Encoder, decoder, encoding method, and decoding method

A decoder comprising:

• circuitry;
• and
• memory,
• wherein the circuitry, using the memory, performs:
• decoding a signal which indicates whether a non-separable inverse transform is performed or not from a bitstream;
• generating first transform coefficients by performing the non-separable inverse-transform on the second transform coefficients when it is determined that the non-separable inverse-transform is to be performed for the current block;
• and
• generating residuals by performing a horizontal inverse-transform and a vertical inverse-transform on the first transform coefficients using a horizontal inverse-transform basis and a vertical inverse-transform basis, respectively, when it is determined that the horizontal inverse-transform and the vertical inverse-transform are to be performed for the current block,
• wherein (i) when it is determined that a selection of a transform basis based on a size of the current block is performed for the current block, the circuitry performs, before performing the horizontal inverse-transform and the vertical inverse-transform:
• selecting a first inverse-transform basis, as the horizontal inverse-transform basis, from among inverse-transform basis candidates when a horizontal size of the current block is a first horizontal size that is greater than a threshold size;
• selecting a second inverse-transform basis, as the horizontal inverse-transform basis, from among the inverse-transform basis candidates when the horizontal size of the current block is a second horizontal size that is smaller than or equal to the threshold size, the second inverse-transform basis being different from the first inverse-transform basis;
• selecting the first inverse-transform basis, as the vertical inverse-transform basis, from among the inverse-transform basis candidates when a vertical size of the current block is a first vertical size that is greater than the threshold size;
• and
• selecting the second inverse-transform basis, as the vertical inverse-transform basis, from among the inverse-transform basis candidates when the vertical size of the current block is a second vertical size that is smaller than or equal to the threshold size, and
• wherein (ii) when the non-separable inverse-transform is performed for the current block, a basic inverse-transform basis is selected as the vertical inverse-transform basis and the horizontal inverse-transform basis.

An encoding method comprising:

• generating first transform coefficients by performing a horizontal transform and a vertical transform on residuals using a horizontal transform basis and a vertical transform basis, respectively, when it is determined that the horizontal transform and the vertical transform are to be performed for the current block;
• generating second transform coefficients by performing a non-separable transform on the first transform coefficients when it is determined that the non-separable transform is to be performed for the current block;
• and
• encoding a signal which indicates whether the non-separable transform is performed or not,
• wherein (i) when it is determined that a selection of a transform basis based on a size of the current block is performed for the current block, the encoding method further comprising, before performing the horizontal transform and the vertical transform:
• selecting a first transform basis, as the horizontal transform basis, from among transform basis candidates when a horizontal size of the current block is a first horizontal size that is greater than a threshold size;
• selecting a second transform basis, as the horizontal transform basis, from among the transform basis candidates when the horizontal size of the current block is a second horizontal size that is smaller than or equal to the threshold size, the second transform basis being different from the first transform basis;
• selecting the first transform basis, as the vertical transform basis, from among the transform basis candidates when a vertical size of the current block is a first vertical size that is greater than the threshold size;
• and
• selecting the second transform basis, as the vertical transform basis, from among the transform basis candidates when the vertical size of the current block is a second vertical size that is smaller than or equal to the threshold size, and
• wherein (ii) when the non-separable transform is performed for the current block, a basic transform basis is selected as the vertical transform basis and the horizontal transform basis.

A decoding method comprising:

• decoding a signal which indicates whether a non-separable inverse transform is performed or not from a bitstream;
• generating first transform coefficients by performing the non-separable inverse-transform on second transform coefficients when it is determined that the non-separable inverse-transform is to be performed for the current block;
• and
• generating residuals by performing a horizontal inverse-transform and a vertical inverse-transform on the first transform coefficients using a horizontal inverse-transform basis and a vertical inverse-transform basis, respectively, when it is determined that the horizontal inverse-transform and the vertical inverse-transform are to be performed for the current block,
• wherein (i) when it is determined that a selection of a transform basis based on a size of the current block is performed for the current block, the circuitry performs, before performing the horizontal inverse-transform and the vertical inverse-transform:
• selecting a first inverse-transform basis, as the horizontal inverse-transform basis, from among inverse-transform basis candidates when a horizontal size of the current block is a first horizontal size that is greater than a threshold size;
• selecting a second inverse-transform basis, as the horizontal inverse-transform basis, from among the inverse-transform basis candidates when the horizontal size of the current block is a second horizontal size that is smaller than or equal to the threshold size, the second inverse-transform basis being different from the first inverse-transform basis;
• selecting the first inverse-transform basis, as the vertical inverse-transform basis, from among the inverse-transform basis candidates when a vertical size of the current block is a first vertical size that is greater than the threshold size;
• and
• selecting the second inverse-transform basis, as the vertical inverse-transform basis, from among the inverse-transform basis candidates when the vertical size of the current block is a second vertical size that is smaller than or equal to the threshold size, and
• wherein (ii) when the non-separable inverse-transform is performed for the current block, a basic inverse-transform basis is selected as the vertical inverse-transform basis and the horizontal inverse-transform basis.