 89, −50} 
     {36, −83, 83, −36, −36, 83, −83, 36} 
     {18, −50, 75, −89, 89, −75, 50, −18} 
     nS=16 
     {64 64 64 64 64 64 64 64 64 64 64 64 64 64 64 64} 
     {90 87 80 70 57 43 25 9-9-25-43-57-70-80-87-90} 
     {89 75 50 18-18-50-75-89-89-75-50-18 18 50 75 89} 
     {87 57 9-43-80-90-70-25 25 70 90 80 43-9-57-87} 
     {83 36-36-83-83-36 36 83 83 36-36-83-83-36 36 83} 
     {80 9-70-87-25 57 90 43-43-90-57 25 87 70-9-80} 
     {75-18-89-50 50 89 18-75-75 18 89 50-50-89-18 75} 
     {70-43-87 9 90 25-80-57 57 80-25-90-9 87 43-70} 
     {64-64-64 64 64-64-64 64 64-64-64 64 64-64-64 64} 
     {57-80-25 90-9-87 43 70-70-43 87 9-90 25 80-57} 
     {50-89 18 75-75-18 89-50-50 89-18-75 75 18-89 50} 
     {43-90 57 25-87 70 9-80 80-9-70 87-25-57 90-43} 
     {36-83 83-36-36 83-83 36 36-83 83-36-36 83-83 36} 
     {25-70 90-80 43 9-57 87-87 57-9-43 80-90 70-25} 
     {18-50 75-89 89-75 50-18-18 50-75 89-89 75-50 18} 
     {9-25 43-57 70-80 87-90 90-87 80-70 57-43 25-9} 
     nS=32 
     {64 64 64 64 64 64 64 64 64 64 64 64 64 64 64 64 64 64 64 64 64 64 64 64 64 64 64 64 64 64 64 64} 
     {90 90 88 85 82 78 73 67 61 54 46 38 31 22 13 4-4-13-22-31-38-46-54-61-67-73-78-82-85-88-90-90} 
     {90 87 80 70 57 43 25 9-9-25-43-57-70-80-87-90-90-87-80-70-57-43-25-9 9 25 43 57 70 80 87 90} 
     {90 82 67 46 22-4-31-54-73-85-90-88-78-61-38-13 13 38 61 78 88 90 85 73 54 31 4-22-46-67-82-90} 
     {89 75 50 18-18-50-75-89-89-75-50-18 18 50 75 89 89 75 50 18-18-50-75-89-89-75-50-18 18 50 75 89} 
     {88 67 31-13-54-82-90-78-46-4 38 73 90 85 61 22-22-61-85-90-73-38 4 46 78 90 82 54 13-31-67-88} 
     {87 57 9-43-80-90-70-25 25 70 90 80 43-9-57-87-87-57-9 43 80 90 70 25-25-70-90-80-43 9 57 87} 
     {85 46-13-67-90-73-22 38 82 88 54-4-61-90-78-31 31 78 90 61 4-54-88-82-38 22 73 90 67 13-46-85} 
     {83 36-36-83-83-36 36 83 83 36-36-83-83-36 36 83 83 36-36-83-83-36 36 83 83 36-36-83-83-36 36 83} 
     {82 22-54-90-61 13 78 85 31-46-90-67 4 73 88 38-38-88-73-4 67 90 46-31-85-78-13 61 90 54-22-82} 
     {80 9-70-87-25 57 90 43-43-90-57 25 87 70-9-80-80-9 70 87 25-57-90-43 43 90 57-25-87-70 9 80} 
     {78-4-82-73 13 85 67-22-88-61 31 90 54-38-90-46 46 90 38-54-90-31 61 88 22-67-85-13 73 82 4-78} 
     {75-18-89-50 50 89 18-75-75 18 89 50-50-89-18 75 75-18-89-50 50 89 18-75-75 18 89 50-50-89-18 75} 
     {73-31-90-22 78 67-38-90-13 82 61-46-88-4 85 54-54-85 4 88 46-61-82 13 90 38-67-78 22 90 31-73} 
     {70-43-87 9 90 25-80-57 57 80-25-90-9 87 43-70-70 43 87-9-90-25 80 57-57-80 25 90 9-87-43 70} 
     {67-54-78 38 85-22-90 4 90 13-88-31 82 46-73-61 61 73-46-82 31 88-13-90-4 90 22-85-38 78 54-67} 
     {64-64-64 64 64-64-64 64 64-64-64 64 64-64-64 64 64-64-64 64 64-64-64 64 64-64-64 64 64-64-64 64} 
     {61-73-46 82 31-88-13 90-4-90 22 85-38-78 54 67-67-54 78 38-85-22 90 4-90 13 88-31-82 46 73-61} 
     {57-80-25 90-9-87 43 70-70-43 87 9-90 25 80-57-57 80 25-90 9 87-43-70 70 43-87-9 90-25-80 57} 
     {54-85-4 88-46-61 82 13-90 38 67-78-22 90-31-73 73 31-90 22 78-67-38 90-13-82 61 46-88 4 85-54} 
     {50-89 18 75-75-18 89-50-50 89-18-75 75 18-89 50 50-89 18 75-75-18 89-50-50 89-18-75 75 18-89 50} 
     {46-90 38 54-90 31 61-88 22 67-85 13 73-82 4 78-78-4 82-73-13 85-67-22 88-61-31 90-54-38 90-46} 
     {43-90 57 25-87 70 9-80 80-9-70 87-25-57 90-43-43 90-57-25 87-70-9 80-80 9 70-87 25 57-90 43} 
     {38-88 73-4-67 90-46-31 85-78 13 61-90 54 22-82 82-22-54 90-61-13 78-85 31 46-90 67 4-73 88-38} 
     {36-83 83-36-36 83-83 36 36-83 83-36-36 83-83 36 36-83 83-36-36 83-83 36 36-83 83-36-36 83-83 36} 
     {31-78 90-61 4 54-88 82-38-22 73-90 67-13-46 85-85 46 13-67 90-73 22 38-82 88-54-4 61-90 78-31} 
     {25-70 90-80 43 9-57 87-87 57-9-43 80-90 70-25-25 70-90 80-43-9 57-87 87-57 9 43-80 90-70 25} 
     {22-61 85-90 73-38-4 46-78 90-82 54-13-31 67-88 88-67 31 13-54 82-90 78-46 4 38-73 90-85 61-22} 
     {18-50 75-89 89-75 50-1 8-1 8 50-75 89-89 75-50 18 18-50 75-89 89-75 50-1 8-1 8 50-75 89-89 75-50 18} 
     {13-38 61-78 88-90 85-73 54-31 4 22-46 67-82 90-90 82-67 46-22-4 31-54 73-85 90-88 78-61 38-13} 
     {9-25 43-57 70-80 87-90 90-87 80-70 57-43 25-9-9 25-43 57-70 80-87 90-90 87-80 70-57 43-25 9} 
     {4-13 22-31 38-46 54-61 67-73 78-82 85-88 90-90 90-90 88-85 82-78 73-67 61-54 46-38 31-22 13-4} 
     2.4.2. Quantization 
     The HEVC quantizer design is similar to that of H.264/AVC where a quantization parameter (QP) in the range of 0-51 (for 8-bit video sequences) is mapped to a quantizer step size that doubles each time the QP value increases by 6. A key difference, however, is that the transform basis norm correction factors incorporated into the descaling matrices of H.264/AVC are no longer needed in HEVC simplifying the quantizer design. A QP value can be transmitted (in the form of delta QP) for a quantization group as small as 8×8 samples for rate control and perceptual quantization purposes. The QP predictor used for calculating the delta QP uses a combination of left, above and previous QP values. HEVC also supports frequency-dependent quantization by using quantization matrices for all transform block sizes. Details will be described in section 2.4.3. 
     The quantized transform coefficients q ij  (i, j=0 . . . nS−1) are derived from the transform coefficients d ij  (i, j=0 . . . nS−1) as:
 
 q   ij =( d   ij   *f [ QP %6]+offset)&gt;&gt;(29+ QP/ 6 −nS −BitDepth),with i,j= 0, . . . , nS− 1
 
where
 
 f [ x ]={26214,23302,20560,18396,16384,14564}, x= 0, . . . ,5 2 28+QP/6−nS-BitDepth &lt;offset&lt;2 29+QP/6−nS-BitDepth  
 
     QP represents the quantization parameter for one transform unit, and BitDepth represents the bit depth associated with the current color component. 
     In HEVC, the range of QP is [0, 51]. 
     2.4.3. Quantization Matrix 
     Quantization matrix (QM) has been adopted in image coding standards such as JPEG and JPEG-2000, as well as in video standards such as MPEG2, MPEG4 and H.264/AVC. QM can improve the subjective quality through frequency weighting on different frequency coefficients. In the HEVC standard, the quantization block sizes can go up to 32×32. QMs with the size of 4×4, 8×8, 16×16, 32×32 could be encoded in the bitstream. For each block size, intra/inter prediction types and Y/Cb/Cr color components need different quantization matrix. In total 24 quantization matrices (separate matrices for 4×4, 8×8, 16×16 and 32×32 four block sizes, intra/inter and Y, U, V components) should be encoded. 
     The parameters for a quantization matrix may be directly copied from a reference quantization matrix or may be explicitly signaled. When they are explicitly signaled, the first parameter (a.k.a., value of the (0,0) component of the matrix) is directly coded. And the remaining parameters are coded with predictive coding according to the raster scan of the matrix. 
     Encoding and signalling of scaling matrices in HEVC implies three modes: OFF, DEFAULT, and USER_DEFINED. It is noted that: for transform unit sizes larger than 8×8 (i.e., 16×16, 32×32), the scaling matrix is obtained from the 8×8 scaling matrix by upsampling to a bigger size (duplication of elements). An additional DC value has to be signalled for scaling matrices of TBs bigger than 8×8. 
     The maximum number of coded values for one scaling matrix in HEVC is equal to 64. 
     The DC value for DEFAULT mode is equal to 16 for all TB sizes. 
     2.4.3.1. Syntax and Semantics 
     7.3.2.2 Sequence Parameter Set RBSP Syntax 
     7.3.2.2.1 General Sequence Parameter Set RBSP Syntax 
                                                 Descriptor                          seq_parameter_set_rbsp( ) {                sps_video_parameter_set_id   u(4)           ...                max_transform_hierarchy_depth_intra   ue(v)            scaling_list_enabled_flag   u(1)            if( scaling_list_enabled_flag ) {                 sps_scaling_list_data_present_flag   u(1)             if( sps_scaling_list_data_present_flag )                  scaling_list_data( )                }                amp_enabled_flag   u(1)           ...                rbsp_trailing_bits( )               }                        
7.3.2.3 Picture Parameter Set RBSP Syntax
 
7.3.2.3.1 General Picture Parameter Set RBSP Syntax
 
                                                 Descriptor                          pic_parameter_set_rbsp( ) {                pps_pic_parameter_set_id   ue(v)           ...                if( deblocking_filter_control_present_flag ) {               ...                }                pps_scaling_list_data_present_flag   u(1)            if( pps_scaling_list_data_present_flag )                 scaling_list_data( )                lists_modification_present_flag   u(1)           ...                rbsp_trailing_bits( )               }                        
7.3.4 Scaling List Data Syntax
 
     
       
         
           
               
               
             
               
                   
               
               
                   
                 Descriptor 
               
               
                   
               
             
            
               
                 scaling_list_data( ) { 
                   
               
               
                  for( sizeId = 0; sizeId &lt; 4; sizeId++ ) 
                   
               
               
                   for( matrixId = 0; matrixId &lt; 6; matrixId += ( sizeId ==  
                   
               
               
                   3) ? 3 : 1 ) { 
                   
               
               
                    scaling_list_pred_mode_flag[ sizeId ][ matrixId ] 
                 u(1) 
               
               
                    if( !scaling_list_pred_mode_flag[ sizeId ][ matrixId ]) 
                   
               
               
                     scaling_list_pred_matrix_id_delta[ sizeId ][  
                 ue(v) 
               
               
                     matrixId ] 
                   
               
               
                    else { 
                   
               
               
                     nextCoef = 8 
                   
               
               
                     coefNum = Min( 64, ( 1 &lt;&lt; ( 4 + ( sizeId &lt;&lt;  
                   
               
               
                     1 ) ) ) ) 
                   
               
               
                     if( sizeId &gt; 1 ) { 
                   
               
               
                      scaling_list_dc_coef_minus8[ sizeId - 2 ][  
                 se(v) 
               
               
                      matrixId ] 
                   
               
               
                      nextCoef = scaling_list_dc_coef_minus8[  
                   
               
               
                      sizeId - 2 ][ matrixId ] + 8 
                   
               
               
                     } 
                   
               
               
                     for( i = 0; i &lt; coefNum, i++) { 
                   
               
               
                      scaling_list_detta_coef 
                 se(v) 
               
               
                      nextCoef = ( nextCoef + scaling_list_delta_coef +  
                   
               
               
                      256 ) % 256 
                   
               
               
                      ScalingList[ sizeId ][ matrixId ][ i ] = nextCoef 
                   
               
               
                     } 
                   
               
               
                    } 
                   
               
               
                   } 
                   
               
               
                 } 
               
               
                   
               
            
           
         
       
     
     scaling_list_enabled_flag equal to 1 specifies that a scaling list is used for the scaling process for transform coefficients. scaling_list_enabled_flag equal to 0 specifies that scaling list is not used for the scaling process for transform coefficients. 
     sps_scaling_list_data_present_flag equal to 1 specifies that the scaling_list_data( ) syntax structure is present in the SPS. sps_scaling_list_data_present_flag equal to 0 specifies that the scaling_list_data( ) syntax structure is not present in the SPS. When not present, the value of sps_scaling_list_data_present_flag is inferred to be equal to 0. 
        equal to 1 specifies that the scaling list data used for the pictures referring to the PPS are derived based on the scaling lists specified by the active SPS and the scaling lists specified by the PPS. pps_scaling_list_data_present_flag equal to 0 specifies that the scaling list data used for the pictures referring to the PPS are inferred to be equal to those specified by the active SPS. When scaling_list_enabled_flag is equal to 0, the value of pps_scaling_list_data_present_flag shall be equal to 0. When scaling_list_enabled_flag is equal to 1, sps_scaling_list_data_present_flag is equal to 0, and pps_scaling_list_data_prent_flag is equal to 0, the default scaling list data are used to derive the array ScalingFactor as described in the scaling list data semantics as specified in clause 7.4.5. 
     7.4.5 Scaling List Data Semantics 
       [sizeId][matrixId] equal to 0 specifies that the values of the scaling list are the same as the values of a reference scaling list. The reference scaling list is specified by scaling_list_pred_matrix_id_delta[sizeId][matrixId]. scaling_list_pred_mode_flag[sizeId][matrixId] equal to 1 specifies that the values of the scaling list are explicitly signalled.
   [sizeId][matrixId] specifies the reference scaling list used to derive ScalingList[sizeId][matrixId] as follows:
         If scaling_list_pred_matrix_id_delta[sizeId][matrixId] is equal to 0, the scaling list is inferred from the default scaling list ScalingList[sizeId][matrixId][i] as specified in Table 7-5 and Table 7-6 for i=0 . . . Min(63, (1&lt;&lt;(4+(sizeId&lt;&lt;1)))−1).   Otherwise, the scaling list is inferred from the reference scaling list as follows:
 
refMatrixId=matrixId−scaling_list_pred_matrix_id_delta[sizeId][matrixId]*(sizeId==3?3:1)   (7-42)
 
ScalingList[sizeId][matrixId][ i ]=ScalingList[sizeId][refMatrixId][ i ] with i= 0 . . . Min(63,(1&lt;&lt;(4+(sizeId&lt;&lt;1)))−1)  (7-43)
 
If sizeId is less than or equal to 2, the value of scaling_list_pred_matrix_id_delta[sizeId][matrixId] shall be in the range of 0 to matrixId, inclusive. Otherwise (sizeId is equal to 3), the value of scaling_list_pred_matrix_id_delta[sizeId][matrixId] shall be in the range of 0 to matrixId/3, inclusive.
       
     
       
         
           
               
             
               
                 TABLE 7-3 
               
             
            
               
                   
               
               
                 Specification of sizeId 
               
            
           
           
               
               
               
            
               
                   
                 
                   
                 
                   
               
               
                   
                 
                   
                 
                 
                   
                 
               
               
                   
                   
               
               
                   
                 4 × 4 
                 0 
               
               
                   
                 8 × 8 
                 1 
               
               
                   
                 16 × 16 
                 2 
               
               
                   
                 32 × 32 
                 3 
               
               
                   
                   
               
            
           
         
       
     
                     TABLE 7-4                  Specification of matrixId according to sizeld,       prediction mode and colour component                                                                                                                0, 1, 2, 3   MODE_INTRA   0 (Y)   0       0, 1, 2, 3   MODE_INTRA   1 (Cb)   1       0, 1, 2, 3   MODE_INTRA   2 (Cr)   2       0, 1, 2, 3   MODE_INTER   0 (Y)   3       0, 1, 2, 3   MODE_INTER   1 (Cb)   4       0, 1, 2, 3   MODE_INTER   2 (Cr)   5                      [sizeId−2][matrixId] plus 8 specifies the value of the variable ScalingFactor[2][matrixId][0][0] for the scaling list for the 16×16 size when sizeId is equal to 2 and specifies the value of ScalingFactor[3][matrixId][0][0] for the scaling list for the 32×32 size when sizeId is equal to 3. The value of scaling_list_dc_coef_minus8[sizeId−2][matrixId] shall be in the range of −7 to 247, inclusive.
 
