Transmitting apparatus, encoding method thereof, receiving apparatus, and decoding method thereof

A receiving apparatus comprising:

• a frame decoder configured to divide a plurality of frames received from a signal transmitted by a transmitting apparatus into a plurality of frame groups and provide Reed Solomon (RS)-decoded frames by RS-decoding each of the plurality of frame groups in a vertical direction for error correction,
• wherein, if a number of the RS-decoded frames is greater than a maximum number of frames that can be generated by RS encoding in a predetermined Galois field, the frame decoder determines a number of the plurality of frame groups based on a number of the RS-decoded frames and the maximum number of frames that can be generated by RS decoding in a predetermined Galois field, and divides the plurality of frames into the plurality of frame groups based on the determined number of the plurality of frame groups, and
• wherein the vertical direction is perpendicular to a direction in which bits are arranged in a frame of the plurality of frames, and
• wherein the frame decoder is configured to calculate the number of the plurality of frame groups using a mathematical formula as below:
• B
• =
• ⌊
• N
• N
• ′
• ⌋
• +
• 1
• ,
• where B is the number of the plurality of frame groups, N is the number of the RS-decoded frames, and N′ is the maximum number of the frames that can be generated by RS encoding in the predetermined Galois field.

An encoding method comprising:

• dividing a plurality of frames into a plurality of frame groups;
• providing Reed Solomon (RS)-encoded frames by RS encoding each of the plurality of frame groups in a vertical direction for error correction;
• and
• transmitting a signal which is generated based on the RS-encoded frames,
• wherein, if a number of the RS-encoded frames is greater than a maximum number of frames that can be generated by RS encoding in a predetermined Galois field, the dividing determines a number of the plurality of frame groups based on a number of the RS-encoded frames and the maximum number of frames that can be generated by RS encoding in a predetermined Galois field, and divides the plurality of frames into the plurality of frame groups based on the determined number of the plurality of frame groups, and
• wherein the vertical direction is perpendicular to a direction in which bits are arranged in a frame of the plurality of frames, and
• wherein the dividing comprises calculating the number of the plurality of frame groups using a mathematical formula as below:
• B
• =
• ⌊
• N
• N
• ′
• ⌋
• +
• 1
• ,
• where B is the number of the plurality of frame groups, N is the number of the RS-encoded frames, and N′ is the maximum number of the frames that can be generated by RS encoding in the predetermined Galois field.

A decoding method comprising:

• dividing a plurality of frames received from a signal transmitted by a transmitting apparatus into a plurality of frame groups;
• and
• provide Reed Solomon (RS)-decoded frames by RS decoding each of the plurality of frame groups in a vertical direction for error correction,
• wherein, if a number of the RS-decoded frames is greater than a maximum number of frames that can be generated by RS decoding in a predetermined Galois field, the dividing determines a number of the plurality of frame groups based on a number of the RS-decoded frames and the maximum number of frames that can be generated by RS decoding in a predetermined Galois field, and divides the plurality of frames into the plurality of frame groups based on the determined number of the plurality of frame groups, and
• wherein the vertical direction is perpendicular to a direction in which bits are arranged in a frame of the plurality of frames;
• wherein the dividing comprises calculating the number of the plurality of frame groups using a mathematical formula as below:
• B
• =
• ⌊
• N
• N
• ′
• ⌋
• +
• 1
• ,
• where B is the number of the plurality of frame groups, N is the number of the RS-decoded frames, and N′ is the maximum number of the frames that can be generated by RS encoding in the predetermined Galois field.