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

1. An apparatus for decoding last position information indicating a horizontal position and a vertical position of a last non-zero coefficient in a predetermined order within a current block to be decoded, the current block being included in a picture and including a plurality of coefficients, the apparatus comprising:

one or more processors;

a communication unit; and

storage coupled to the one or more processors and the communication unit;

wherein the communication unit is configured to:

transmit a request for a bitstream to an external system; and

receive the bitstream from the external system; and

wherein the one or more processors are configured to:

obtain the bitstream including a first partial signal, a second partial signal, a third partial signal, and a fourth partial signal, in this order;

perform first arithmetic decoding on a first partial signal and a third partial signal, respectively, to obtain a decoded first partial signal and a decoded third partial signal, wherein in the first arithmetic decoding, decoding is performed on the third partial signal when the first partial signal indicates a greater value than a predetermined value;

perform second arithmetic decoding on a second partial signal and a fourth partial signal, respectively, to obtain a decoded second partial signal and a decoded fourth partial signal, the second arithmetic decoding being different from the first arithmetic decoding, wherein in the second arithmetic decoding, decoding is performed on the fourth partial signal when the second partial signal indicates a greater value than the predetermined value;

derive a horizontal component of the last position information indicating the horizontal position of the non-zero coefficient from the decoded first partial signal and the decoded third partial signal; and

derive a vertical component of the last position information indicating the vertical position of the non-zero coefficient from the decoded second partial signal and the decoded fourth partial signal.

2. A system for decoding last position information indicating a horizontal position and a vertical position of a last non-zero coefficient in a predetermined order within a current block to be decoded, the current block being included in a picture and including a plurality of coefficients, the system comprising:

a first apparatus;

a second apparatus coupled to the first apparatus; and

a display coupled to the second apparatus;

wherein the first apparatus is configured to perform operations for transmitting a request for a bitstream to an external apparatus and letting the second apparatus receive the bitstream;

wherein the second apparatus includes:

one or more processors; and

storage coupled to the one or more processors, the one or more processors being configured to perform operations for:

obtaining the bitstream including a first partial signal, a second partial signal, a third partial signal, and a fourth partial signal, in this order;

performing first arithmetic decoding on a first partial signal and a third partial signal, respectively, to obtain a decoded first partial signal and a decoded third partial signal, wherein in the first arithmetic decoding, decoding is performed on the third partial signal when the first partial signal indicates a greater value than a predetermined value;

performing second arithmetic decoding on a second partial signal and a fourth partial signal, respectively, to obtain a decoded second partial signal and a decoded fourth partial signal, the second arithmetic decoding being different from the first arithmetic decoding, wherein in the second arithmetic decoding, decoding is performed on the fourth partial signal when the second partial signal indicates a greater value than the predetermined value;

deriving a horizontal component of the last position information indicating the horizontal position of the non-zero coefficient from the decoded first partial signal and the decoded third partial signal;

deriving a vertical component of the last position information indicating the vertical position of the non-zero coefficient from the decoded second partial signal and the decoded fourth partial signal; and

generating a reconstructed picture of the current block;

wherein the display is configured to display the reconstructed picture.

3. A displaying method using a communication system, the displaying method comprising:

transmitting a request for a bitstream including an encoded picture;

receiving the bitstream from an external apparatus through a network;

obtaining a bitstream including a first partial signal, a second partial signal, a third partial signal, and a fourth partial signal, in this order;

performing first arithmetic decoding on a first partial signal and a third partial signal, respectively, to obtain a decoded first partial signal and a decoded third partial signal, wherein in the first arithmetic decoding, decoding is performed on the third partial signal when the first partial signal indicates a greater value than a predetermined value;

performing second arithmetic decoding on a second partial signal and a fourth partial signal, respectively, to obtain a decoded second partial signal and a decoded fourth partial signal, the second arithmetic decoding being different from the first arithmetic decoding, wherein in the second arithmetic decoding, decoding is performed on the fourth partial signal when the second partial signal indicates a greater value than the predetermined value;

deriving a horizontal component of a last position information indicating a horizontal position of a non-zero coefficient which is last in a predetermined order, from the decoded first partial signal and the decoded third partial signal;

deriving a vertical component of a last position information indicating a vertical position of the non-zero coefficient, from the decoded second partial signal and the decoded fourth partial signal;

generating a reconstructed picture of the current block; and

displaying the reconstructed picture.