When scaling_list_pred_mode_flag[sizeId][matrixId] is equal to 0, scaling_list_pred_matrix_id_delta[ sizeId][matrixId] is equal to 0, and sizeId is greater than 1, the value of scaling_list_dc_coef_minus8[sizeId−2][matrixId] is inferred to be equal to 8.
 
When scaling_list_pred_matrix_id_delta[sizeId][matrixId] is not equal to 0 and sizeId is greater than 1, the value of scaling_list_dc_coef_minus8[sizeId−2][matrixId] is inferred to be equal to scaling_list_dc_coef_minus8[sizeId−2][refMatrixId], where the value of refMatrixId is given by Equation 7-42.
 
  specifies the difference between the current matrix coefficient ScalingList[sizeId][matrixId][i] and the previous matrix coefficient ScalingList[sizeId][matrixId][i−1], when scaling_list_pred_mode_flag[sizeId][matrixId] is equal to 1. The value of scaling_list_delta_coef shall be in the range of −128 to 127, inclusive. The value of ScalingList[sizeId][matrixId][i] shall be greater than 0.
 
     
       
         
           
               
             
               
                 TABLE 7-5 
               
             
            
               
                   
               
               
                 Specification of default values of ScalingList[0][matrixId][i] with i = 0 . . . 15 
               
            
           
           
               
               
            
               
                   
                 i 
               
            
           
           
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
            
               
                   
                 0 
                 1 
                 2 
                 3 
                 4 
                 5 
                 6 
                 7 
                 8 
                 9 
                 10 
                 11 
                 12 
                 13 
                 14 
                 15 
               
               
                   
               
               
                 ScalingList[0] 
                 16 
                 16 16 
                 16 
                 16 
                 16 
                 16 
                 16 
                 16 
                 16 
                 16 
                 16 
                 16 
                 16 
                 16 
                 16 
                 16 
               
               
                 [0. . . 5][i] 
               
               
                   
               
            
           
         
       
     
                     TABLE 7-6               Specification of default values of ScalingList[1 . . . 3 ][matrixId[i] with i = 0 . . . 63                                            i                                                                                     0   1   2   3   4   5   6   7   8   9   10   11   12   13   14   15               ScalingList[1 . . . 3][0 . . . 2][i]   16   16   16   16   16   16   16   16   16   16   17   16   17   16   17   18       ScalingList[1 . . . 3][3 . . . 5][i]   16   16   16   16   16   16   16   16   16   16   17   17   17   17   17   18                                 i - 16                                                                                      0   1   2   3   4   5   6   7   8   9   10   11   12   13   14   15               ScalingList[1 . . . 3][0 . . . 2][i]   17   18   18   17   18   21   19   20   21   20   19   21   24   22   22   24       ScalingList[1 . . . 3][3 . . . 5][i]   18   18   18   18   18   20   20   20   20   20   20   20   24   24   24   24                                 i - 32                                                                                      0   1   2   3   4   5   6   7   8   9   10   11   12   13   14   15               ScalingList[1 . . . 3][0 . . . 2][i]   24   22   22   24   25   25   27   30   27   25   25   29   31   35   35   31       ScalingList[1 . . . 3][3 . . . 5][i]   24   24   24   24   25   25   25   25   25   25   25   28   28   28   28   28                                 i - 48                                                                                      0   1   2   3   4   5   6   7   8   9   10   11   12   13   14   15               ScalingList[1 . . . 3][0 . . . 2][i]   29   36   41   44   41   36   47   54   54   47   65   70   65   88   88   115       ScalingList[1 . . . 3][3 . . . 5][i]   28   33   33   33   33   33   41   41   41   41   54   54   54   71   71   91                    
The four-dimensional array ScalingFactor[sizeId][matrixId][x][y], with x, y=0 . . . (1&lt;&lt;(2+sizeId))−1, specifies the array of scaling factors according to the variables sizeId specified in Table 7-3 and matrixId specified in Table 7-4
 
The elements of the quantization matrix of size 4×4, ScalingFactor[0][matrixId][ ][ ], are derived as follows:
 
ScalingFactor[0][matrixId][ x ][ y ]=ScalingList[0][matrixId][ i ]  (7-44)
         with i=0 . . . 15, matrixId=0 . . . 5, x=ScanOrder[2][0][i][0], and y=ScanOrder[2][0][i][1]
 
The elements of the quantization matrix of size 8×8, ScalingFactor[1][matrixId][ ][ ], are derived as follows:
 
ScalingFactor[1][matrixId][ x ][ y ]=ScalingList[1][matrixId][ i ]  (7-45)
   with i=0 . . . 63, matrixId=0 . . . 5, x=ScanOrder[3][0][i][0], and y=ScanOrder[3][0][i][1]
 
The elements of the quantization matrix of size 16×16, ScalingFactor[2][matrixId][ ][ ], are derived as follows:
 
ScalingFactor[2][matrixId][ x* 2+ k ][ y* 2+ j ]=ScalingList[ 2 ][matrixId][ i ]  (7-46)
   with i=0 . . . 63, j=0 . . . 1, k=0 . . . 1, matrixId=0 . . . 5, x=ScanOrder[3][0][i][0], and y=ScanOrder[3][0][i][1]
 
ScalingFactor[2][matrixId][0][0]=scaling_list_dc_coef_minus8[0][matrixId]+8   (7-47)
   with matrixId=0 . . . 5
 
The elements of the quantization matrix of size 32×32, ScalingFactor[3][matrixId][ ][ ], are derived as follows:
 
ScalingFactor[3][matrixId][ x* 4+ k ][ y* 4+ j ]=ScalingList[3][matrixId][ i ]   (7-48)
   with i=0 . . . 63, j=0 . . . 3, k=0 . . . 3, matrixId=0,3, x=ScanOrder[3][0][i][0], and y=ScanOrder[3][0][i][1]
 
ScalingFactor[3][matrixId][0][0]=scaling_list_dc_coef_minus8[1][matrixId]+8   (7-49)
   with matrixId=0, 3
 
When ChromaArrayType is equal to 3, the elements of the chroma quantization matrix of size 32×32, ScalingFactor[3][matrixId][ ][ ], with matrixId=1, 2, 4, and 5, are derived as follows:
 
ScalingFactor[3][matrixId][ x* 4+ k ][ y* 4+ j ]=ScalingList[2][matrixId][ i ]  (7-50)
   with i=0 . . . 63, j=0 . . . 3, k=0 . . . 3, x=ScanOrder[3][0][i][0], and y=ScanOrder[3][0][i][1]
 
ScalingFactor[3][matrixId][0][0]=scaling_list_dc_coef_minus8[0][matrixId]+8   (7-51)
 
2.5. Transform and Quantization Design in VVC
 
2.5.1. MTS (Multiple Transform Selection)
       

     The discrete sinusoidal transform families include the well-known discrete Fourier, cosine, sine, and the Karhunen-Loeve (underfirst-order Markov condition) transforms. Among all the members, there are 8 types of transforms based on cosine functions and 8 types of transforms based on sine functions, namely DCT-I, II, . . . , VIII, and DST-I, II, . . . , VIII, respectively. These variants of discrete cosine and sine transforms originate from the different symmetry of their corresponding symmetric-periodic sequences [22]. The transform basis functions of selected types of DCT and DST, as utilized in the proposed methods, are formulated in below Table 1. 
     
       
         
           
               
             
               
                 TABLE 1 
               
             
            
               
                   
               
               
                 Transform basis functions of DCT-II/V/VIII and  
               
               
                 DSTI/VII for N-point input. 
               
            
           
           
               
               
               
            
               
                   
                 Transform 
                   
               
               
                   
                 Type 
                 Basis function T i  (j), i, j = 0, 1, . . . , N − 1 
               
               
                   
                   
               
               
                   
                 DCT2 
                 
                   
                     
                       
                         
                           
                             T 
                             i 
                           
                           ⁡ 
                           
                             ( 
                             j 
                             ) 
                           
                         
                         = 
                         
                           
                             ω 
                             0 
                           
                           · 
                           
                             
                               2 
                               N 
                             
                           
                           · 
                           
                             cos 
                             ⁡ 
                             
                               ( 
                               
                                 
                                   π 
                                   · 
                                   i 
                                   · 
                                   
                                     ( 
                                     
                                       
                                         2 
                                         ⁢ 
                                         j 
                                       
                                       + 
                                       1 
                                     
                                     ) 
                                   
                                 
                                 
                                   2 
                                   ⁢ 
                                   N 
                                 
                               
                               ) 
                             
                           
                         
                       
                     
                   
                 
               
               
                   
                   
               
               
                   
                   
                 
                   
                     
                       
                         
                           where 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             ω 
                             0 
                           
                         
                         = 
                         
                           { 
                           
                             
                               
                                 
                                   
                                     2 
                                     N 
                                   
                                 
                               
                               
                                 
                                   i 
                                   = 
                                   0 
                                 
                               
                             
                             
                               
                                 1 
                               
                               
                                 
                                   i 
                                   ≠ 
                                   0 
                                 
                               
                             
                           
                         
                       
                     
                   
                 
               
               
                   
                   
               
               
                   
                 DCT5 
                 
                   
                     
                       
                         
                           
                             
                               T 
                               i 
                             
                             ⁡ 
                             
                               ( 
                               j 
                               ) 
                             
                           
                           = 
                           
                             
                               ω 
                               0 
                             
                             · 
                             
                               ω 
                               1 
                             
                             · 
                             
                               
                                 2 
                                 
                                   
                                     2 
                                     ⁢ 
                                     N 
                                   
                                   - 
                                   1 
                                 
                               
                             
                             · 
                             
                               cos 
                               ⁡ 
                               
                                 ( 
                                 
                                   
                                     2 
                                     ⁢ 
                                     
                                       π 
                                       · 
                                       i 
                                       · 
                                       j 
                                     
                                   
                                   
                                     
                                       2 
                                       ⁢ 
                                       N 
                                     
                                     - 
                                     1 
                                   
                                 
                                 ) 
                               
                             
                           
                         
                         , 
                       
                     
                   
                 
               
               
                   
                   
               
               
                   
                   
                 
                   
                     
                       
                         
                           where 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             ω 
                             0 
                           
                         
                         = 
                         
                           { 
                           
                             
                               
                                 
                                   
                                     
                                       2 
                                       N 
                                     
                                   
                                 
                                 
                                   
                                     i 
                                     = 
                                     0 
                                   
                                 
                               
                               
                                 
                                   1 
                                 
                                 
                                   
                                     i 
                                     ≠ 
                                     0 
                                   
                                 
                               
                             
                             , 
                             
                               
                                 ω 
                                 1 
                               
                               = 
                               
                                 { 
                                 
                                   
                                     
                                       
                                         
                                           2 
                                           N 
                                         
                                       
                                     
                                     
                                       
                                         j 
                                         = 
                                         0 
                                       
                                     
                                   
                                   
                                     
                                       1 
                                     
                                     
                                       
                                         j 
                                         ≠ 
                                         0 
                                       
                                     
                                   
                                 
                               
                             
                           
                         
                       
                     
                   
                 
               
               
                   
                   
               
               
                   
                 DCT8 
                 
                   
                     
                       
                         
                           
                             T 
                             i 
                           
                           ⁡ 
                           
                             ( 
                             j 
                             ) 
                           
                         
                         = 
                         
                           
                             
                               4 
                               
                                 
                                   2 
                                   ⁢ 
                                   N 
                                 
                                 + 
                                 1 
                               
                             
                           
                           · 
                           
                             cos 
                             ⁡ 
                             
                               ( 
                               
                                 
                                   π 
                                   · 
                                   
                                     ( 
                                     
                                       
                                         2 
                                         ⁢ 
                                         i 
                                       
                                       + 
                                       1 
                                     
                                     ) 
                                   
                                   · 
                                   
                                     ( 
                                     
                                       
                                         2 
                                         ⁢ 
                                         j 
                                       
                                       + 
                                       1 
                                     
                                     ) 
                                   
                                 
                                 
                                   
                                     4 
                                     ⁢ 
                                     N 
                                   
                                   + 
                                   2 
                                 
                               
                               ) 
                             
                           
                         
                       
                     
                   
                 
               
               
                   
                   
               
               
                   
                 DST1 
                 
                   
                     
                       
                         
                           
                             T 
                             i 
                           
                           ⁡ 
                           
                             ( 
                             j 
                             ) 
                           
                         
                         = 
                         
                           
                             
                               2 
                               
                                 N 
                                 + 
                                 1 
                               
                             
                           
                           · 
                           
                             sin 
                             ⁡ 
                             
                               ( 
                               
                                 
                                   π 
                                   · 
                                   
                                     ( 
                                     
                                       i 
                                       + 
                                       1 
                                     
                                     ) 
                                   
                                   · 
                                   
                                     ( 
                                     
                                       j 
                                       + 
                                       1 
                                     
                                     ) 
                                   
                                 
                                 
                                   N 
                                   + 
                                   1 
                                 
                               
                               ) 
                             
                           
                         
                       
                     
                   
                 
               
               
                   
                   
               
               
                   
                 DST7 
                 
                   
                     
                       
                         
                           
                             T 
                             i 
                           
                           ⁡ 
                           
                             ( 
                             j 
                             ) 
                           
                         
                         = 
                         
                           
                             
                               4 
                               
                                 
                                   2 
                                   ⁢ 
                                   N 
                                 
                                 + 
                                 1 
                               
                             
                           
                           · 
                           
                             sin 
                             ⁡ 
                             
                               ( 
                               
                                 
                                   π 
                                   · 
                                   
                                     ( 
                                     
                                       
                                         2 
                                         ⁢ 
                                         i 
                                       
                                       + 
                                       1 
                                     
                                     ) 
                                   
                                   · 
                                   
                                     ( 
                                     
                                       j 
                                       + 
                                       1 
                                     
                                     ) 
                                   
                                 
                                 
                                   
                                     2 
                                     ⁢ 
                                     N 
                                   
                                   + 
                                   1 
                                 
                               
                               ) 
                             
                           
                         
                       
                     
                   
                 
               
               
                   
                   
               
            
           
         
       
     
     For one block, either transform skip or DCT2/DST7/DCT8 may be selected. Such a method is called multiple transform selection (MTS). 
     In order to control MTS scheme, separate enabling flags are specified at SPS level for intra and inter, respectively. When MTS is enabled at SPS, a CU level flag is signalled to indicate whether MTS is applied or not. Here, MTS is applied only for luma. The MTS CU level flag is signalled when the following conditions are satisfied.
         Both width and height smaller than or equal to 32   CBF flag is equal to one       

     If MTS CU flag is equal to zero, then DCT2 is applied in both directions. However, if MTS CU flag is equal to one, then two other flags are additionally signalled to indicate the transform type for the horizontal and vertical directions, respectively. Transform and signalling mapping table as shown in the table below. When it comes to transform matrix precision, 8-bit primary transform cores are used. Therefore, all the transform cores used in HEVC are kept as the same, including 4-point DCT-2 and DST-7, 8-point, 16-point and 32-point DCT-2. Also, other transform cores including 64-point DCT-2, 4-point DCT-8, 8-point, 16-point, 32-point DST-7 and DCT-8, use 8-bit primary transform cores. 
     
       
         
           
               
             
               
                 TABLE 6 
               
             
            
               
                   
               
               
                 Transform basis functions of DCT-II/V/VIII and  
               
               
                 DSTI/VII for N-point input. 
               
