Encoding method, decoding method, encoder, and decoder

An encoder comprising:

• circuitry;
• and
• memory,
• wherein, using the memory, the circuitry:
• derives a residual signal of a current block;
• performs, depending on a size of the current block, either (i) a primary transform on the residual signal and a secondary transform on a result of the primary transform, or (ii) a primary transform on the residual signal and a secondary transform on a part of the result of the primary transform, the secondary transform being performed using a secondary transform basis selected from among secondary transform basis candidates;
• quantizes a result of the secondary transform;
• encodes a result of the quantization to generate coded data;
• and
• generates a bitstream including the coded data,
• wherein the secondary transform is a non-separable transform.

A decoding method comprising:

• inverse quantizing quantized coefficients of a current block;
• performing, depending on a size of the current block, either (i) an inverse secondary transform on a part of a result of the inverse quantization and an inverse primary transform on a result of the inverse secondary transform and another part of the result of the inverse quantization, or (ii) the inverse secondary transform on the result of the inverse quantization and the inverse primary transform on the result of the inverse secondary transform, the inverse secondary transform being performed using an inverse secondary transform basis selected from among inverse secondary transform basis candidates;
• and
• deriving an image based on a residual signal derived from a result of the inverse primary transform,
• wherein the inverse secondary transform is a non-separable transform.

An encoding method comprising:

• deriving a residual signal of a current block;
• performing, depending on a size of the current block, either (i) a primary transform on the residual signal and a secondary transform on a result of the primary transform, or (ii) a primary transform on the residual signal and a secondary transform on a part of the result of the primary transform, the secondary transform being performed using a secondary transform basis selected from among secondary transform basis candidates;
• quantizing a result of the secondary transform;
• encoding a result of the quantization to generate coded data;
• and
• generating a bitstream including the coded data,
• wherein the secondary transform is a non-separable transform.

A non-transitory computer readable medium storing a bitstream and computer-executable instructions, the bitstream including coded data of a current block and signals according to which the computer-executable instructions cause a decoder to perform a decoding method comprising:

• inverse quantizing quantized coefficients of the current block;
• performing, depending on a size of the current block, either (i) an inverse secondary transform on a part of a result of the inverse quantization and an inverse primary transform on a result of the inverse secondary transform and another part of the result of the inverse quantization, or (ii) the inverse secondary transform on the result of the inverse quantization and the inverse primary transform on the result of the inverse secondary transform, the inverse secondary transform being performed using an inverse secondary transform basis selected from among inverse secondary transform basis candidates;
• and
• deriving an image based on a residual signal derived from a result of the inverse primary transform,
• wherein the inverse secondary transform is a non-separable transform.

A method of transmitting a bitstream, the method comprising:

• deriving a residual signal of a current block;
• performing, depending on a size of the current block, either (i) a primary transform on the residual signal and a secondary transform on a result of the primary transform, or (ii) a primary transform on the residual signal and a secondary transform on a part of the result of the primary transform, the secondary transform being performed using a secondary transform basis selected from among secondary transform basis candidates;
• quantizing a result of the secondary transform;
• encoding a result of the quantization to generate coded data;
• generating a bitstream including the coded data;
• and
• transmitting the bitstream,
• wherein the secondary transform is a non-separable transform.