Image coding method, image coding apparatus, image decoding method and image decoding apparatus

An encoding and decoding apparatus, comprising:

• an encoding apparatus which encodes first last position information indicating a horizontal position and a vertical position of a last non-zero coefficient in a predetermined order from among a plurality of coefficients within a first current block to be encoded in a first picture;
• and
• a decoding apparatus which decodes second last position information indicating a horizontal position and a vertical position of a last non-zero coefficient in a predetermined order from among a plurality of coefficients within a second current block to be decoded in a second picture,
• wherein the encoding apparatus includes:
• one or more first processors;
• and
• a first memory accessible from the one or more first processors,
• wherein the one or more first processors executes, using the first memory, encoding processes including:
• binarizing a horizontal component of the first last position information and a vertical component of the first last position information into a first binary signal and a second binary signal, respectively, the horizontal component indicating the horizontal position of the last non-zero coefficient within the first current block, the vertical component indicating the vertical position of the last non-zero coefficient within the first current block;
• encoding a first partial signal and a second partial signal respectively into an encoded first partial signal and an encoded second partial signal, by first arithmetic encoding, the first partial signal being a part of the first binary signal, the second partial signal being a part of the second binary signal;
• encoding a third partial signal and a fourth partial signal respectively into an encoded third partial signal and an encoded fourth partial signal, by second arithmetic encoding, the second arithmetic encoding being different from the first arithmetic encoding, the third partial signal being another part of the first binary signal, the fourth partial signal being another part of the second binary signal;
• and
• arranging the encoded first partial signal, the encoded second partial signal, the encoded third partial signal, and the encoded fourth partial signal, in this order, and
• wherein the decoding apparatus includes:
• one or more second processors;
• and
• a second memory accessible from the one or more second processors,
• wherein the one or more second processors executes, using the second memory, decoding processes including:
• obtaining a second bitstream including a fifth partial signal, a sixth partial signal, a seventh partial signal, and an eighth partial signal, in this order;
• performing first arithmetic decoding on the fifth partial signal and the seventh partial signal, respectively, to obtain a decoded fifth partial signal and a decoded seventh partial signal;
• performing second arithmetic decoding on the sixth partial signal and the eighth partial signal, respectively, to obtain a decoded sixth partial signal and a decoded eighth partial signal, the second arithmetic decoding being different from the first arithmetic decoding;
• deriving a horizontal component of the second last position information from the decoded fifth partial signal and the decoded seventh partial signal, the horizontal component indicating the horizontal position of the last non-zero coefficient within the second current block;
• and
• deriving a vertical component of the second last position information from the decoded sixth partial signal and the decoded eighth partial signal, the vertical component indicating the vertical position of the last non-zero coefficient within the second current block.