            
           
           
               
               
               
               
               
            
               
                   
                 MTS_CU_ 
                 MTS_Hor_ 
                 MTS_Ver_ 
                 Infra/inter 
               
            
           
           
               
               
               
               
               
               
            
               
                   
                 flag 
                 flag 
                 flag 
                 Horizontal 
                 Vertical 
               
               
                   
                   
               
            
           
           
               
               
               
               
               
            
               
                   
                 0 
                   
                   
                 DCT2 
               
            
           
           
               
               
               
               
               
               
            
               
                   
                 1 
                 0 
                 0 
                 DST7 
                 DST7 
               
               
                   
                   
                 0 
                 1 
                 DCT8 
                 DST7 
               
               
                   
                   
                 1 
                 0 
                 DST7 
                 DCT8 
               
               
                   
                   
                 1 
                 1 
                 DCT8 
                 DCT8 
               
               
                   
                   
               
            
           
         
       
     
     As in HEVC, the residual of a block can be coded with transform skip mode. To avoid the redundancy of syntax coding, the transform skip flag is not signalled when the CU level MTS_CU_flag is not equal to zero. The block size limitation for transform skip is the same to that for MTS in JEM4, which indicate that transform skip is applicable for a CU when both block width and height are equal to or less than 32. 
     2.5.1.1. Zeroing-Out of High Frequency 
     In VTM4, large block-size transforms, up to 64×64 in size, are enabled, which is primarily useful for higher resolution video, e.g., 1080p and 4K sequences. High frequency transform coefficients are zeroed out for the transform blocks with size (width or height, or both width and height) equal to 64, so that only the lower-frequency coefficients are retained. For example, for an M×N transform block, with M as the block width and N as the block height, when M is equal to 64, only the left 32 columns of transform coefficients are kept. Similarly, when N is equal to 64, only the top 32 rows of transform coefficients are kept. When transform skip mode is used for a large block, the entire block is used without zeroing out any values. 
     To reduce the complexity of large size DST-7 and DCT-8, High frequency transform coefficients are zeroed out for the DST-7 and DCT-8 blocks with size (width or height, or both width and height) equal to 32. Only the coefficients within the 16×16 lower-frequency region are retained. 
     2.5.2. Reduced Secondary Transform 
     In JEM, secondary transform is applied between forward primary transform and quantization (at encoder) and between de-quantization and inverse primary transform (at decoder side). As shown in  FIG.  2   , 4×4 (or 8×8) secondary transform is performed depends on block size. For example, 4×4 secondary transform is applied for small blocks (i.e., min (width, height)&lt;8) and 8×8 secondary transform is applied for larger blocks (i.e., min (width, height)&gt;4) per 8×8 block. 
     For the secondary transforms, non-separable transforms are applied, therefore, it is also named as Non-Separable Secondary Transform (NSST). There are totally 35 transform sets and 3 non-separable transform matrices (kernels, each one with 16×16 matrix) per transform set are used. 
     The Reduced Secondary Transform (RST) was introduced in JVET-K0099 and 4 transform sets (instead of 35 transform sets) mapping introduced in JVET-L0133 according to intra prediction direction. In this contribution, 16×48 and 16×16 matrices are employed for 8×8 and 4×4 blocks, respectively. For notational convenience, 16×48 transform is denoted as RST8×8 and the 16×16 one as RST4×4. Such a method was recently adopted by VVC. 
       FIG.  3    shows an example of a Reduced Secondary Transform (RST). 
     Secondary forward and inverse transforms are a separate process step from that of primary transforms 
     For encoder, the primary forward transform is performed first, then followed by secondary forward transform and quantization, and CABAC bit encoding. For decoder, CABAC bit decoding and inverse quantization, then Secondary inverse transform is performed first, then followed by primary inverse transform. 
     RST applies only to intra coded TUs. 
     2.5.3. Quantization 
     In VTM4, Maximum QP was extended from 51 to 63, and the signaling of initial QP was changed accordingly. The initial value of SliceQpY is modified at the slice segment layer when a non-zero value of slice_qp_delta is coded. Specifically, the value of init_qp_minus26 is modified to be in the range of −(26+QpBdOffsetY) to +37. 
     In addition, the same HEVC scalar quantization is used with a new concept called dependent scalar quantization. Dependent scalar quantization refers to an approach in which the set of admissible reconstruction values for a transform coefficient depends on the values of the transform coefficient levels that precede the current transform coefficient level in reconstruction order. The main effect of this approach is that, in comparison to conventional independent scalar quantization as used in HEVC, the admissible reconstruction vectors are packed denser in the N-dimensional vector space (N represents the number of transform coefficients in a transform block). That means, for a given average number of admissible reconstruction vectors per N-dimensional unit volume, the average distortion between an input vector and the closest reconstruction vector is reduced. The approach of dependent scalar quantization is realized by: (a) defining two scalar quantizers with different reconstruction levels and (b) defining a process for switching between the two scalar quantizers. 
       FIG.  4    is an illustration of the two scalar quantizers used in the proposed approach of dependent quantization. 
     The two scalar quantizers used, denoted by Q0 and Q1, are illustrated in  FIG.  4   . The location of the available reconstruction levels is uniquely specified by a quantization step size Δ. The scalar quantizer used (Q0 or Q1) is not explicitly signalled in the bitstream. Instead, the quantizer used for a current transform coefficient is determined by the parities of the transform coefficient levels that precede the current transform coefficient in coding/reconstruction order. 
     As illustrated in  FIG.  5   , the switching between the two scalar quantizers (Q0 and Q1) is realized via a state machine with four states. The state can take four different values: 0, 1, 2, 3. It is uniquely determined by the parities of the transform coefficient levels preceding the current transform coefficient in coding/reconstruction order. At the start of the inverse quantization for a transform block, the state is set equal to 0. The transform coefficients are reconstructed in scanning order (i.e., in the same order they are entropy decoded). After a current transform coefficient is reconstructed, the state is updated as shown in  FIG.  5   , where k denotes the value of the transform coefficient level. 
     2.5.4. User-Defined Quantization Matrix in JVET-N0847 
     In this contribution, it is proposed to add support for signalling the default and user-defined scaling matrices on top of VTM4.0. The proposal is conforming to the bigger size range for the blocks (from 4×4 to 64×64 for luma, from 2×2 to 32×32 for chroma), rectangular TBs, dependent quantization, multiple transform selection (MTS), large transform with zeroing-out high frequency coefficients (aligned to the one-step definition procedure of scaling matrices for TBs), intra subblock partitioning (ISP), and intra block copy (IBC, also known as current picture referencing, CPR). 
     It is proposed to add syntax to support signaling of default and user-defined scaling matrices on top of VTM4.0 conforming to following:
         three modes for scaling matrices: OFF, DEFAULT, and USER_DEFINED   bigger size range for the blocks (from 4×4 to 64×64 for luma, 2×2 to 32×32 for chroma)   rectangular transform blocks (TBs)   dependent quantization   multiple transform selection (MTS)   large transforms with zeroing-out high frequency coefficients   intra sub-block partitioning (ISP)   intra block copy (IBC, also known as current picture referencing, CPR), share the same QMs as Intra coded blocks   DEFAULT scaling matrices are flat for all TB sizes, with the default value 16   Scaling matrices shall NOT be applied for
           TS for all TB sizes   secondary transform (a.k.a. RST)
 
2.5.4.1. Signaling of QM for Square Transform Sizes
 
2.5.4.1.1. Scanning Order of Elements in a Scaling Matrix
   
               

     The elements are coded in a scanning order which is the same as that used for coefficient coding, i.e., diagonal scan order. An example of the diagonal scan order is depicted in  FIGS.  6 A- 6 B . 
       FIGS.  6 A- 6 B  show examples of diagonal scan orders.  FIG.  6 A  shows scanning direction example.  FIG.  6 B  shows coordinates and scan order index for each element. 
     The corresponding specification for this order is defined as follows: 
     6.5.2 Up-Right Diagonal Scan Order Array Initialization Process 
     Input to this process is a block width blkWidth and a block size height blkHeight. 
     Output of this process is the array diagScan[sPos][sComp]. The array index sPos specify the scan position ranging from 0 to (blkWidth*blkHeight)−1. The array index sComp equal to 0 specifies the horizontal component and the array index sComp equal to 1 specifies the vertical component. Depending on the value of blkWidth and blkHeight, the array diagScan is derived as follows: 
                                                i = 0   (6-11)           x = 0               y = 0               stopLoop = FALSE               while( !stopLoop ) {                while( y &gt;= 0) {                 if( x &lt; blkWidth &amp;&amp; y &lt; blkHeight ) {                   diagScan[ i ][ 0 ] = x                  diagScan[ i ][ 1 ] = y                  i++                 }                 y− −                 x++                }                y = x                x = 0                if( i &gt;= blkWidth * blkHeight )                 stopLoop = TRUE               }                        
2.5.4.1.2. Coding of Selective Elements
 
     The DC values (i.e., element located at scanning index equal to 0, top-left of the matrix) are separately coded for following scaling matrices: 16×16, 32×32, and 64×64. 
     For TBs (N×N) of size smaller than or equal to 8×8 (N&lt;=8) 
     For TBs of size smaller than or equal to 8×8, all elements in one scaling matrix are signaled. 
     For TBs (N×N) of size greater than 8×8 (N&gt;8) 
     If the TBs have size greater than 8×8, only 64 elements in one 8×8 scaling matrix are signaled as a base scaling matrix. The 64 elements are corresponding to coordinates (m*X, m*Y) wherein m=N/8 and X, Y being [0 . . . 7]. In other words, one N×N block is split to multiple m*m non-overlapped regions, and for each region, they share the same element, and this shared element is signaled. 
     For obtaining square matrices of size greater than 8×8, the 8×8 base scaling matrix is up-sampled (by duplication of elements) to the corresponding square size (i.e. 16×16, 32×32, 64×64). 
     Taking 32×32 and 64×64 as examples, the selected positions for elements to be signaled marked with circle. Each square represents one element. 
       FIG.  7    shows an example of selected positions for QM signaling (32×32 transform size). 
       FIG.  8    shows an example of selected positions for QM signaling (64×64 transform size). 
     2.5.4.2. Derivation of QMs for Non-Square Transform Sizes 
     There is no additional signaling of QMs for non-square transform sizes. Instead, the QM for the non-square transform sizes is derived from that for square transform sizes. Examples are depicted in  FIG.  7   . 
     More specifically, when generating a scaling matrix for rectangular TBs, two cases are considered:
         1. Height of the rectangular matrix H is greater than width W, then scaling matrix Scaling Matrix for rectangular TB of size W×H is defined from the reference scaling matrix of size baseL×baseL as follows, where baseL is equal to min (log 2(H), 3):       

     
       
         
           
             
               
                 
                   
                     
                       ScalingMatrix 
                       ⁡ 
                       
                         ( 
                         
                           i 
                           , 
                           j 
                         
                         ) 
                       
                     
                     = 
                     
                       ScalingList 
                       ⁡ 
                       
                         [ 
                         
                           
                             
                               base 
                               ⁢ 
                               L 
                             
                             · 
                             
                               int 
                               ⁡ 
                               
                                 ( 
                                 
                                   j 
                                   
                                     ratio 
                                     ⁢ 
                                     H 
                                   
                                 
                                 ) 
                               
                             
                           
                           + 
                           
                             int 
                             ⁡ 
                             
                               ( 
                               
                                 
                                   i 
                                   · 
                                   
                                     ratio 
                                     ⁢ 
                                     HW 
                                   
                                 
                                 
                                   ratio 
                                   ⁢ 
                                   H 
                                 
                               
                               ) 
                             
                           
                         
                         ] 
                       
                     
                   
                   ⁢ 
                   
                     
 
                   
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   
                     
                       
                         for 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         i 
                       
                       = 
                       
                         0 
                         : 
                         
                           W 
                           - 
                           1 
                         
                       
                     
                     , 
                     
                       
 
                     
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     
                       j 
                       = 
                       
                         0 
                         : 
                         
                           H 
                           - 
                           1 
                         
                       
                     
                     , 
                     
                       
 
                     
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     and 
                   
                   ⁢ 
                   
                     
 
                   
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   
                     
                       
                         ratio 
                         ⁢ 
                         H 
                       
                       = 
                       
                         H 
                         
                           base 
                           ⁢ 
                           L 
                         
                       
                     
                     , 
                     
                       
 
                     
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     
                       
                         ratio 
                         ⁢ 
                         WH 
                       
                       = 
                       
                         
                           W 
                           H 
                         
                         . 
                       
                     
                   
                 
               
               
                 
                   ( 
                   1 
                   ) 
                 
               
             
           
         
       
         
         
           
             2. Height of the rectangular matrix H is less than width W, then scaling matrix Scaling Matrix for rectangular TB of size W×H is defined from the reference scaling matrix of size baseL×baseL as follows, where baseL is equal to min (log 2(W), 3): 
           
         
       
    
     
       
         
           
             
               
                 
                   
                     
                       ScalingMatrix 
                       ⁡ 
                       
                         ( 
                         
                           i 
                           , 
                           j 
                         
                         ) 
                       
                     
                     = 
                     
                       ScalingList 
                       ⁡ 
                       
                         [ 
                         
                           
                             
                               base 
                               ⁢ 
                               L 
                             
                             · 
                             
                               int 
                               ⁡ 
                               
                                 ( 
                                 
                                   
                                     j 
                                     + 
                                     
                                       ratio 
                                       ⁢ 
                                       WH 
                                     
                                   
                                   
                                     ratio 
                                     ⁢ 
                                     W 
                                   
                                 
                                 ) 
                               
                             
                           
                           + 
                           
                             int 
                             ⁡ 
                             
                               ( 
                               W 
                               ) 
                             
                           
                         
                         ] 
                       
                     
                   
                   ⁢ 
                   
                     
 
                   
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   
                     
                       
                         for 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         i 
                       
                       = 
                       
                         0 
                         : 
                         
                           W 
                           - 
                           1 
                         
                       
                     
                     , 
                     
                       
 
                     
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     
                       j 
                       = 
                       
                         0 
                         : 
                         
                           H 
                           - 
                           1 
                         
                       
                     
                     , 
                     
                       
 
                     
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     and 
                   
                   ⁢ 
                   
                     
 
                   
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   
                     
                       
                         ratio 
                         ⁢ 
                         W 
                       
                       = 
                       
                         W 
                         
                           base 
                           ⁢ 
                           L 
                         
                       
                     
                     , 
                     
                       
 
                     
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     
                       
                         ratio 
                         ⁢ 
                         WH 
                       
                       = 
                       
                         
                           W 
                           H 
                         
                         . 
                       
                     
                   
                 
               
               
                 
                   ( 
                   2 
                   ) 
                 
               
             
           
         
       
         
         
           
             Here int(x) is modifying value of x by truncating the fractional part. 
           
         
       
    
       FIG.  8    shows examples of QM derivation for non-square blocks from square blocks. (a) QM of 2×8 block derived from the 8×8 block, (b) QM of 8×2 block derived from that 8×8 block, 
     2.5.4.3. Signaling of QM for Transform Blocks with Zeroing-Out 
     In addition, when the zeroing-out of the high frequency coefficients for 64-point transform is applied, corresponding high frequencies of the scaling matrices are also zeroed out. That is, if the width or height of the TB is greater than or equal to 32, only left or top half of the coefficients is kept, and the remaining coefficients are assigned to zero, as shown in  FIG.  9   . For this, a check is performed when obtaining rectangular matrices according to equations (1) and (2) and corresponding elements in ScalingMatrix(i,j) are assigned to 0. 
     2.5.4.4. Syntax, Semantics for Quantization Matrix 
     The same syntax elements as that in HEVC are added to SPS and PPS. However, the signaling of scaling list data syntax is changed: 
     7.3.2.11 Scaling List Data Syntax 
                                     Descriptor                  scaling_list_data( ) {            for( sizeId = 1; sizeId &lt; 7; sizeId++ )             for( matrixId = 0; matrixId &lt; 6; matrixId ++ ) {              if( ! ( (( sizeId == 1 ) &amp;&amp; ( matrixId % 3 == 0 ) ) ∥ ((            sizeId == 6 ) &amp;&amp; ( matrixId % 3 != 0 ) )) ) {               scaling_list_pred_mode_flag[ sizeId ][ matrixId ]   u(1)           if( !scaling_list_pred_mode_flag[ sizeId ][ matrixId ])                scaling_list_pred_matrix_id_delta[ sizeId ][ matrixId ]   ue(v)           else {                nextCoef = 8                coefNum = Min( 64, ( 1 &lt;&lt; ( sizeId &lt;&lt; 1 ) ) )                if( sizeId &gt; 3 ) {                 scaling_list_dc_coef_minus8[ sizeId - 4 ][ matrixId ]   se(v)             nextCoef =           scaling_list_dc_coef_minus8[ sizeId - 4 ][ matrixId ] + 8                }                for( i = 0; i &lt; coef Num; i++ ) {                  x = DiagScanOrder[ 3 ][ 3 ][ i ][ 0 ]                  y = DiagScanOrder[ 3 ][ 3 ][ i ][ 1 ]                  if ( !(sizeId==6 &amp;&amp;x&gt;=4 &amp;&amp; y&gt;=4) ) {                  scaling_list_delta_coef   se(v)              nextCoef = ( nextCoef + scaling_list_delta_coef +                   256) % 256                  ScalingList[ sizeId ][ matrixId ][ i ] = nextCoef                  }                }               }              }             }            }           }                    
7.4.3.11 Scaling List Data Semantics
 
 [sizeId][matrixId] equal to 0 specifies that the values of the scaling list are the same as the values of a reference scaling list. The reference scaling list is specified by scaling_list_pred_matrix_id_delta[sizeId][matrixId]. scaling_list_pred_mode_flag[sizeId][matrixId] equal to 1 specifies that the values of the scaling list are explicitly signalled.
 
 [sizeId][matrixId] specifies the reference scaling list used to derive ScalingList[sizeId][matrixId], the derivation of ScalingList[sizeId][matrixId] is bad on scaling_list_pred_matrix_id_delta[sizeId][matrixId] as follows:
         If scaling_list_pred_matrix_id_delta[sizeId][matrixId] is equal to 0, the scaling list is inferred from the default scaling list ScalingList[ sizeId][matrixId][i] as specified in Table 7-15, Table 7-16, Table 7-17, Table 7-18 for i=0 . . . Min(63, (1&lt;&lt;(sizeId&lt;&lt;1))−1).   Otherwise, the scaling list is inferred from the reference scaling list as follows:
           For sizeId=1 . . . 6,
 
refMatrixId=matrixId−scaling_list_pred_matrix_id_delta[sizeId][matrixId]*(sizeId==6?3:1)  (7-XX)
 
If sizeId is equal to 1, the value of refMatrixId shall not be equal to 0 or 3. Otherwise, if sizeId is less than or equal to 5, the value of scaling_list_pred_matrix_id_delta[sizeId][matrixId] shall be in the range of 0 to matrixId, inclusive. Otherwise (sizeId is equal to 6), the value of scaling_list_pred_matrix_id_delta[sizeId][matrixId] shall be in the range of 0 to matrixId/3, inclusive.
   
