`
`1. A decoder that decodes an image, the decoder comprising:
`
`circuitry; and
`
`memory coupled to the circuitry, wherein
`
`5
`
`in operation, the circuitry:
`
`splits a current picture to be decoded into two or moretiles; and
`
`decodes the current picture by performing the decoding on a
`
`slice, the slice being rectangular-shaped, the slice being made up of one or more
`
`tiles or a part of a tile obtained by thesplitting,
`
`10
`
`in the decoding of
`
`the current picture,
`
`the circuitry sets first
`
`information on a region in a predetermined mannerwithoutretrieving the first
`
`information from header information, the region being occupied by a slice
`
`located at a lower-right corner of the current picture, and
`
`the first information is not included in the header information.
`
`15
`
`20
`
`25
`
`2. The decoder according to claim 1, wherein
`
`the first
`
`information is
`
`information indicating a position of a
`
`lower-right corner of the slice located at the lower-right corner of the current
`
`picture.
`
`3. The decoder according to claim 1, wherein
`
`the first
`
`information is information indicating a position of an
`
`upper-left corner and a position of a lower-right cornerof the slice located at the
`
`lower-right corner of the current picture.
`
`4. The decoder according to claim 1, wherein
`
`the first information is information represented by syntax.
`
`153
`
`
`
`5. The decoder according to claim 1, wherein
`
`in operation, the circuitry further
`
`in the decoding of the current picture, decodes position information of
`
`an upper-left corner of a slice located at the beginning of the current picture
`
`from information indicating a position of an upper-left corner of the current
`
`picture, the information indicating the position of the upper-left corner of the
`
`current picture being included in the header information.
`
`10
`
`6. The decoder according to claim 1, wherein
`
`the predetermined manneris
`
`calculating the first information using second information included in
`
`the header information and different from the first information.
`
`15
`
`7. The decoder according to claim 6, wherein
`
`the second information is a tile index or a tile index difference included
`
`in the header information.
`
`8. The decoder according to claim 7, wherein
`
`20
`
`the tile index difference is a difference between (i) a tile index ofa tile
`
`located at an upper-left corner of the slice located at the lower-right corner of
`
`the current picture and(i) a tile indexofa tile located at a lower-right corner of
`
`the slice located at the lower-right cornerof the current picture.
`
`25
`
`9. A decoding method of decoding an image,
`
`the decoding method
`
`comprising:
`
`splitting a current picture to be decoded into two or moretiles; and
`
`154
`
`
`
`decoding the current picture by performing the decoding onaslice, the
`
`slice being rectangular-shaped, the slice being made up of one or moretiles or a
`
`part of a tile obtained by the splitting, wherein
`
`the decoding of the current picture includes setting first information on
`
`a region in a predetermined manner without retrieving the first information
`
`from header information, the region being occupied by a slice located at a
`
`lower-right corner of the current picture, and
`
`the first information is not included in the header information.
`
`10
`
`10. A decoder comprising:
`
`memory; and
`
`a processor coupled to the memory and configured to:
`
`split a current picture into tiles;
`
`generate a slice having a rectangular shape and located at a
`
`15
`
`lower-right corner of the current picture, the slice including at least a part of a
`
`tile amongthetiles;
`
`generate first information on a region of the slice with header
`
`information, the header information not including information identical to the
`
`first information; and
`
`20
`
`decode the slice with the first information.
`
`11. The decoder according to claim 10, wherein the processor is
`
`configured to generate the first information with second information which is
`
`different from the first information and which is included in the header
`
`25
`
`information.
`
`12. The decoder according to claim 11, wherein the second information
`
`155
`
`
`
`indicates one of a tile index and a difference of tile indices.
`
`13. The decoder according to claim 12, wherein the difference is a
`
`difference between (i) a first tile index of a first tile located at an upper-left
`
`corner of the slice and Gi) a second tile index of a second tile located at a
`
`lower-right corner of theslice.
`
`156
`
`
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