Picture coding method and picture decoding method

A coding and decoding system which includes a coding apparatus for coding picture data on a block-by-block basis and a decoding apparatus for decoding, on a block-by-block basis, a coded stream obtained by coding picture data on a block-by-block basis,

• wherein the coding apparatus includes:
• a picture data receiving unit operable to receive the picture data;
• a predicted error generating unit operable to generate a predicted error between a reference image and the received picture data, by referring to a motion vector of the received picture data;
• an orthogonal transformation size selecting unit operable to select, as orthogonal transformation sizes of all blocks included in the picture data on which orthogonal transformation should be performed, a first size or a mixture size of the first size and a second size, the first size being smaller than the second size;
• a predicted error transforming unit operable to orthogonally transform the predicted error of each block, among all blocks included in the picture data, having the selected orthogonal transformation size to obtain transformation coefficients;
• a quantizing unit operable to quantize the transformation coefficients using a quantization matrix corresponding to the selected orthogonal transformation size;
• a variable-length coding unit operable to variable-length code the quantized transformation coefficients to obtain a coded stream;
• and
• a size information inserting unit operable to insert, into the coded stream, size information indicating whether orthogonal transformation sizes of all blocks included in the picture data are the first size or the mixture of the first size and the second size,
• wherein, in the case where a motion compensation block size, which is used to perform motion compensation on the block on which orthogonal transformation should be performed, is smaller than the second size, only the first size is selected as the orthogonal transformation size in said orthogonal transformation size selecting unit;
• wherein said decoding apparatus includes:
• a size information obtaining unit operable to obtain, from the coded stream, size information indicating whether an inverse orthogonal transformation size of a block on which inverse orthogonal transformation should be performed is a first size or a mixture of the first size and a second size, wherein the first size is smaller than the second size;
• an inverse orthogonal transformation size deriving unit operable to derive the inverse orthogonal transformation size of the block on which inverse orthogonal transformation should be performed, based on the size information included in the coded stream;
• a variable length decoding unit operable to variable length decode coded data included in the coded stream to obtain transformation coefficients of each block;
• an inverse quantizing unit operable to inverse quantize the transformation coefficients of each block using a quantization matrix corresponding to the derived inverse orthogonal transformation size;
• and
• an inverse orthogonal transforming unit operable to inverse orthogonal transform the inverse quantized transform coefficients of each block, based on the derived inverse orthogonal transformation size,
• wherein, in the case where the size information indicates that the inverse orthogonal transformation size of the block on which inverse orthogonal transformation should be performed is a mixture of the first size and the second size and a motion compensation block size, which is used to perform motion compensation on the block on which inverse orthogonal transformation should be performed, is smaller than the second size, a subsequent inverse orthogonal transforming is performed using only the first size as the inverse orthogonal transformation size.