               

     
       
         
           
               
             
               
                 TABLE 7-13 
               
             
            
               
                   
               
               
                 Specification of sizeId 
               
            
           
           
               
               
               
            
               
                   
                 Size of quantization 
                   
               
               
                   
                 matrix 
                 sizeId 
               
               
                   
                   
               
               
                   
                 1 × 1 
                 0 
               
               
                   
                 2 × 2 
                 1 
               
               
                   
                 4 × 4 
                 2 
               
               
                   
                 8 × 8 
                 3 
               
               
                   
                 16 × 16 
                 4 
               
               
                   
                 32 × 32 
                 5 
               
               
                   
                 64 × 64 
                 6 
               
               
                   
                   
               
            
           
         
       
     
                     TABLE 7-14                  Specification of matrixId according to sizeId,       prediction mode and colour component                                     cIdx                   (Colour           sizeId   CuPredMode   component)   matrixId               2, 3 ,4, 5, 6   MODE_INTRA   0 (Y)   0       1, 2, 3, 4, 5   MODE_INTRA   1 (Cb)   1       1, 2, 3, 4, 5   MODE_INTRA   2 (Cr)   2       2, 3, 4, 5, 6   MODE_INTER   0 (Y)   3       1, 2, 3, 4, 5   MODE_INTER   1 (Cb)   4       1, 2, 3, 4, 5   MODE_INTER   2 (Cr)   5       2, 3, 4, 5, 6   MODE_IBC   0 (Y)   0       1, 2, 3, 4, 5   MODE_IBC   1 (Cb)   1       1, 2, 3, 4, 5   MODE_IBC   2 (Cr)   2                      [sizeId][matrixId] plus 8 specifies the value of the variable ScalingFactor[411 matrixId][0][0] for the scaling list for the 16×16 size when sizeId is equal to 4 and specifies the value of ScalingFactor[5][matrixId][0][0] for the scaling list for the 32×32 size when sizeId is equal to 5, and specifies the value of ScalingFactor[611 matrixId][0][0] for the scaling list for the 64×64 size when sizeId is equal to 6. The value of scaling_list_dc_coef_minus8[ sizeId][matrixId] shall be in the range of −7 to 247, inclusive.
 
When scaling_list_pred_mode_flag[sizeId][matrixId] is equal to 0, scaling_list_pred_matrix_id_delta[sizeId][matrixId] is equal to 0 and sizeId is greater than 3, the value of scaling_list_dc_coef_minus8[ sizeId][matrixId] is inferred to be equal to 8.
 
When scaling_list_pred_matrix_id_delta[sizeId][matrixId] is not equal to 0 and sizeId is greater than 3, the value of scaling_list_dc_coef_minus8[sizeId][matrixId] is inferred to be equal to scaling_list_dc_coef_minus8[sizeId][refMatrixId], where the value of refMatrixId is given by Equation 7-XX.
 
  specifies the difference between the current matrix coefficient ScalingList[sizeId][matrixId][i] and the previous matrix coefficient ScalingList[sizeId][matrixId][i−1], when scaling_list_pred_mode_flag[sizeId][matrixId] is equal to 1. The value of scaling_list_delta_coef shall be in the range of −128 to 127, inclusive. The value of ScalingList[sizeId][matrixId][i] shall be greater than 0. When scaling_list_pred_mode_flag[sizeId][matrixId] is equal to 1 and scaling_list_delta_coef is not present, the value of ScalingList[ sizeId][matrixId][i] is inferred to be 0.
 
     
       
         
           
               
             
               
                 TABLE 7-15 
               
               
                   
               
               
                 Specification of default values of  
               
               
                 ScalingList[ 1 ][matrixId][ i ]with i = 0..3 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
            
               
                 i 
                 0 
                 1 
                 2 
                 3 
               
               
                 ScalingList[ 1 ] [1,2,4,5] 
                 1 
                 1 
                 1 
                 1 
               
               
                 [ i ] 
                 6 
                 6 
                 6 
                 6 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 7-16 
               
             
            
               
                   
               
               
                 Specification of default values of ScalingList[1][matrixId][i] with i = 0 . . . 15 
               
            
           
           
               
               
            
               
                   
                 i 
               
            
           
           
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
            
               
                   
                 0 
                 1 
                 2 
                 3 
                 4 
                 5 
                 6 
                 7 
                 8 
                 9 
                 10 
                 111 
                 12 
                 13 
                 14 
                 15 
               
               
                   
               
               
                 ScalingList[2][0 . . . 5][i] 
                 16 
                 16 
                 16 
                 16 
                 16 
                 16 
                 16 
                 16 
                 16 
                 16 
                 16 
                 16 
                 16 
                 16 
                 16 
                 16 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 7-17 
               
               
                   
               
               
                 Specification of default values of ScalingList[3 . . . 6][matrixId][i] with i = 0 . . . 63 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
            
               
                   
                 i 
               
            
           
           
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
            
               
                   
                 0 
                 1 
                 2 
                 3 
                 4 
                 5 
                 6 
                 7 
                 8 
                 9 
                 10 
                 11 
                 12 
                 13 
                 14 
                 15 
               
               
                   
               
               
                 ScalingList[3 . . . 5][0 . . . 5][i] 
                 16 
                 16 
                 16 
                 16 
                 16 
                 16 
                 16 
                 16 
                 16 
                 16 
                 16 
                 16 
                 16 
                 16 
                 16 
                 16 
               
               
                   
               
            
           
           
               
               
            
               
                   
                 i - 16 
               
            
           
           
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
            
               
                   
                 0 
                 1 
                 2 
                 3 
                 4 
                 5 
                 6 
                 7 
                 8 
                 9 
                 10 
                 11 
                 12 
                 13 
                 14 
                 15 
               
               
                   
               
               
                 ScalingList[3 . . . 5][0 . . . 5][i] 
                 16 
                 16 
                 16 
                 16 
                 16 
                 16 
                 16 
                 16 
                 16 
                 16 
                 16 
                 16 
                 16 
                 16 
                 16 
                 16 
               
               
                   
               
            
           
           
               
               
            
               
                   
                 i - 32 
               
            
           
           
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
            
               
                   
                 0 
                 1 
                 2 
                 3 
                 4 
                 5 
                 6 
                 7 
                 8 
                 9 
                 10 
                 11 
                 12 
                 13 
                 14 
                 15 
               
               
                   
               
               
                 ScalingList[3 . . . 5][0 . . . 5][i] 
                 16 
                 16 
                 16 
                 16 
                 16 
                 16 
                 16 
                 16 
                 16 
                 16 
                 16 
                 16 
                 16 
                 16 
                 16 
                 16 
               
               
                   
               
            
           
           
               
               
            
               
                   
                 i - 48 
               
            
           
           
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
            
               
                   
                 0 
                 1 
                 2 
                 3 
                 4 
                 5 
                 6 
                 7 
                 8 
                 9 
                 10 
                 11 
                 12 
                 13 
                 14 
                 15 
               
               
                   
               
               
                 ScalingList[3 . . . 5][0 . . . 5][i] 
                 16 
                 16 
                 16 
                 16 
                 16 
                 16 
                 16 
                 16 
                 16 
                 16 
                 16 
                 16 
                 16 
                 16 
                 16 
                 16 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 7-18 
               
               
                   
               
               
                 Specification of default values of ScalingLst[6][matrixId][i]with i = 0 . . . 63 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
            
               
                   
                 i 
               
            
           
           
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
            
               
                   
                 0 
                 1 
                 2 
                 3 
                 4 
                 5 
                 6 
                 7 
                 8 
                 9 
                 10 
                 11 
                 12 
                 13 
                 14 
                 15 
               
               
                   
               
               
                 ScalingList[6][0, 3][i] 
                 16 
                 16 
                 16 
                 16 
                 16 
                 16 
                 16 
                 16 
                 16 
                 16 
                 16 
                 16 
                 16 
                 16 
                 16 
                 16 
               
               
                   
               
            
           
           
               
               
            
               
                   
                 i - 16 
               
            
           
           
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
            
               
                   
                 0 
                 1 
                 2 
                 3 
                 4 
                 5 
                 6 
                 7 
                 8 
                 9 
                 10 
                 11 
                 12 
                 13 
                 14 
                 15 
               
               
                   
               
               
                 ScalingList[6][0, 3][i] 
                 16 
                 16 
                 16 
                 16 
                 16 
                 16 
                 16 
                 16 
                 16 
                 16 
                 16 
                 16 
                 16 
                 16 
                 16 
                 16 
               
               
                   
               
            
           
           
               
               
            
               
                   
                 i - 32 
               
            
           
           
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
            
               
                   
                 0 
                 1 
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                 ScalingList[6][0, 3][i] 
                 16 
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                 16 
                 16 
                 16 
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                 i - 48 
               
            
           
           
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
            
               
                   
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                 ScalingList[6][0, 3][i] 
                 16 
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                 16 
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     The five-dimensional array ScalingFactor[sizeId][sizeId][matrixId][x][y], with x, y=0 . . . (1&lt;&lt;sizeId)−1, specifies the array of scaling factors according to the variables sizeId specified in Table 7-13 and matrixId specified in Table 7-14. 
     The elements of the quantization matrix of size 2×2, ScalingFactor[1][matrixId][ ][ ], are derived as follows:
 
ScalingFactor[1][1][matrixId][ x ][ y ]=ScalingList[1][matrixId][ i ]  (7-XX)
 
     with i=0 . . . 3, matrixId=1, 2, 4, 5, x=DiagScanOrder[1][1][i][0], and y=DiagScanOrder[1][1][i][1] 
     The elements of the quantization matrix of size 4×4, ScalingFactor[2][matrixId][ ][ ], are derived as follows:
 
ScalingFactor[2][2][matrixId][ x ][ y ]=ScalingList[2][matrixId][ i ]  (7-XX)
         with i=0 . . . 15, matrixId=0 . . . 5, x=DiagScanOrder[2][2][i][0], and y=DiagScanOrder[2][2][i][1]
 
The elements of the quantization matrix of size 8×8, ScalingFactor[3][matrixId][ ][ ], are derived as follows:
 
ScalingFactor[3][3][matrixId][ x ][ y ]=ScalingList[3][matrixId][ i ]  (7-XX)
   with i=0 . . . 63, matrixId=0 . . . 5, x=DiagScanOrder[3][3][i][0], and y=DiagScanOrder[3][3][i][1]
 
The elements of the quantization matrix of size 16×16, ScalingFactor[4][matrixId][ ][ ], are derived as follows:
 
ScalingFactor[4][4][matrixId][ x* 2+ k ][ y* 2+ j ]=ScalingList[4][matrixId][ i ]  (7-XX)
   with i=0 . . . 63, j=0 . . . 1, k=0 . . . 1, matrixId=0 . . . 5, x=DiagScanOrder[3][3][i][ 0 ], and y=DiagScanOrder[3][3][i][ 1 ]
 
ScalingFactor[4][4][matrixId][ 0 ][ 0 ]=scaling_list_dc_coef_minus8[0][matrixId]+8   (7-XX)
   with matrixId=0 . . . 5
 
The elements of the quantization matrix of size 32×32, ScalingFactor[5][matrixId][ ][ ], are derived as follows:
 
ScalingFactor[5][5][matrixId][ x* 4+ k ][ y* 4+ j ]=ScalingList[5][matrixId][ i ]  (7-XX)
   with i=0 . . . 63, j=0 . . . 3, k=0 . . . 3, matrixId=0 . . . 5, x=DiagScanOrder[3][3][i][0], and y=DiagScanOrder[3][3][i][1]
 
ScalingFactor[5][5][matrixId][0][0]=scaling_list_dc_coef_minus8[1][matrixId]+8   (7-XX)
   with matrixId=0 . . . 5
 
The elements of the quantization matrix of size 64×64, ScalingFactor[6][matrixId][ ][ ], are derived as follows:
 
ScalingFactor[6][6][matrixId][ x* 8+ k ][ y* 8+ j ]=ScalingList[6][matrixId][ i ]  (7-XX)
   with i=0 . . . 63, j=0 . . . 7, k=0 . . . 7, matrixId=0, 3, x=DiagScanOrder[3][3][i][0], and y=DiagScanOrder[3][3][i][1]
 
ScalingFactor[6][6][matrixId][0][0]=scaling_list_dc_coef_minus8[2][matrixId]+8   (7-XX)
   with matrixId=0, 3
 
When ChromaArrayType is equal to 3, the elements of the chroma quantization matrix of size 64×64, ScalingFactor[6][6][matrixId][ ][ ], with matrixId=1, 2, 4 and 5 are derived as follows:
 
ScalingFactor[6][6][matrixId][ x* 8+ k ][ y* 8+ j ]=ScalingList[5][matrixId][ i ]  (7-XX)
   with i=0 . . . 63, j=0 . . . 7, k=0 . . . 7, x=DiagScanOrder[3][3][i][0], and y=DiagScanOrder[3][3][i][1]
 
ScalingFactor[6][6][matrixId][0][0]=scaling_list_dc_coef_minus8[1][matrixId]+8   (7-XX)
 
 
 
   
 
                     
 
     .  
 
                 ,              
                                                                                                                       

                     TABLE 7-19                  Specification of sizeIdW and sizeIdH                         Size of quantization               matrix   sizeIdW   sizeIdH               1   0   0       2   1   1       4   2   2       8   3   3       16    4   4       32    5   5       64    6   6                    
2.6 Quantized Residual Block Differential Pulse-Code Modulation
 
     In JVET-M0413, a quantized residual block differential pulse-code modulation (QR-BDPCM) is proposed to code screen contents efficiently. 
     The prediction directions used in QR-BDPCM can be vertical and horizontal prediction modes. The intra prediction is done on the entire block by sample copying in prediction direction (horizontal or vertical prediction) similar to intra prediction. The residual is quantized and the delta between the quantized residual and its predictor (horizontal or vertical) quantized value is coded. This can be described by the following: Fora block of size M (rows)×N (cols), let r i,j , 0≤i≤M−1, 0≤j≤N−1 be the prediction residual after performing intra prediction horizontally (copying left neighbor pixel value across the predicted block line by line) or vertically (copying top neighbor line to each line in the predicted block) using unfiltered samples from above or left block boundary samples. Let Q(r r,j ), 0≤i≤M−1, 0≤j≤N−1 denote the quantized version of the residual r i,j , where residual is difference between original block and the predicted block values. Then the block DPCM is applied to the quantized residual samples, resulting in modified M×N array {tilde over (R)} with elements {tilde over (r)} i,j . When vertical BDPCM is signalled: 
     
       
         
           
             
               
                 
                   
                     
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     For horizontal prediction, similar rules apply, and the residual quantized samples are obtained by 
     
       
         
           
             
               
                 
                   
                     
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     The residual quantized samples {tilde over (r)} i,j  are sent to the decoder. 
     On the decoder side, the above calculations are reversed to produce Q(r i,j ), 0≤i≤M−1, 0≤j≤N−1. For vertical prediction case,
 
 Q ( r   i,j )=Σ k=0   i   {tilde over (r)}   k,j ,0≤ i ≤( M −1),0≤ j ≤( N −1)  (2-7-3)
 
For horizontal case,
 
 Q ( r   i,j )=Σ k=0   j   {tilde over (r)}   i,k ,0≤ i ≤( M− 1),0≤ j ≤( N− 1)  (2-7-4)
 
     The inverse quantized residuals, Q −1  (Q(r i,j )), are added to the intra block prediction values to produce the reconstructed sample values. 
     The main benefit of this scheme is that the inverse DPCM can be done on the fly during coefficient parsing simply adding the predictor as the coefficients are parsed or it can be performed after parsing. 
     The draft text changes of QR-BDPCM are shown as follows. 
     7.3.6.5 Coding Unit Syntax 
                                     Descriptor                  coding_unit( x0, y0, cbWidth, cbHeight, treeType ) {            if( tile_group_type != I || sps_ibc_enabled_flag ) {             if( treeType != DUAL_TREE_CHROMA )              cu_skip_flag[ x0 ][ y0 ]   ae(v)         if( cu_skip_flag[ x0 ][ y0 ] == 0 &amp;&amp; tile_group_type != I )              pred_mode_flag   ae(v)         if( ( ( tile_group_type == I &amp;&amp; cu_skip_flag[ x0 ][ y0 ]== 0 ) ||              ( tile_group_type != I &amp;&amp; CuPredMode[ x0 ][ y0 ] !=            MODE_INTRA ) ) &amp;&amp;              sps_ibc_enabled_flag )              pred_mode_ibc_flag   ae(v)        }            if( CuPredMode[ x0 ][ y0 ]== MODE_INTRA ) {             if( pred_mode_flag == MODE_INTRA &amp;&amp; ( cIdx == 0 ) &amp;&amp;              ( cbWidth +21= 32) &amp;&amp; ( CbHeight &lt;= 32 )) {              bdpcm_flag[ x0 ][ y0 ]   ae(v)          if( bdpcm_flag[ x0 ][ y0 ]) {               bdpcm_dir_flag[ x0 ][ y0 ]   ae(v)          }              else {             if( sps_pcm_enabled_flag &amp;&amp;              cbWidth &gt;= MinIpcmCbSizeY &amp;&amp; cbWidth &lt;=               MaxIpcmCbSizeY &amp;&amp; cbHeight &gt;= MinIpcmCbSizeY               &amp;&amp; cbHeight &lt;= MaxIpcmCbSizeY )              pcm_flag[ x0 ][y0 ]   ae(v)         if( pcm_flag[ x0 ][ y0 ]) {              while( !byte_aligned( ) )               pcm_alignment_zero_bit   f(1)          pcm_sample( cbWidth, cbHeight, treeType)             } else {              if( treeType == SINGLE_TREE || treeType ==            DUAL_TREE_LUMA ) {               if( ( y0 % CtbSizeY ) &gt; 0 )                intraluma_ref_idx[ x0 ][ y0 ]   ae(v)           if (intra_luma_ref_idx[ x0 ][ y0 ] == 0 &amp;&amp;                ( cbWidth &lt;= MaxTbSizeY || cbHeight &lt;=                 MaxTbSizeY ) &amp;&amp;                ( cbWidth * cbHeight &gt; MinTbSizeY * MinTbSizeY ))                intra_subpartitions_mode_flag[ x0 ][ y0 ]   ae(v)           if( intra_subpartitions_mode_flag[ x0 ][ y0 ] == 1 &amp;&amp;                cbWidth &lt;= MaxTbSizeY &amp;&amp; cbHeight &lt;=                 MaxTbSizeY )                intra_subpartitions_split flag[ x0 ][ y0 ]   ae(v)           if( intra_luma_ref_idx[ x0 ][ y0 ] == 0 &amp;&amp;                intra_subpartitions_mode_flag[ x0 ][ y0 ] == 0 )                intraluma_mpm_flag[ x0 ][ y0 ]   ae(v)           if( intra_luma_mpm_flag[ x0 ][ y0 ])                intraluma_mpm_idx[ x0 ][ y0 ]   ae(v)           else                intraluma_mpm_remainder[ x0 ][ y0 ]   ae(v)          }              }              if( treeType == SINGLE_TREE || treeType ==           DUAL_TREE_CHROMA)               intra_chroma_pred_mode[ x0 ][ y0 ]   ae(v)         }            }else if( treeType != DUAL_TREE_CHROMA )            {/* MODE_INTER or MODE_IBC */           ...           }                    
bdpcm_flag[x0][y0] equal to 1 specifies that a bdpcm_dir_flag is present in the coding unit including the luma coding block at the location (x0, y0)
 
bdpcm_dir_flag[x0][y0] equal to 0 specifies that the prediction direction to be used in a bdpcm block is horizontal, otherwise it is vertical.
 
