Abstract: An encoder includes: circuitry; and memory coupled to the circuitry. In the encoder, in operation, the circuitry: performs calculation that involves multiplication and from which a plurality of discrete integers are yieldable as a calculation result, to derive one of the plurality of discrete integers as a quantization parameter threshold; and when orthogonal transform is skipped for a current block of an image, determines a quantization parameter value for the current block, using the quantization parameter threshold. The calculation involves multiplying a first value by a first fixed value, the first value and the first fixed value being each an integer. The first value is a limit value to be included in a header of a bitstream.

Abstract: A decoder includes circuitry which, in operation, parses a first flag indicating whether a CCALF (cross component adaptive loop filtering) process is enabled for a first block located adjacent to a left side of a current block; parses a second flag indicating whether the CCALF process is enabled for a second block located adjacent to an upper side of the current block; determines a first index associated with a color component of the current block; and derives a second index indicating a context model, using the first flag, the second flag, and the first index. The circuitry, in operation, performs entropy decoding of a third flag indicating whether the CCALF process is enabled for the current block, using the context model indicated by the second index; and performs the CCALF process on the current block in response to the third flag indicating the CCALF process is enabled for the current block.

Abstract: An encoder includes circuitry and memory coupled to the circuitry. The circuitry, in operation: determines whether a size of a current block, which is a unit for which a vector candidate list including vector candidates is generated, is less than or equal to a threshold; when the size of the current block is less than or equal to the threshold, generates the vector candidate list by registering a history-based motion vector predictor (HMVP) vector candidate in the vector candidate list from an HMVP table without performing a first pruning process; when the size of the current block is greater than the threshold, generates the vector candidate list by performing the first pruning process and registering the HMVP vector candidate in the vector candidate list from the HMVP table; and encodes the current block using the vector candidate list.

Abstract: An encoder includes circuitry and memory coupled to the circuitry. In operation, the circuitry writes, into a bitstream, a first flag indicating whether or not to enable a first process of applying a filter to a first image to generate a second image, holding the second image as a reference image, and displaying the second image. When the first process is not enabled, circuitry writes, into the bitstream, one or more parameters for controlling a second process of applying the filter to the first image to generate the second image, holding the first image as a reference image, and displaying the second image.

Abstract: A decoder includes circuitry which, in operation, parses a first flag indicating whether a CCALF (cross component adaptive loop filtering) process is enabled for a first block located adjacent to a left side of a current block; parses a second flag indicating whether the CCALF process is enabled for a second block located adjacent to an upper side of the current block; determines a first index associated with a color component of the current block; and derives a second index indicating a context model, using the first flag, the second flag, and the first index. The circuitry, in operation, performs entropy decoding of a third flag indicating whether the CCALF process is enabled for the current block, using the context model indicated by the second index; and performs the CCALF process on the current block in response to the third flag indicating the CCALF process is enabled for the current block.

Abstract: An encoder includes circuitry which generates a first coefficient value by applying a CCALF process to a first reconstructed image sample of a luma component; generates a second coefficient value by applying an ALF process to a second reconstructed image sample of a chroma component; generates a third coefficient value by adding the first coefficient value to the second coefficient value; and encodes a third reconstructed image sample of the chroma component using the third coefficient value. The circuitry writes a first parameter into a sequence parameter set; writes a second parameter into a parameter set of a picture in response to a value of the first parameter being 1; writes a third parameter into a slice header in response to the value of the first parameter being 1; and writes a fourth parameter into a coding tree unit in response to a value of the third parameter being 1.

Abstract: A decoder includes memory and a processor coupled to the memory and configured to: generate a first coefficient value by applying a CCALF (cross component adaptive loop filtering) process to a first reconstructed image sample of a luma component; clip the first coefficient value such that the clipped first coefficient value is within a first range from ?27 to 27?1; generate a second coefficient value by applying an ALF (adaptive loop filtering) process to a second reconstructed image sample of a chroma component; clip the second coefficient value such that the clipped second coefficient value is within a second range different from the first range; generate a third coefficient value by adding the clipped first coefficient value to the clipped second coefficient value; and generate a third reconstructed image sample of the chroma component using the third coefficient value.