     3. Example Technical Problems Solved by Embodiments and Techniques 
     The current VVC design has the following problems in terms of quantization matrices:
         1. For QR-BDPCM and BDPCM-blocks, transform is not applied. Therefore, applying scaling matrix to such blocks in a similar way as other transform-applied blocks is not optimal.   2. IBC and intra coding modes share the same scaling matrices. However, IBC is more likely an inter coding tool. Such a design seems to be not reasonable.   3. For larger blocks with zeroing-out, several elements are signaled, but reset to zero in the decoding process which wastes bits.   4. In some frameworks, quantization is performed as always applying quantization matrices. Thus, quantization matrices for small block may lead to frequent matrices changed.       

     4. A Listing of Embodiments and Techniques 
     The detailed inventions below should be considered as examples to explain general concepts. These inventions should not be interpreted in a narrow way. Furthermore, these inventions can be combined in any manner.
         1. When the transform skip (TS) flag is not signaled in the bit stream, how to set the value of this flag may depend on coded mode information.
           a. In one example, for BDPCM/QR-BDPCM coded blocks, the TS flag is inferred to be 1.   b. In one example, for non-BDPCM/QR-BDPCM coded blocks, the TS flag is inferred to be 0.   
           2. It is proposed that scaling matrix may be applied on BDPCM/QR-BDPCM coded blocks.
           a. Alternatively, it is proposed to disallow scaling matrix for BDPCM/QR-BDPCM coded blocks.   b. In one example, how to select scaling matrix for BDPCM/QR-BDPCM coded blocks may be performed in the same way as transform skip coded blocks.   c. In one example, how to select the scaling matrix for a BDPCM/QR-BDPCM coded block may depend on whether one or multiple transforms are applied to the block.
               i. In one example, if one or multiple transforms are applied to a BDPCM/QR-BDPCM coded block, the scaling matrix may be allowed.   ii. In one example, if one or multiple transforms are applied to a BDPCM/QR-BDPCM coded block, how to select the scaling matrix for BDPCM/QR-BDPCM coded blocks may be performed in the same way as an intra coded block.   
               
           3. Whether to and/or how to filter samples/edges between two adjacent blocks in in-loop filters (de-blocking filters) and/or other post-reconstruction filters may depend on whether any or both two adjacent blocks are coded with transform skip (TS) mode.
           a. Whether to and/or how to filter samples/edges between two adjacent blocks in in-loop filters (de-blocking filters) and/or other post-reconstruction filters may depend on whether two adjacent blocks coded with TS, BDPCM, QR-BDPCM, palette mode.   b. In one example, the derivation of boundary filtering strength may depend on the TS mode flag(s) of one or both of the two adjacent blocks.   c. In one example, for the samples located at the TS-coded blocks, deblocking filter/Sample adaptive Offset/adaptive loop filter/other kinds of in-loop filters/other post-reconstruction filters may be disabled.
               i. In one example, if two adjacent blocks are both coded with transform skipped mode, there is no need to filter such an edge between these two.   ii. In one example, if one of two adjacent blocks is coded with transform skipped mode and the other one is not, there is no need to filter samples located at the TS-coded block.   
               d. Alternatively, for the samples located at the TS-coded blocks, a different filter (e.g., smoother filter) may be allowed.   e. During the process of in-loop filters (e.g., de-blocking filters) and/or other post-reconstruction filters (e.g., bilateral filter, diffusion filter), a block coded with PCM/BDPCM/QR-BDPCM and/or other kinds of modes which transform are not applied on, may be treated in the same way as coded with TS mode, such as mentioned above.   
           4. Blocks coded with IBC and inter coding modes may share the same scaling matrices.   5. Scaling matrix selection may depend on the transform matrix type.
           a. In one example, selection of scaling matrices may depend on whether the block uses a default transform such as DCT2 or not.   b. In one example, scaling matrices may be signaled for multiple transform matrix types separately.   
           6. Scaling matrix selection may depend on the motion information of a block.
           a. In one example, scaling matrix selection may depend on whether the block is coded with a sub-block coding mode (such as affine mode) or not.   b. In one example, scaling matrices may be signaled for affine and non-affine modes separately.   c. In one example, scaling matrix selection may depend on the block is coded with affine intra prediction mode or not.   
           7. Instead of disabling scaling matrices for secondary transform coded blocks, it is proposed to enable scaling matrices. Suppose the transform block size is denoted by K×L, and secondary transform is applied to the top-left M×N block.
           a. Scaling matrices may be signaled in tile group header/slice header/PPS/VPS/SPS for secondary transform or/and reduced secondary transform or/and rotation transform.   b. In one example, scaling matrices may be selected according to whether secondary transform is applied or not.
               i. In one example, elements of a scaling matrix for the top-left M×N block may be signaled separately for the secondary transform is applied or not   
               c. Alternatively, furthermore, scaling matrices may be only applicable to regions which secondary transform is not applied.   d. In one example, the remaining part except the top-left M×N region could still apply scaling matrices.   e. Alternatively, scaling matrices may be only applicable to regions where secondary transform is applied.   
           8. Instead of deriving scaling matrices for non-square blocks from square blocks, it is proposed to signal scaling matrices for non-square blocks.
           a. In one example, scaling matrices for non-square blocks may be coded with prediction from square blocks may be enabled.   
           9. It is proposed to disable usage of scaling matrix for some positions and enable usage of scaling matrix for remaining positions within a block.
           a. For example, fora block contains more than M*N positions, only the top-left M*N region may use scaling matrices.   b. For example, fora block contains more than M*N positions, only the top M*N positions may use scaling matrices.   c. For example, for a block contains more than M*N positions, only the left M*N positions may use scaling matrices.   
           10. How many elements in a scaling matrix to be signaled may be dependent on whether zeroing-out is applied.
           a. In one example, for the 64×64 transform, suppose only the top-left M×N transform coefficients are kept and all the remaining coefficients are zeroing-out. Then the number of elements to be signaled may be derived as M/8*N/8.   
           11. For transforms with zeroing-out, it is proposed to disable signaling of elements in a scaling matrix located at the zeroing-out region. Suppose for the K×L transform, only the top-left M×N transform coefficients are kept and all the remaining coefficients are zeroing-out.
           a. In one example, K=L=64, and M=N=32.   b. In one example, signaling of the elements in a scaling matrix corresponding to locations outside of the top-left M×N region are skipped.   
             FIG.  10    shows an example of only selected elements in the dashed region (e.g., the M×N region) are signaled.
           c. In one example, the sub-sampling ratio for selecting elements in a scaling matrix may be determined by K and/or L.
               i. For example, the transform block is split to multiple sub-regions and each sub-region size is Uw*Uh. One element located within each sub-region of the top-left M×N region may be signaled.   ii. Alternatively, furthermore, how many elements to be coded may depend on the M and/or N.
                   1) In one example, how many elements to be coded for such K×L transforms with zeroing-out is different from that for a M×N transform block without zeroing-out.   
                   
               d. In one example, the sub-sampling ratio for selecting elements in a scaling matrix may be determined by M and/or N instead of K and L.
               i. For example, the M×N region is split to multiple sub-regions. One element within each (M/Uw, N/Uh) region may be signaled.   ii. Alternatively, furthermore, how many elements to be coded for such K×L transforms with zeroing-out is the same as that fora M×N transform block without zeroing-out.   
               e. In one example, K=L=64, M=N=32, Uw=Uh=8.   
           12. It is proposed to use only one quantization matrix for certain block sizes, such as for small size blocks.
           a. In one example, all blocks smaller than WxH, regardless of block type, may not be allowed to use two or more quantization matrices.   b. In one example, all blocks with width smaller than a threshold, may not be allowed to use two or more quantization matrices.   c. In one example, all blocks with height smaller than a threshold, may not be allowed to use two or more quantization matrices.   d. In one example, quantization matrix may be not applied for small size blocks.   
           13. The above bullets may be applicable to other coding methods that do not apply transform (or do not apply Identity transform).
           a. In one example, the above bullets may be applicable to palette mode coded blocks by replacing TS/BDPCM/QR-BDPCM′ by ‘Palette’.   
               

     5. Embodiments 
     5.1. Embodiment #1 on Deblocking Filter 
     The changes on top of VVC working draft version 5 are highlighted in bold italicized text. One or multiple of highlighted conditions may be added. 
     8.8.2 Deblocking Filter Process 
     8.8.2.1 General 
     Inputs to this process are the reconstructed picture prior to deblocking, i.e., the array recPicture L  and, when ChromaArrayType is not equal to 0, the arrays recPicture Cb  and recPicture Cr . 
     Outputs of this process are the modified reconstructed picture after deblocking, i.e., the array recPicture L  and, when ChromaArrayType is not equal to 0, the arrays recPicture Cb  and recPicture Cr . 
     The vertical edges in a picture are filtered first. Then the horizontal edges in a picture are filtered with samples modified by the vertical edge filtering process as input. The vertical and horizontal edges in the CTBs of each CTU are processed separately on a coding unit basis. The vertical edges of the coding blocks in a coding unit are filtered starting with the edge on the left-hand side of the coding blocks proceeding through the edges towards the right-hand side of the coding blocks in their geometrical order. The horizontal edges of the coding blocks in a coding unit are filtered starting with the edge on the top of the coding blocks proceeding through the edges towards the bottom of the coding blocks in their geometrical order. 
     NOTE—Although the filtering process is specified on a picture basis in this Specification, the filtering process can be implemented on a coding unit basis with an equivalent result, provided the decoder properly accounts for the processing dependency order so as to produce the same output values. 
     The deblocking filter process is applied to all coding subblock edges and transform block edges of a picture, except the following types of edges:
         Edges that are at the boundary of the picture,   Edges that coincide with the virtual boundaries of the picture when pps_loop_filter_across_virtual_boundaries_disabled_flag is equal to 1,   Edges that coincide with brick boundaries when loop_filter_across_bricks_enabled_flag is equal to 0,   Edges that coincide with upper or left boundaries of slices with slice_loop_filter_across_slices_enabled_flag equal to 0 or slice_deblocking_filter_disabled_flag equal to 1,   Edges within slices with slice_deblocking_filter_disabled_flag equal to 1,   Edges that do not correspond to 8×8 sample grid boundaries of the considered component,   Edges within chroma components for which both sides of the edge use inter prediction,   Edges of chroma transform blocks that are not edges of the associated transform unit.   Edges across the luma transform blocks of a coding unit that has an IntraSubPartitionsSplit value not equal to ISP_NO_SPLIT.                                                       

     5.2. Embodiment #2 on Scaling Matrix 
     This section provides an example of bullet 11.d in section 4. 
     The changes on top of JVET-N0847 are highlighted in   and removed text are marked with  . One or multiple of highlighted conditions may be added. 
     The elements of the quantization matrix of size 64×64, ScalingFactor[6][matrixId][ ][ ], are derived as follows:
 
ScalingFactor[6][6][matrixId][ x*       +k ][ y*       +j ]=ScalingList[6][matrixId][ i ]   (7-XX)
         with i=0 . . . 63, j=0 . . . 3 , k=0 . . . 3  matrixId=0, 3, x=DiagScanOrder[3][3][i][0], and y=DiagScanOrder[3][3][i][1]
 
 
 
       
 
 
 
ScalingFactor[6][6][matrixId][0][0]=scaling_list_dc_coef_minus8[2][matrixId]+8   (7-XX)
   with matrixId=0, 3
 
 
 
A quantization matrix with rectangular size shall be zeroed out for the samples satisfying to the following conditions
               the decoded tu is not coded by default transform mode, (1&lt;&lt;sizeIdW)==32 and x&gt;16   the decoded tu is not coded by default transform mode, (1&lt;&lt;sizeIdH)==32 and y&gt;16       

     5.3. Embodiment #3 on Scaling Matrix 
     This section provides an example of bullets 9, 11.c in section 4. 
     The changes on top of JVET-N0847 are highlighted in   and removed text are marked with  . One or multiple of highlighted conditions may be added. 
     7.3.2.11 Scaling List Data Syntax 
                                     Descriptor                  scaling_list_data( ) {            for( sizeId = 1; sizeId &lt; 7; sizeId++ )             for( matrixId = 0; matrixId &lt; 6; matrixId ++ ) {              if( ! ( (( sizeId == 1) &amp;&amp; ( matrixId % 3 == 0 ) ) ∥ (( sizeId ==            6 ) &amp;&amp; (matrixId % 3 != 0 ) )) ) {               scaling_list_pred_mode_flag[ sizeId ][ matrixId ]   u(1)           if( !scaling_list_pred_mode_flag[ sizeId ][ matrixId ] )                scaling_list_pred_matrix_id_delta[ sizeId ][ matrixId ]   ue(v)           else {                nextCoef = 8                coefNum =    Min( 64, ( 1 &lt;&lt; ( sizeId &lt;&lt;                 1 ) ) ) )                if( sizeId &gt; 3 ) {                 scaling_list_dc_coef_minus8[ sizeId - 4 ][ matrixId ]   se(v)             nextCoef =           scaling_list_dc_coef_minus8[ sizeId - 4 ][ matrixId ] + 8                }                for( i =0; i &lt; coefNum; i++ ) {                 x = DiagScanOrder[ 3 ][ 3 ][ i ][ 0 ]                 y = DiagScanOrder[ 3 ][ 3 ][ i ][ 1 ]                 if ( !(sizeId==6 &amp;&amp; x&gt;=4 &amp;&amp; y&gt;=4) ) {                 scaling_list_delta_coef   se(v)             nextCoef = ( nextCoef + scaling_list_delta_coef +                  256 ) % 256                 Scaling List[ sizeId ][ matrixId ][ i ] = nextCoef                 }                }               }              }             }            }           }                    
The elements of the quantization matrix of size 64×64, ScalingFactor[6][matrixId][ ][ ], are derived as follows:
 
ScalingFactor[6][6][matrixId][ x* 8+ k ][ y* 8+ j ]=ScalingList[6][matrixId][ i ]   (7-XX)
         with i=0 . . .    , j=0 . . . 7, k=0 . . . 7, matrixId=0, 3, x=DiagScanOrder[3][3][i][0], and y=DiagScanOrder[3][3][i][ 1 ]
 
 
 
       
 
 
 
ScalingFactor[6][6][matrixId][0][0]=scaling_list_dc_coef_minus8[2][matrixId]+8   (7-XX)
   with matrixId=0, 3
 
 
 
A quantization matrix with rectangular size shall be zeroed out for the samples satisfying to the following conditions
               the decoded tu is not coded by default transform mode, (1&lt;&lt;sizeIdW==32 and x&gt;16   the decoded tu is not coded by default transform mode, (1&lt;&lt;sizeIdH)==32 and y&gt;16       

     5.4. Embodiment #4 on Scaling Matrix 
     This section provides an example of disallowing scaling matrix for QR-BDPCM coded blocks. The changes on top of JVET-N0847 are highlighted in   and removed text are marked with  . One or multiple of highlighted conditions may be added. 
     8.7.3 Scaling Process for Transform Coefficients 
     Inputs to this process are: 
     
         
         
           
             a luma location (xTbY, yTbY) specifying the top-left sample of the current luma transform block relative to the top-left luma sample of the current picture, 
             a variable nTbW specifying the transform block width, 
             a variable nTbH specifying the transform block height, 
             a variable cIdx specifying the colour component of the current block, 
             a variable bitDepth specifying the bit depth of the current colour component.
 