Abstract: An encoder includes circuitry and memory coupled to the circuitry. The circuitry, in operation, generates a first coefficient value by applying a CCALF (cross component adaptive loop filtering) process to a first reconstructed image sample of a luma component, and generates a second coefficient value by applying an ALF (adaptive loop filtering) process to a second reconstructed image sample of a chroma component. The circuitry modifies the first coefficient value by performing an arithmetic right shift by 7 bits on the first coefficient value. The circuitry generates a third coefficient value by adding the modified first coefficient value to the second coefficient value, and encodes a third reconstructed image sample of the chroma component using the third coefficient value.

Abstract: An encoder includes circuitry and memory coupled to the circuitry. The circuitry, in operation, generates a first coefficient value by applying a CCALF (cross component adaptive loop filtering) process to a first reconstructed image sample of a luma component, and generates a second coefficient value by applying an ALF (adaptive loop filtering) process to a second reconstructed image sample of a chroma component. The circuitry modifies the first coefficient value by performing an arithmetic right shift by 7 bits on the first coefficient value. The circuitry generates a third coefficient value by adding the modified first coefficient value to the second coefficient value, and encodes a third reconstructed image sample of the chroma component using the third coefficient value.

Abstract: A decoder includes memory and a processor coupled to the memory and configured to: generate a first coefficient value by applying a CCALF (cross component adaptive loop filtering) process to a first reconstructed image sample of a luma component; clip the first coefficient value such that the clipped first coefficient value is within a first range from ?27 to 27?1; generate a second coefficient value by applying an ALF (adaptive loop filtering) process to a second reconstructed image sample of a chroma component; clip the second coefficient value such that the clipped second coefficient value is within a second range different from the first range; generate a third coefficient value by adding the clipped first coefficient value to the clipped second coefficient value; and generate a third reconstructed image sample of the chroma component using the third coefficient value.

Abstract: An encoder includes circuitry and memory coupled to the circuitry. The circuitry: executes a second process of applying a second filter to the first image to generate a second image, not holding the second image as a reference image, holding the first image as a reference image, and displaying the second image; writes coefficients of each of one or more filter candidates that are candidates for the second filter into a bitstream, wherein the coefficients are included in a first storage location when written into the bitstream; and writes a parameter that specifies, for each image, one of the one or more filter candidates as the second filter into the bitstream, wherein the parameter is included in a second storage location when written into the bitstream, and the second storage location is different from the first storage location.

Abstract: An encoder: includes circuitry, and memory coupled to the circuitry; stores a first parameter into a bitstream, the first parameter indicating whether a syntax element related to a chroma tool offset is present in the bitstream; when the first parameter indicates that the syntax element is present in the bitstream, (i) stores, in the bitstream, one or more second parameters that are used in deblocking filtering for a chroma sample of a current image, in addition to the syntax element, (ii) performs the deblocking filtering using the one or more second parameters, and (iii) encodes the current image; and when the first parameter indicates that the syntax element is not present in the bitstream, encodes the current image without storing the one or more second parameters into the bitstream.

Abstract: An encoder includes circuitry and memory. The circuitry, in operation, generates a first coefficient value by applying a CCALF (cross component adaptive loop filtering) process to a first reconstructed image sample of a luma component. The circuitry generates a second coefficient value by applying an ALF (adaptive loop filtering) process to a second reconstructed image sample of a chroma component. The circuitry generates a third coefficient value by adding the first coefficient value to the second coefficient value, and encodes a third reconstructed image sample of the chroma component using the third coefficient value. In the CCALF process, in response to a coordinate of the second reconstructed image sample being (x, y), coordinates of the first reconstructed image samples are (2x, 2y?1), (2x?1, 2y), (2x, 2y), (2x+1, 2y), (2x?1, 2y+1), (2x, 2y+1), (2x+1, 2y+1), and (2x, 2y+2).