Output of this process is the (nTbW)×(nTbH) array d of scaled transform coefficients with elements d[x][y].
 
The quantization parameter qP is derived as follows:
 
             If cIdx is equal to 0, the following applies:
 
 qP=Qp′   Y   (8-1019)
 
             Otherwise, if cIdx is equal to 1, the following applies:
 
 qP=Qp′   Cb   (8-1020)
 
             Otherwise (cIdx is equal to 2), the following applies:
 
 qP=Qp′   Cr   (8-1021)
 
The variable rectNonTsFlag is derived as follows:
 
rectNonTsFlag=(((Log 2(nTbW)+Log 2(nTbH))&amp;1)==1&amp;&amp; transform_skip_flag[xTbY][yTbY]==0)  (8-1022)
 
The variables bdShift, rectNorm and bdOffset are derived as follows:
 
bdShift=bitDepth+((rectNonTsFlag?8:0)+(Log 2(nTbW)+Log 2(nTbH))/2)−5+dep_quant_enabled_flag  (8-1023)
 
rectNorm=rectNonTsFlag?181:1  (8-1024)
 
bdOffset=(1&lt;&lt;bdShift)&gt;&gt;1  (8-1025)
 
The list levelScale[ ] is specified as levelScale[k={40, 45, 51, 57, 64, 72} with k=0 . . . 5.
 
For the derivation of the scaled transform coefficients d[x][y] with x=0 . . . nTbW−1, y=0 . . . nTbH−1, the following applies:
 
             The intermediate scaling factor m[x][y] is derived as follows:
           If one or more of the following conditions are true, m[x][y] is set equal to 16:
               scaling_list_enabled_flag is equal to 0.   transform_skip_flag[xTbY][yTbY] is equal to 1.         
               Otherwise, the following applies:
 
 m [ x ][ y ]=ScalingFactor[sizeIdW][sizeIdH][matrixId][ x ][ y ]  (8-XXX)
 
Where sizeIdW is set equal to Log 2(nTbW), sizeIdH is set equal to Log 2(nTbH) and matrixId is specified in Table 7-14.
   
         
             The scaling factor Is [x][y] is derived as follows:
           If dep_quant_enabled_flag is equal to 1, the following applies:
 
Is [ x ][ y ]=( m [ x ][ y ]*levelScale[( qP+ 1)%6])&lt;&lt;(( qP+ 1)/6)  (8-1026)
   Otherwise (dep_quant_enabled_flag is equal to 0), the following applies:
 
Is [ x ][ y ]=( m [ x ][ y ]*levelScale[ qP %6])&lt;&lt;( qP/ 6)  (8-1027)
   
         
             The value dnc[x][y] is derived as follows:
 
dnc[ x ][ y ]=(TransCoeffLevel[xTbY][yTbY][cIdx][ x ][ y ]*ls[ x ][ y ]*rectNorm+bdOffset)&gt;&gt;bdShift  (8-1028)
 
             The scaled transform coefficient d[x][y] is derived as follows:
 
 d [ x ][ y ]=Clip3(CoeffMin,CoeffMax,dnc[ x ][ y ])  (8-1029)
 
           
         
       
    
     5.5. Embodiment #5 on Semantics of Transform Skip Flag 
     transform_skip_flag[x0][y0] specifies whether a transform is applied to the luma transform block or not. The array indices x0, y0 specify the location (x0, y0) of the top-left luma sample of the considered transform block relative to the top-left luma sample of the picture. transform_skip_flag[x0][y0] equal to 1 specifies that no transform is applied to the luma transform block. transform_skip_flag[x0][y0] equal to 0 specifies that the decision whether transform is applied to the luma transform block or not depends on other syntax elements. When transform_skip_flag[x0][y0] is not present  , it is inferred to be equal to 0. When transform_skip_flag[x0][y0] is not present     it is inferred to be equal to 0. 
       FIG.  11    is a block diagram of a video processing apparatus  1100 . The apparatus  1100  may be used to implement one or more of the methods described herein. The apparatus  1100  may be embodied in a smartphone, tablet, computer, Internet of Things (IoT) receiver, and so on. The apparatus  1100  may include one or more processors  1102 , one or more memories  1104  and video processing hardware  1106 . The processor(s)  1102  may be configured to implement one or more methods described in the present document. The memory (memories)  1104  may be used for storing data and code used for implementing the methods and techniques described herein. The video processing hardware  1106  may be used to implement, in hardware circuitry, some techniques described in the present document. 
     The following solutions may be implemented as preferred solutions in some embodiments. 
     The following solutions may be implemented together with additional techniques described in items listed in the previous section (e.g., item 1). 
     1. A method of video processing (e.g., method  1200  depicted in  FIG.  12   ), comprising: determining ( 1202 ), fora conversion between a coded representation of a video block of a video and the video block, based on a coded mode information, whether a transform skip mode is enabled for the conversion; and performing ( 1204 ) the conversion based on the determining; wherein, in the transform skip mode, application of a transform to at least some coefficients representing the video block is skipped during the conversion. 
     2. The method of solution 1, wherein the transform skip mode is determined to be enabled due to the coded mode information indicating a block differential pulse code modulation (BDPCM) or a quantized residual BDPCM (QR-BDPCM) mode. 
     3. The method of solution 1, wherein a flag in the coded representation indicating the transform skip mode is not parsed. 
     4. The method of solution 1, wherein a flag in the coded representation indicating the transform skip mode is skipped from parsing. 
     The following solutions may be implemented together with additional techniques described in items listed in the previous section (e.g., item 2). 
     5. A method of video processing, comprising: determining to use a scaling matrix for a conversion between a coded representation of a video block and the video block due to a use of a block differential pulse code modulation (BDPCM) or a quantized residual BDPCM (QR-BDPCM) mode for the conversion; and performing the conversion using the scaling matrix; wherein the scaling matrix is used to scale at least some coefficients representing the video block during the conversion. 
     6. The method of solution 5, wherein the conversion includes applying the scaling matrix according to a mode that is dependent on a number of transforms applied to the coefficients during the conversion. 
     7. A method of video processing, comprising: determining to disable use of a scaling matrix for a conversion between a coded representation of a video block and the video block due to a use of a block differential pulse code modulation (BDPCM) or a quantized residual BDPCM (QR-BDPCM) mode for the conversion; and performing the conversion using the scaling matrix; wherein the scaling matrix is used to scale at least some coefficients representing the video block during the conversion. 
     The following solutions may be implemented together with additional techniques described in items listed in the previous section (e.g., item 3). 
     8. A method of video processing, comprising: determining, fora conversion between a coded representation of a video block of a video and the video block, an applicability of an in-loop filter depending on whether a transform skip mode is enabled for the conversion; and performing the conversion based on the applicability of the in-loop filter, wherein, in the transform skip mode, application of a transform to at least some coefficients representing the video block is skipped during the conversion. 
     9. The method of solution 8, wherein the in-loop filter comprises a de-blocking filter. 
     10. The method of any of solutions 8-9, further including, determining a strength of the in-loop filter based on the transform skip mode of the video block and another transform skip mode of a neighboring block. 
     11. The method of any of solutions 8-9, wherein the determining includes determining that the in-loop filter is not applicable due to the transform skip mode being disabled for the video block. 
     The following solutions may be implemented together with additional techniques described in items listed in the previous section (e.g., items 4 and 5). 
     12. A method of video processing, comprising: selecting a scaling matrix for a conversion between video blocks of a video and a coded representation of the video blocks such that a same scaling matrix is selected for inter coding and intra block copy coding based conversion, and performing the conversion using the selected scaling matrix, wherein the scaling matrix is used to scale at least some coefficients of the video blocks. 
     The following solutions may be implemented together with additional techniques described in items listed in the previous section (e.g., item 6). 
     13. A method of video processing, comprising: selecting a scaling matrix for a conversion between video blocks of a video and a coded representation of the video blocks based on a transform matrix selected for the conversion, and performing the conversion using the selected scaling matrix, wherein the scaling matrix is used to scale at least some coefficients of the video blocks and wherein the transform matrix is used to transform at least some coefficients of the video block during the conversion. 
     14. The method of solution 13, wherein the selecting the scaling matrix is based on whether the conversion of the video block uses a sub-block coding mode. 
     15. The method of solution 14, wherein the sub-block coding mode is an affine coding mode. 
     16. The method of solution 15, wherein the scaling matrix for the affine coding mode is different for another scaling matrix for another video block whose conversion does not use the affine coding mode. 
     The following solutions may be implemented together with additional techniques described in items listed in the previous section (e.g., item 7). 
     17. A method of video processing, comprising: selecting a scaling matrix for a conversion between video blocks of a video and a coded representation of the video blocks based on a secondary transform matrix selected for the conversion, and performing the conversion using the selected scaling matrix, wherein the scaling matrix is used to scale at least some coefficients of the video blocks and wherein the secondary transform matrix is used to transform at least some residual coefficients of the video block during the conversion. 
     18. The method of solution 17, wherein the secondary transform matrix is applied to an M×N top left portion of the video block, and wherein the scaling matrix is applied to more than the M×N top left portion of the video block. 
     19. The method of solution 17, wherein the secondary transform matrix is applied to an M×N top left portion of the video block, and wherein the scaling matrix is applied only to the M×N top left portion of the video block. 
     20. The method of any of solution 17-19, wherein a syntax element in the coded representation indicates the scaling matrix. 
     The following solutions may be implemented together with additional techniques described in items listed in the previous section (e.g., item 8). 
     21. A method of video processing, comprising: determining, fora video block that has a non-square shape, a scaling matrix for use in a conversion between the video block and a coded representation of the video block, wherein a syntax element in the coded representation signals the scaling matrix; and performing the conversion based on the scaling matrix, wherein the scaling matrix is used to scale at least some coefficients of the video blocks during the conversion. 
     22. The method of solution 21, wherein the syntax element predictively codes the scaling matrix from a previous square block&#39;s scaling matrix. 
     The following solutions may be implemented together with additional techniques described in items listed in the previous section (e.g., item 9). 
     23. A method of video processing, comprising: determining that a scaling matrix is to be applied partially during a conversion between a coded representation of a video block and the video block; and performing the conversion based by partially applying the scaling matrix such that the scaling matrix is applied in a first set of positions and disabled at remaining positions in the video block. 
     24. The method of solution 23, wherein the first set of positions comprises top-left M*N positions of the video block. 
     25. The method of solution 23, wherein the first set of positions comprises top M*N positions of the video block. 
     26. The method of solution 23, wherein the first set of positions comprises left M*N positions of the video block. 
     The following solutions may be implemented together with additional techniques described in items listed in the previous section (e.g., items 10 and 11). 
     27. A method of video processing, comprising: determining that a scaling matrix is to be applied during a conversion between a coded representation of a video block and the video block; and performing the conversion based on the scaling matrix; wherein the coded representation signals a number of elements of the scaling matrix, wherein the number depends on application of coefficient zeroing out in the conversion. 
     28. The method of solution 27, wherein the conversion includes zeroing out all but top-left M×N positions of the video block, and wherein the number is M/8*N/8. 
     The following solutions may be implemented together with additional techniques described in items listed in the previous section (e.g., item 11). 
     29. The method of solutions 27-28, wherein the number depends on a transform matrix used during the conversion. 
     30. The method of solution 29, wherein the transform matrix is of size K×L and wherein only top M×N coefficients are not zeroed out. 
     31. The method of any of solutions 27-30, wherein the scaling matrix is applied by sub-sampling by a factor determined from K or L. 
     The following solutions may be implemented together with additional techniques described in items listed in the previous section (e.g., item 12). 
     32. A method of video processing, comprising: determining, during a conversion between a video block and a coded representation of the video block, a single quantization matrix to use based on a size of the video block being of a specific type; and performing the conversion using the quantization matrix. 
     33. The method of solution 32, wherein the size of the video block is smaller than W×H, where W and H are integers. 
     34. The method of any of solutions 32-33, wherein a width of the video block is smaller than a threshold. 
     35. The method of any of solutions 32-33, wherein a height of the video block is smaller than a threshold. 
     36. The method of solution 32, wherein the quantization matrix is an identity quantization matrix that does not affect quantized values. 
     37. The method of any of solutions 1 to 36, wherein the conversion comprises encoding the video into the coded representation. 
     38. The method of any of solutions 1 to 36, wherein the conversion comprises decoding the coded representation to generate pixel values of the video. 
     39. A video decoding apparatus comprising a processor configured to implement a method recited in one or more of solutions 1 to 38. 
     40. A video encoding apparatus comprising a processor configured to implement a method recited in one or more of solutions 1 to 38. 
     41. A computer program product having computer code stored thereon, the code, when executed by a processor, causes the processor to implement a method recited in any of solutions 1 to 38. 
     42. A method, apparatus or system described in the present document. 
     Some embodiments of the disclosed technology include making a decision or determination to enable a video processing tool or mode. In an example, when the video processing tool or mode is enabled, the encoder will use or implement the tool or mode in the processing of a block of video, but may not necessarily modify the resulting bitstream based on the usage of the tool or mode. That is, a conversion from the block of video to the bitstream representation of the video will use the video processing tool or mode when it is enabled based on the decision or determination. In another example, when the video processing tool or mode is enabled, the decoder will process the bitstream with the knowledge that the bitstream has been modified based on the video processing tool or mode. That is, a conversion from the bitstream representation of the video to the block of video will be performed using the video processing tool or mode that was enabled based on the decision or determination. 
     Some embodiments of the disclosed technology include making a decision or determination to disable a video processing tool or mode. In an example, when the video processing tool or mode is disabled, the encoder will not use the tool or mode in the conversion of the block of video to the bitstream representation of the video. In another example, when the video processing tool or mode is disabled, the decoder will process the bitstream with the knowledge that the bitstream has not been modified using the video processing tool or mode that was disabled based on the decision or determination. 
       FIG.  15    is a block diagram that illustrates an example video coding system  100  that may utilize the techniques of this disclosure. As shown in  FIG.  15   , video coding system  100  may include a source device  110  and a destination device  120 . Source device  110  generates encoded video data which may be referred to as a video encoding device. Destination device  120  may decode the encoded video data generated by source device  110  which may be referred to as a video decoding device. Source device  110  may include a video source  112 , a video encoder  114 , and an input/output (I/O) interface  116 . 
     Video source  112  may include a source such as a video capture device, an interface to receive video data from a video content provider, and/or a computer graphics system for generating video data, or a combination of such sources. The video data may comprise one or more pictures. Video encoder  114  encodes the video data from video source  112  to generate a bitstream. The bitstream may include a sequence of bits that form a coded representation of the video data. The bitstream may include coded pictures and associated data. The coded picture is a coded representation of a picture. The associated data may include sequence parameter sets, picture parameter sets, and other syntax structures. I/O interface  116  may include a modulator/demodulator (modem) and/or a transmitter. The encoded video data may be transmitted directly to destination device  120  via I/O interface  116  through network  130   a . The encoded video data may also be stored onto a storage medium/server  130   b  for access by destination device  120 . 
     Destination device  120  may include an I/O interface  126 , a video decoder  124 , and a display device  122 . 
     I/O interface  126  may include a receiver and/or a modem. I/O interface  126  may acquire encoded video data from the source device  110  or the storage medium/server  130   b . Video decoder  124  may decode the encoded video data. Display device  122  may display the decoded video data to a user. Display device  122  may be integrated with the destination device  120 , or may be external to destination device  120  which be configured to interface with an external display device. 
     Video encoder  114  and video decoder  124  may operate according to a video compression standard, such as the High Efficiency Video Coding (HEVC) standard, Versatile Video Coding (VVM) standard and other current and/or further standards. 
       FIG.  16    is a block diagram illustrating an example of video encoder  200 , which may be video encoder  114  in the system  100  illustrated in  FIG.  15   . 
     Video encoder  200  may be configured to perform any or all of the techniques of this disclosure. In the example of  FIG.  16   , video encoder  200  includes a plurality of functional components. The techniques described in this disclosure may be shared among the various components of video encoder  200 . In some examples, a processor may be configured to perform any or all of the techniques described in this disclosure. 
     The functional components of video encoder  200  may include a partition unit  201 , a predication unit  202  which may include a mode select unit  203 , a motion estimation unit  204 , a motion compensation unit  205  and an intra prediction unit  206 , a residual generation unit  207 , a transform unit  208 , a quantization unit  209 , an inverse quantization unit  210 , an inverse transform unit  211 , a reconstruction unit  212 , a buffer  213 , and an entropy encoding unit  214 . 
     In other examples, video encoder  200  may include more, fewer, or different functional components. In an example, predication unit  202  may include an intra block copy (IBC) unit. The IBC unit may perform predication in an IBC mode in which at least one reference picture is a picture where the current video block is located. 
     Furthermore, some components, such as motion estimation unit  204  and motion compensation unit  205  may be highly integrated, but are represented in the example of  FIG.  16    separately for purposes of explanation. 
     Partition unit  201  may partition a picture into one or more video blocks. Video encoder  200  and video decoder  300  may support various video block sizes. 
     Mode select unit  203  may select one of the coding modes, intra or inter, e.g., based on error results, and provide the resulting intra- or inter-coded block to a residual generation unit  207  to generate residual block data and to a reconstruction unit  212  to reconstruct the encoded block for use as a reference picture. In some example, Mode select unit  203  may select a combination of intra and inter predication (CIIP) mode in which the predication is based on an inter predication signal and an intra predication signal. Mode select unit  203  may also select a resolution fora motion vector (e.g., a sub-pixel or integer pixel precision) for the block in the case of inter-predication. 
     To perform inter prediction on a current video block, motion estimation unit  204  may generate motion information for the current video block by comparing one or more reference frames from buffer  213  to the current video block. Motion compensation unit  205  may determine a predicted video block for the current video block based on the motion information and decoded samples of pictures from buffer  213  other than the picture associated with the current video block. 
     Motion estimation unit  204  and motion compensation unit  205  may perform different operations fora current video block, for example, depending on whether the current video block is in an I slice, a P slice, or a B slice. 
     In some examples, motion estimation unit  204  may perform uni-directional prediction for the current video block, and motion estimation unit  204  may search reference pictures of list 0 or list 1 for a reference video block for the current video block. Motion estimation unit  204  may then generate a reference index that indicates the reference picture in list 0 or list 1 that contains the reference video block and a motion vector that indicates a spatial displacement between the current video block and the reference video block. Motion estimation unit  204  may output the reference index, a prediction direction indicator, and the motion vector as the motion information of the current video block. Motion compensation unit  205  may generate the predicted video block of the current block based on the reference video block indicated by the motion information of the current video block. 
     In other examples, motion estimation unit  204  may perform bi-directional prediction for the current video block, motion estimation unit  204  may search the reference pictures in list 0 fora reference video block for the current video block and may also search the reference pictures in list 1 for another reference video block for the current video block. Motion estimation unit  204  may then generate reference indexes that indicate the reference pictures in list 0 and list 1 containing the reference video blocks and motion vectors that indicate spatial displacements between the reference video blocks and the current video block. Motion estimation unit  204  may output the reference indexes and the motion vectors of the current video block as the motion information of the current video block. Motion compensation unit  205  may generate the predicted video block of the current video block based on the reference video blocks indicated by the motion information of the current video block. 
     In some examples, motion estimation unit  204  may output a full set of motion information for decoding processing of a decoder. 
     In some examples, motion estimation unit  204  may do not output a full set of motion information for the current video. Rather, motion estimation unit  204  may signal the motion information of the current video block with reference to the motion information of another video block. For example, motion estimation unit  204  may determine that the motion information of the current video block is sufficiently similar to the motion information of a neighboring video block. 
     In one example, motion estimation unit  204  may indicate, in a syntax structure associated with the current video block, a value that indicates to the video decoder  300  that the current video block has the same motion information as the another video block. 
     In another example, motion estimation unit  204  may identify, in a syntax structure associated with the current video block, another video block and a motion vector difference (MVD). The motion vector difference indicates a difference between the motion vector of the current video block and the motion vector of the indicated video block. The video decoder  300  may use the motion vector of the indicated video block and the motion vector difference to determine the motion vector of the current video block. 
     As discussed above, video encoder  200  may predictively signal the motion vector. Two examples of predictive signaling techniques that may be implemented by video encoder  200  include advanced motion vector predication (AMVP) and merge mode signaling. 
     Intra prediction unit  206  may perform intra prediction on the current video block. When intra prediction unit  206  performs intra prediction on the current video block, intra prediction unit  206  may generate prediction data for the current video block based on decoded samples of other video blocks in the same picture. The prediction data for the current video block may include a predicted video block and various syntax elements. 
     Residual generation unit  207  may generate residual data for the current video block by subtracting (e.g., indicated by the minus sign) the predicted video block(s) of the current video block from the current video block. The residual data of the current video block may include residual video blocks that correspond to different sample components of the samples in the current video block. 
     In other examples, there may be no residual data for the current video block for the current video block, for example in a skip mode, and residual generation unit  207  may not perform the subtracting operation. 
     Transform processing unit  208  may generate one or more transform coefficient video blocks for the current video block by applying one or more transforms to a residual video block associated with the current video block. 
     After transform processing unit  208  generates a transform coefficient video block associated with the current video block, quantization unit  209  may quantize the transform coefficient video block associated with the current video block based on one or more quantization parameter (QP) values associated with the current video block. 
     Inverse quantization unit  210  and inverse transform unit  211  may apply inverse quantization and inverse transforms to the transform coefficient video block, respectively, to reconstruct a residual video block from the transform coefficient video block. Reconstruction unit  212  may add the reconstructed residual video block to corresponding samples from one or more predicted video blocks generated by the predication unit  202  to produce a reconstructed video block associated with the current block for storage in the buffer  213 . 
     After reconstruction unit  212  reconstructs the video block, loop filtering operation may be performed reduce video blocking artifacts in the video block. 
     Entropy encoding unit  214  may receive data from other functional components of the video encoder  200 . When entropy encoding unit  214  receives the data, entropy encoding unit  214  may perform one or more entropy encoding operations to generate entropy encoded data and output a bitstream that includes the entropy encoded data. 
       FIG.  13    is a block diagram illustrating an example of video decoder  300  which may be video decoder  114  in the system  100  illustrated in  FIG.  15   . 
     The video decoder  300  may be configured to perform any or all of the techniques of this disclosure. In the example of  FIG.  13   , the video decoder  300  includes a plurality of functional components. The techniques described in this disclosure may be shared among the various components of the video decoder  300 . In some examples, a processor may be configured to perform any or all of the techniques described in this disclosure. 
     In the example of  FIG.  13   , video decoder  300  includes an entropy decoding unit  301 , a motion compensation unit  302 , an intra prediction unit  303 , an inverse quantization unit  304 , an inverse transformation unit  305 , and a reconstruction unit  306  and a buffer  307 . Video decoder  300  may, in some examples, perform a decoding pass generally reciprocal to the encoding pass described with respect to video encoder  200  ( FIG.  16   ). 
     Entropy decoding unit  301  may retrieve an encoded bitstream. The encoded bitstream may include entropy coded video data (e.g., encoded blocks of video data). Entropy decoding unit  301  may decode the entropy coded video data, and from the entropy decoded video data, motion compensation unit  302  may determine motion information including motion vectors, motion vector precision, reference picture list indexes, and other motion information. Motion compensation unit  302  may, for example, determine such information by performing the AMVP and merge mode. 
     Motion compensation unit  302  may produce motion compensated blocks, possibly performing interpolation based on interpolation filters. Identifiers for interpolation filters to be used with sub-pixel precision may be included in the syntax elements. 
     Motion compensation unit  302  may use interpolation filters as used by video encoder  20  during encoding of the video block to calculate interpolated values for sub-integer pixels of a reference block. Motion compensation unit  302  may determine the interpolation filters used by video encoder  200  according to received syntax information and use the interpolation filters to produce predictive blocks. 
     Motion compensation unit  302  may uses some of the syntax information to determine sizes of blocks used to encode frame(s) and/or slice(s) of the encoded video sequence, partition information that describes how each macroblock of a picture of the encoded video sequence is partitioned, modes indicating how each partition is encoded, one or more reference frames (and reference frame lists) for each inter-encoded block, and other information to decode the encoded video sequence. 
     Intra prediction unit  303  may use intra prediction modes for example received in the bitstream to form a prediction block from spatially adjacent blocks. Inverse quantization unit  303  inverse quantizes, i.e., de-quantizes, the quantized video block coefficients provided in the bitstream and decoded by entropy decoding unit  301 . Inverse transform unit  303  applies an inverse transform. 
     Reconstruction unit  306  may sum the residual blocks with the corresponding prediction blocks generated by motion compensation unit  202  or intra-prediction unit  303  to form decoded blocks. If desired, a deblocking filter may also be applied to filter the decoded blocks in order to remove blockiness artifacts. The decoded video blocks are then stored in buffer  307 , which provides reference blocks for subsequent motion compensation/intra predication and also produces decoded video for presentation on a display device. 
     In the present document, the term “video processing” may refer to video encoding, video decoding, video compression or video decompression. For example, video compression algorithms may be applied during conversion from pixel representation of a video to a corresponding bitstream representation or vice versa. The bitstream representation, or coded representation, of a current video block may, for example, correspond to bits that are either co-located or spread in different places within the bitstream, as is defined by the syntax. For example, a video block may be encoded in terms of transformed and coded error residual values and also using bits in headers and other fields in the bitstream. Furthermore, during conversion, a decoder may parse a bitstream with the knowledge that some fields may be present, or absent, based on the determination, as is described in the above solutions. Similarly, an encoder may determine that certain syntax fields are or are not to be included and generate the coded representation accordingly by including or excluding the syntax fields from the coded representation. 
       FIG.  14    is a block diagram showing an example video processing system  2000  in which various techniques disclosed herein may be implemented. Various implementations may include some or all of the components of the system  2000 . The system  2000  may include input  2002  for receiving video content. The video content may be received in a raw or uncompressed format, e.g., 8 or 10 bit multi-component pixel values, or may be in a compressed or encoded format. The input  2002  may represent a network interface, a peripheral bus interface, or a storage interface. Examples of network interface include wired interfaces such as Ethernet, passive optical network (PON), etc. and wireless interfaces such as Wi-Fi or cellular interfaces. 
     The system  2000  may include a coding component  2004  that may implement the various coding or encoding methods described in the present document. The coding component  2004  may reduce the average bitrate of video from the input  2002  to the output of the coding component  2004  to produce a coded representation of the video. The coding techniques are therefore sometimes called video compression or video transcoding techniques. The output of the coding component  2004  may be either stored, or transmitted via a communication connected, as represented by the component  2006 . The stored or communicated bitstream (or coded) representation of the video received at the input  2002  may be used by the component  2008  for generating pixel values or displayable video that is sent to a display interface  2010 . The process of generating user-viewable video from the bitstream representation is sometimes called video decompression. Furthermore, while certain video processing operations are referred to as “coding” operations or tools, it will be appreciated that the coding tools or operations are used at an encoder and corresponding decoding tools or operations that reverse the results of the coding will be performed by a decoder. 