Abstract: An encoder includes circuitry and memory. The circuitry, in operation, generates a first coefficient value by applying a CCALF (cross component adaptive loop filtering) process to a first reconstructed image sample of a luma component. The circuitry generates a second coefficient value by applying an ALF (adaptive loop filtering) process to a second reconstructed image sample of a chroma component. The circuitry generates a third coefficient value by adding the first coefficient value to the second coefficient value, and encodes a third reconstructed image sample of the chroma component using the third coefficient value. In the CCALF process, in response to a coordinate of the second reconstructed image sample being (x, y), coordinates of the first reconstructed image samples are (2x, 2y?1), (2x?1, 2y), (2x, 2y), (2x+1, 2y), (2x?1, 2y+1), (2x, 2y+1), (2x+1, 2y+1), and (2x, 2y+2).

Abstract: An encoder includes circuitry and memory coupled to the circuitry. The circuitry: executes a second process of applying a second filter to the first image to generate a second image, not holding the second image as a reference image, holding the first image as a reference image, and displaying the second image; writes coefficients of each of one or more filter candidates that are candidates for the second filter into a bitstream, wherein the coefficients are included in a first storage location when written into the bitstream; and writes a parameter that specifies, for each image, one of the one or more filter candidates as the second filter into the bitstream, wherein the parameter is included in a second storage location when written into the bitstream, and the second storage location is different from the first storage location.

Abstract: An encoder includes circuitry and memory coupled to the circuitry. In operation, the circuitry: encodes information for deriving a parameter into a header of a bitstream; filters reconstructed samples in a first image using a filtering process, to generate a second image; determines whether the parameter has a predefined value; encodes a third image using the second image when the parameter has the predefined value; and encodes the third image using the first image when the parameter does not have the predefined value.

Abstract: An encoder includes circuitry and memory coupled to the circuitry. The circuitry, in response to a first reconstructed image sample being located outside a virtual boundary, duplicates a reconstructed sample located inside and adjacent to the virtual boundary to generate the first reconstructed image sample. The circuitry generates a first coefficient value by applying a CCALF (cross component adaptive loop filtering) process to the first reconstructed image sample of a luma component. The circuitry generates a second coefficient value by applying an ALF (adaptive loop filtering) process to a second reconstructed image sample of a chroma component. The circuitry generates a third coefficient value by adding the first coefficient value to the second coefficient value, and encodes a third reconstructed image sample of the chroma component using the third coefficient value.

Abstract: An encoder includes circuitry and memory coupled to the circuitry. The circuitry, in operation, generates a first coefficient value by applying a CCALF (cross component adaptive loop filtering) process to a first reconstructed image sample of a luma component, generates a second coefficient value by applying an ALF (adaptive loop filtering) process to a second reconstructed image sample of a chroma component, and clips the second coefficient value. The circuitry generates a third coefficient value by adding the first coefficient value to the clipped second coefficient value, and clips the third coefficient value. The circuitry encodes a third reconstructed image sample of the chroma component using the clipped third coefficient value.

Abstract: An encoder includes circuitry and memory. The circuitry, in operation, generates a first coefficient value by applying a CCALF (cross component adaptive loop filtering) process to a first reconstructed image sample of a luma component. The circuitry generates a second coefficient value by applying an ALF (adaptive loop filtering) process to a second reconstructed image sample of a chroma component. The circuitry generates a third coefficient value by adding the first coefficient value to the second coefficient value, and encodes a third reconstructed image sample of the chroma component using the third coefficient value. The circuitry determines a first parameter having the same value for Cb component and Cr component of the chroma component. The circuitry determines, using the first parameter, a model of entropy coding from a plurality of models. The circuitry performs, using the model, the entropy coding of a second parameter of the CCALF process.

Abstract: An encoder includes circuitry and memory. The circuitry, in operation, generates a first coefficient value by applying a CCALF (cross component adaptive loop filtering) process to a first reconstructed image sample of a luma component. The circuitry generates a second coefficient value by applying an ALF (adaptive loop filtering) process to a second reconstructed image sample of a chroma component. The circuitry generates a third coefficient value by adding the first coefficient value to the second coefficient value, and encodes a third reconstructed image sample of the chroma component using the third coefficient value. In the CCALF process, in response to a coordinate of the second reconstructed image sample being (x, y), coordinates of the first reconstructed image samples are (2x, 2y?1), (2x?1, 2y), (2x, 2y), (2x+1, 2y), (2x?1, 2y+1), (2x, 2y+1), (2x+1, 2y+1), and (2x, 2y+2).