     Examples of a peripheral bus interface or a display interface may include universal serial bus (USB) or high definition multimedia interface (HDMI) or Displayport, and so on. Examples of storage interfaces include SATA (serial advanced technology attachment), PCI, IDE interface, and the like. The techniques described in the present document may be embodied in various electronic devices such as mobile phones, laptops, smartphones or other devices that are capable of performing digital data processing and/or video display. 
       FIG.  17    is a flowchart of an example method  1700  of video processing. The method  1700  comprises performing ( 1702 ) a conversion between a video block of a video and a coded representation of the video, wherein the coded representation conforms to a format rule, wherein the format rule specifies that applicability of a transform skip mode to the video block is determined by a coding condition of the video block, wherein the format rule specifies that a syntax element indicative of applicability of the transform skip mode is omitted from the coded representation, and wherein the transform skip mode includes, skipping applying a forward transform to at least some coefficients prior to encoding into the coded representation, or during decoding, skipping applying an inverse transform to at least some coefficients prior to decoding from the coded representation. 
       FIG.  18    is a flowchart of an example method  1800  of video processing. The method  1800  comprises determining ( 1802 ), for a conversion between two adjacent video blocks of a video and a coded representation of the video, whether an in-loop filter or a post-reconstruction filter is to be used for the conversion depending on whether a forward transform or an inverse transform is used for the conversion, wherein the forward transform includes, skipping applying the forward transform to at least some coefficients prior to encoding into the coded representation, or during decoding, skipping applying the inverse transform to at least some coefficients to decoding from the coded representation; and performing ( 1804 ) the conversion based on the use of the in-loop filter or the post-reconstruction filter. 
       FIG.  19    is a flowchart of an example method  1900  of video processing. The method  1900  comprises determining ( 1902 ), for a conversion between a video block of a video and a coded representation of the video, to use a scaling tool due to a block differential pulse code modulation (BDPCM) coding tool or a quantized residual BDPCM (QR-BDPCM) coding tool being used for the conversion of the video block; and performing ( 1904 ) the conversion using the scaling tool, wherein a syntax element in the coded representation indicates use of the scaling tool, and wherein the use of the scaling tool comprises: scaling at least some coefficients representing the video block during encoding or descaling at least some coefficients from the coded representation during decoding. 
       FIG.  20    is a flowchart of an example method  2000  of video processing. The method  2000  comprises determining ( 2002 ), for a conversion between a video block of a video and a coded representation of the video, to disable use of a scaling tool due to to a block differential pulse code modulation (BDPCM) coding tool or a quantized residual BDPCM (QR-BDPCM) coding tool for the conversion of the video block; and performing ( 2004 ) the conversion without using the scaling tool, wherein the use of the scaling tool comprises: scaling at least some coefficients representing the video block during encoding or descaling at least some coefficients from the coded representation during decoding. 
       FIG.  21    is a flowchart of an example method  2100  of video processing. The method  2100  comprises selecting ( 2102 ), fora conversion between video blocks of a video and a coded representation of the video, scaling matrices based on a transform matrix selected for the conversion, wherein the scaling matrices are used to scale at least some coefficients of the video blocks, and wherein the transform matrices are used to transform the at least some coefficients of the video blocks during the conversion; and performing ( 2104 ) the conversion using the scaling matrices. 
       FIG.  22    is a flowchart of an example method  2200  of video processing. The method  2200  comprises determining ( 2202 ), according to a rule, whether to apply a scaling matrix based on whether a secondary transform matrix is applied to a portion of a video block of a video, wherein the scaling matrix is used to scale at least some coefficients of the video block, and wherein the secondary transform matrix is used to transform at least some residual coefficients of the portion of the video block during the conversion; and performing ( 2204 ) a conversion between the video block of the video and a bitstream representation of the video using the selected scaling matrix. 
       FIG.  23    is a flowchart of an example method  2300  of video processing. The method  2300  comprises determining ( 2302 ), for a video block that has a non-square shape, a scaling matrix for use in a conversion between the video block of a video and a coded representation of the video, wherein a syntax element in the coded representation signals the scaling matrix, and wherein the scaling matrix is used to scale at least some coefficients of the video blocks during the conversion; and performing ( 2304 ) the conversion based on the scaling matrix. 
       FIG.  24    is a flowchart of an example method  2400  of video processing. The method  2400  comprises performing ( 2402 ) a conversion between a video block of a video and a coded representation of the video, wherein the video block comprises a first number of positions at which a scaling matrix is applied during the conversion and a second number of positions at which the scaling matrix is not applied during the conversion based on a rule. 
       FIG.  25    is a flowchart of an example method  2500  of video processing. The method  2500  comprises determining ( 2502 ) that a scaling matrix is to be applied during a conversion between a video block of a video and a coded representation of the video; and performing the conversion based on the scaling matrix, wherein the coded representation indicates a number of elements of the scaling matrix, and wherein the number depends on whether coefficient zeroing out is applied to coefficients of the video block. 
       FIG.  26    is a flowchart of an example method  2600  of video processing. The method  2600  comprises performing ( 2602 ) a conversion between a video block of a video and a coded representation of the video according to a rule, wherein the video block is represented in the coded representation after zeroing out all but top-left M×N transform coefficients after applying a K×L transform matrix to transform coefficients of the video block, wherein the coded representation is configured to exclude signaling of elements of a scaling matrix at positions corresponding to the zeroing out, wherein the scaling matrix is used for scaling the transform coefficients. 
       FIG.  27    is a flowchart of an example method  2700  of video processing. The method  2700  comprises determining ( 2702 ), during a conversion between a video block of a video and a coded representation of the video, based on a rule whether a single quantization matrix is to be used based on a size of the video block, wherein all video blocks having the size use the single quantization matrix; and performing the conversion using the quantization matrix. 
     The following three section describes example video processing techniques that are numbered. 
     Section A 
     1. A method of video processing, comprising: performing a conversion between a video block of a video and a coded representation of the video, wherein the coded representation conforms to a format rule, wherein the format rule specifies that applicability of a transform skip mode to the video block is determined by a coding condition of the video block, wherein the format rule specifies that a syntax element indicative of applicability of the transform skip mode is omitted from the coded representation, and wherein the transform skip mode includes, skipping applying a forward transform to at least some coefficients to encoding into the coded representation, or during decoding, skipping applying an inverse transform to at least some coefficients prior to decoding from the coded representation. 
     2. The method of example 1, wherein the transform skip mode is determined to be enabled due to the coding condition of the video block indicating that a block differential pulse code modulation (BDPCM) or a quantized residual BDPCM (QR-BDPCM) is used on the video block. 
     3. The method of example 1, wherein the transform skip mode is determined to be disabled due to the coding condition of the video block indicating that a non-block differential pulse code modulation (non-BDPCM) or a non-quantized residual BDPCM (non-QR-BDPCM) is used on the video block. 
     4. A method of video processing, comprising: determining, fora conversion between two adjacent video blocks of a video and a coded representation of the video, whether an in-loop filter or a post-reconstruction filter is to be used for the conversion depending on whether a forward transform or an inverse transform is used for the conversion, wherein the forward transform includes, skipping applying the forward transform to at least some coefficients prior to encoding into the coded representation, or during decoding, skipping applying the inverse transform to at least some coefficients prior to decoding from the coded representation; and performing the conversion based on the use of the in-loop filter or the post-reconstruction filter. 
     5. The method of example 4, wherein the forward transform or inverse transform include a transform skip mode or a block differential pulse code modulation (BDPCM) or a quantized residual BDPCM (QR-BDPCM) or a palette mode, and wherein the use of the in-loop filter or the post-reconstruction filter to the two adjacent video blocks is based on whether the transform skip mode or a block differential pulse code modulation (BDPCM) or a quantized residual BDPCM (QR-BDPCM) or a palette mode is used on the two adjacent video blocks. 
     6. The method of example 4, wherein the forward transform or inverse transform include a transform skip mode, and wherein a derivation of a boundary filtering strength depends on one or more syntax elements that indicates whether the transform skip mode is enabled for one or both of the two adjacent video blocks. 
     7. The method of example 4, wherein the forward transform or inverse transform include a transform skip mode, and wherein a deblocking filter, a sample adaptive offset, an adaptive loop filter, or the post-reconstruction filter are disabled in response to the samples located at the two adjacent video blocks being coded with the transform skip mode. 
     8. The method of example 7, wherein the forward transform or inverse transform include a transform skip mode, and wherein the in-loop filter and the post-reconstruction filter are not applied to the edge between the two adjacent video blocks in response to the transform skip mode being enabled for the two adjacent video blocks. 
     9. The method of example 7, wherein the forward transform or inverse transform include a transform skip mode, and wherein the in-loop filter and the post-reconstruction filter are not applied to the samples between the two adjacent video blocks in response to the transform skip mode being enabled for one of the two adjacent video blocks. 
     10. The method of example 4, wherein the forward transform or inverse transform include a transform skip mode, and wherein the samples are filtered using a filter other than the in-loop filter or the post-reconstruction filter in response to the transform skip mode being enabled for the two adjacent video blocks. 
     11. The method of example 10, wherein the filter comprises a smoother filter. 
     12. The method of example 4, wherein the video comprises a video block that is coded with a pulse code modulation (PCM) or a block differential pulse code modulation (BDPCM) or a quantized residual BDPCM (QR-BDPCM) or another type of mode in which the forward transform or the inverse transform is not applied to the video block, and wherein whether the in-loop filter or the post-reconstruction filter are used for the conversion of the video block is determined in a same way as that for the two adjacent video blocks when a transform skip mode is enabled for the two adjacent video blocks. 
     13. The method of any of examples 4-12, wherein the in-loop filter comprises a de-blocking filter. 
     14. The method of any of examples 4-12, wherein the post-reconstruction filter comprises a bilateral filter or a diffusion filter. 
     15. The method of any of examples 1 to 14, wherein the conversion comprises encoding the video block into the coded representation. 
     16. The method of any of examples 1 to 14, wherein the conversion comprises decoding the coded representation to generate pixel values of the video block. 
     17. A video decoding apparatus comprising a processor configured to implement a method recited in one or more of examples 1 to 16. 
     18. A computer program product having computer code stored thereon, the code, when executed by a processor, causes the processor to implement a method recited in any of examples 1 to 17. 
     Section B 
     1. A method of video processing, comprising: determining, fora conversion between a video block of a video and a coded representation of the video, factors of a scaling tool based on a coding mode of the video block; and performing the conversion using the scaling tool, wherein the use of the scaling tool comprises:scaling at least some coefficients representing the video block during encoding or descaling at least some coefficients from the coded representation during decoding. 
     2. The method of example 1, further comprising: determining the factors of the scaling tool based on a predefined value in response to a block differential pulse code modulation (BDPCM) coding tool or a quantized residual BDPCM (QR-BDPCM) coding tool being used for the conversion of the video block. 
     3. The method of example 2, wherein the factors of the scaling tool used for the video block on which the BDPCM coding tool or the QR-BDPCM coding tool is applied are same as that used for the video block on which a transform skip mode is applied, and wherein the transform skip mode includes, skipping applying a forward transform to the at least some coefficients to encoding into the coded representation, or during decoding, skipping applying an inverse transform to the at least some coefficients prior to decoding from the coded representation. 
     4. The method of example 2, wherein the conversion includes determining the factors of the scaling tool based on one or more transforms applied to the at least some coefficients of the video block during the conversion. 
     5. The method of example 4, wherein the scaling tool is allowed for the conversion in response to the one or more transforms being applied to the at least some coefficients of the video block. 
     6. The method of example 4, wherein a technique for determining the factors of the scaling tool is the same as that used for an intra coded block in response to the one or more transforms being applied to the at least some coefficients of the video block. 
     7. The method of example 1, wherein the factors of the scaling matrix are determined in a same way for video blocks of the video that are coded using an intra block copy mode and an inter mode. 
     8. A method of video processing, comprising: determining, fora conversion between a video block of a video and a coded representation of the video, to disable use of a scaling tool due to a block differential pulse code modulation (BDPCM) coding tool or a quantized residual BDPCM (QR-BDPCM) coding tool for the conversion of the video block; and performing the conversion without using the scaling tool, wherein the use of the scaling tool comprises: scaling at least some coefficients representing the video block during encoding or descaling at least some coefficients from the coded representation during decoding. 
     9. A method of video processing, comprising: selecting, for a conversion between video blocks of a video and a coded representation of the video, scaling matrices based on a transform matrix selected for the conversion, wherein the scaling matrices are used to scale at least some coefficients of the video blocks, and wherein the transform matrices are used to transform the at least some coefficients of the video blocks during the conversion; and performing the conversion using the scaling matrices. 
     10. The method of example 9, wherein the selecting the scaling matrices is based on whether the conversion of the video blocks uses a default transform mode. 
     11. The method of example 10, wherein the default transform mode includes a discrete cosine transform 2 (DCT2). 
     12. The method of example 9, wherein the scaling matrices are separately signaled for multiple transform matrices. 
     13. The method of example 9, wherein the selecting the scaling matrices is based on motion information of the video blocks. 
     15. The method of example 13, wherein the selecting the scaling matrices is based on whether the conversion of the video blocks uses a sub-block coding mode. 
     15. The method of example 14, wherein the sub-block coding mode includes an affine coding mode. 
     16. The method of example 15, wherein a scaling matrix for the affine coding mode is signaled differently than that for another video block whose conversion uses a non-affine coding mode. 
     17. The method of example 13, wherein the selecting the scaling matrices is based on whether the video blocks are coded with affine intra prediction mode. 
     18. The method of any of examples 1 to 17, wherein the conversion comprises encoding the video block or the video blocks into the coded representation. 
     19. The method of any of examples 1 to 17, wherein the conversion comprises decoding the coded representation to generate pixel values of the video block or of the video blocks. 
     20. A video decoding apparatus comprising a processor configured to implement a method recited in one or more of examples 1 to 19. 
     21. A video encoding apparatus comprising a processor configured to implement a method recited in one or more of examples 1 to 19. 
     22. A computer program product having computer code stored thereon, the code, when executed by a processor, causes the processor to implement a method recited in any of examples 1 to 19. 
     Section C 
     1. A method of video processing, comprising: determining, according to a rule, whether to apply a scaling matrix based on whether a secondary transform matrix is applied to a portion of a video block of a video, wherein the scaling matrix is used to scale at least some coefficients of the video block, and wherein the secondary transform matrix is used to transform at least some residual coefficients of the portion of the video block during the conversion; and performing a conversion between the video block of the video and a bitstream representation of the video using the selected scaling matrix. 
     2. The method of example 1, wherein the rule specifies that the scaling matrix is applied to an M×N top left portion of the video block in response to the secondary transform matrix being applied to the M×N top left portion of the video block that includes a K×L transform block size. 
     3. The method of example 1, wherein the scaling matrix is signaled in the bitstream representation. 
     4. The method of example 3, wherein the scaling matrix is signaled in a tile group header, a slide header, a picture parameter set (PPS), a video parameter set (VPS), a sequence parameter set (SPS) for the secondary transform matrix or for a reduced secondary transform or a rotation transform. 
     5. The method of example 1, wherein the bitstream representation includes a first syntax element that indicates whether the scaling matrix is applied, and wherein the bitstream representation includes a second syntax element that indicates whether the secondary transform matrix is applied. 
     6. The method of example 1, wherein the rule specifies that the scaling matrix is only applied to portions of the video block in which the secondary transform matrix is not applied. 
     7. The method of example 1, wherein the rule specifies that the the scaling matrix is applied to portions except a M×N top left portion of the video block on which the secondary transform matrix is applied. 
     8. The method of example 1, wherein the rule specifies that the scaling matrix is applied only to portions of the video block on which the secondary transform matrix is applied. 
     9. A method of video processing, comprising: determining, fora video block that has a non-square shape, a scaling matrix for use in a conversion between the video block of a video and a coded representation of the video, wherein a syntax element in the coded representation signals the scaling matrix, and wherein the scaling matrix is used to scale at least some coefficients of the video blocks during the conversion; and performing the conversion based on the scaling matrix. 
     10. The method of example 9, wherein the syntax element predictively codes the scaling matrix from another scaling matrix of a previous square block of the video. 
     11. A method of video processing, comprising: performing a conversion between a video block of a video and a coded representation of the video, wherein the video block comprises a first number of positions at which a scaling matrix is applied during the conversion and a second number of positions at which the scaling matrix is not applied during the conversion based on a rule. 
     12. The method of example 11, wherein the first number of positions comprises top-left M*N positions of the video block, and wherein the video block comprises more than M*N positions. 
     13. The method of example 11, wherein the first number of positions comprises top M*N positions of the video block, and wherein the video block comprises more than M*N positions. 
     14. The method of example 11, wherein the first number of positions comprises left M*N positions of the video block, and wherein the video block comprises more than M*N positions. 
     15. A method of video processing, comprising: determining that a scaling matrix is to be applied during a conversion between a video block of a video and a coded representation of the video; and performing the conversion based on the scaling matrix, wherein the coded representation indicates a number of elements of the scaling matrix, and wherein the number depends on whether coefficient zeroing out is applied to coefficients of the video block. 
     16. The method of example 15, wherein fora 64×64 transform, the conversion includes zeroing out all but top-left M×N positions of the video block, and wherein the number of elements of the scaling matrix is M/8*N/8. 
     17. A method of video processing, comprising: performing a conversion between a video block of a video and a coded representation of the video according to a rule, wherein the video block is represented in the coded representation after zeroing out all but top-left M×N transform coefficients after applying a K×L transform matrix to transform coefficients of the video block, wherein the coded representation is configured to exclude signaling of elements of a scaling matrix at positions corresponding to the zeroing out, wherein the scaling matrix is used for scaling the transform coefficients. 
     18. The method of example 17, wherein the signaling of elements of the scaling matrix located in regions outside of the top-left M×N coefficients is skipped. 
     19. The method of example 17, wherein the scaling matrix is applied by sub-sampling by a ratio determined from the K and/or the L. 
     20. The method of example 19, wherein the video block is split into multiple sub-regions, and wherein a size of each sub-region is Uw*Uh, and wherein one element of the scaling matrix located within each sub-region of a region comprising a top-left M×N coefficients of the video block is signaled in the coded representation. 
     21. The method of example 19, wherein a number of the elements of the scaling matrix indicated in the coded representation is based on the M and/or the N. 
     22. The method of example 19, wherein a first number of the elements of the scaling matrix indicated in the coded representation for the K×L transform matrix is different from a second number of the elements of the scaling matrix indicated in the coded representation for the top-left M×N coefficients without zeroing out. 
     23. The method of example 17, wherein the scaling matrix is applied by sub-sampling by a ratio determined from the M and/or the N. 
     24. The method of example 23, wherein a region comprising the top-left M×N coefficients is split into multiple sub-regions, wherein a size of each sub-region is Uw*Uh, and wherein one element within each sub-region is signaled in the coded representation. 
     25. The method of example 23, wherein a number of the elements of the scaling matrix indicated in the coded representation for the K×L transform matrix is same as that indicated in the coded representation for the top-left M×N coefficients without zeroing out. 
     26. The method of any of example 17 to 25, wherein K=L=64, and wherein M=N=32. 
     27. The method of any of example 20 or 24, wherein K=L=64, wherein M=N=32, and wherein Uw=Uh=8. 
     28. A method of video processing, comprising: determining, during a conversion between a video block of a video and a coded representation of the video, based on a rule whether a single quantization matrix is to be used based on a size of the video block, wherein all video blocks having the size use the single quantization matrix; and performing the conversion using the quantization matrix. 
     29. The method of example 28, wherein the rule specifies that only the single quantization matrix is allowed in response to the size of the video block being smaller than W×H, where W and H are integers. 
     30. The method of example 28, wherein the rule specifies that only the single quantization matrix is allowed in response to a width of the video block is smaller than a threshold. 
     31. The method of example 28, wherein the rule specifies that only the single quantization matrix is allowed in response to a height of the video block is smaller than a threshold. 
     32. The method of example 28, wherein the rule specifies that the single quantization matrix is not applied to the video block having the size associated with a small size video block. 
     33. The method of any of examples 1 to 32, wherein a palette mode is applied to the video block. 
     34. The method of any of examples 1 to 33, wherein the conversion comprises encoding the video into the coded representation. 
     35. The method of any of examples 1 to 33, wherein the conversion comprises decoding the coded representation to generate pixel values of the video block. 
     36. A video decoding apparatus comprising a processor configured to implement a method recited in one or more of examples 1 to 35. 
     37. A video encoding apparatus comprising a processor configured to implement a method recited in one or more of examples 1 to 35. 
     38. A computer program product having computer code stored thereon, the code, when executed by a processor, causes the processor to implement a method recited in any of examples 1 to 35. 
     The disclosed and other solutions, examples, embodiments, modules and the functional operations described in this document can be implemented in digital electronic circuitry, or in computer software, firmware, or hardware, including the structures disclosed in this document and their structural equivalents, or in combinations of one or more of them. The disclosed and other embodiments can be implemented as one or more computer program products, i.e., one or more modules of computer program instructions encoded on a computer readable medium for execution by, or to control the operation of, data processing apparatus. The computer readable medium can be a machine-readable storage device, a machine-readable storage substrate, a memory device, a composition of matter effecting a machine-readable propagated signal, or a combination of one or more them. The term “data processing apparatus” encompasses all apparatus, devices, and machines for processing data, including by way of example a programmable processor, a computer, or multiple processors or computers. The apparatus can include, in addition to hardware, code that creates an execution environment for the computer program in question, e.g., code that constitutes processor firmware, a protocol stack, a database management system, an operating system, or a combination of one or more of them. A propagated signal is an artificially generated signal, e.g., a machine-generated electrical, optical, or electromagnetic signal, that is generated to encode information for transmission to suitable receiver apparatus. 
     A computer program (also known as a program, software, software application, script, or code) can be written in any form of programming language, including compiled or interpreted languages, and it can be deployed in any form, including as a stand-alone program or as a module, component, subroutine, or other unit suitable for use in a computing environment. A computer program does not necessarily correspond to a file in a file system. A program can be stored in a portion of a file that holds other programs or data (e.g., one or more scripts stored in a markup language document), in a single file dedicated to the program in question, or in multiple coordinated files (e.g., files that store one or more modules, sub programs, or portions of code). A computer program can be deployed to be executed on one computer or on multiple computers that are located at one site or distributed across multiple sites and interconnected by a communication network. 
     The processes and logic flows described in this document can be performed by one or more programmable processors executing one or more computer programs to perform functions by operating on input data and generating output. The processes and logic flows can also be performed by, and apparatus can also be implemented as, special purpose logic circuitry, e.g., an FPGA (field programmable gate array) or an ASIC (application specific integrated circuit). 
     Processors suitable for the execution of a computer program include, by way of example, both general and special purpose microprocessors, and any one or more processors of any kind of digital computer. Generally, a processor will receive instructions and data from a read only memory or a random-access memory or both. The essential elements of a computer are a processor for performing instructions and one or more memory devices for storing instructions and data. Generally, a computer will also include, or be operatively coupled to receive data from or transfer data to, or both, one or more mass storage devices for storing data, e.g., magnetic, magneto optical disks, or optical disks. However, a computer need not have such devices. Computer readable media suitable for storing computer program instructions and data include all forms of non-volatile memory, media and memory devices, including by way of example semiconductor memory devices, e.g., EPROM, EEPROM, and flash memory devices; magnetic disks, e.g., internal hard disks or removable disks; magneto optical disks; and CD ROM and DVD-ROM disks. The processor and the memory can be supplemented by, or incorporated in, special purpose logic circuitry. 
     While this patent document contains many specifics, these should not be construed as limitations on the scope of any subject matter or of what may be claimed, but rather as descriptions of features that may be specific to particular embodiments of particular techniques. Certain features that are described in this patent document in the context of separate embodiments can also be implemented in combination in a single embodiment. Conversely, various features that are described in the context of a single embodiment can also be implemented in multiple embodiments separately or in any suitable subcombination. Moreover, although features may be described above as acting in certain combinations and even initially claimed as such, one or more features from a claimed combination can in some cases be excised from the combination, and the claimed combination may be directed to a subcombination or variation of a subcombination. 
     Similarly, while operations are depicted in the drawings in a particular order, this should not be understood as requiring that such operations be performed in the particular order shown or in sequential order, or that all illustrated operations be performed, to achieve desirable results. Moreover, the separation of various system components in the embodiments described in this patent document should not be understood as requiring such separation in all embodiments. 
     Only a few implementations and examples are described and other implementations, enhancements and variations can be made based on what is described and illustrated in this patent document.