Variable length coding method and variable length decoding method

A picture coding and decoding system comprising:

• a picture coding apparatus which performs arithmetic coding, on a block basis, on coefficients of a two-dimensional array of first frequency components;
• and a picture decoding apparatus which performs arithmetic decoding, on a block basis, on the coefficients of a two-dimensional array of second frequency components, the coefficients being generated by frequency transformation performed on picture data of a block which has a 4×4 size of pixels,
• wherein the picture coding apparatus includes:
• a converting unit operable to, for each of non-zero coefficients of a first block, (i) convert a value of the non-zero coefficient into an absolute value and a sign code and (ii) convert the absolute value of the non-zero coefficient into binary data;
• and
• a coding unit operable to, for each of the non-zero coefficients of the first block, (i) perform a coding process on the sign code of the non-zero coefficient, (ii) perform first arithmetic coding on a first bit of the binary data of the non-zero coefficient, and (iii) perform second arithmetic coding on a bit other than the first bit of the binary data of the non-zero coefficient,
• wherein the first arithmetic coding is performed on a block basis according to a predetermined scanning order starting at a high frequency component toward a low frequency component by switching a plurality of first probability tables,
• wherein the second arithmetic coding is performed on a block basis according to the predetermined scanning order starting at a high frequency component toward a low frequency component by switching a plurality of second probability tables,
• wherein the switching of the plurality of first probability tables includes switching a first probability table to a new first probability table based on a result of a comparison between an absolute value of a target non-zero coefficient to be coded and a predetermined threshold value,
• wherein the switching of the plurality of second probability tables includes switching a second probability table to a new second probability table based on a result of a comparison between an absolute value of a target non-zero coefficient to be coded and the predetermined threshold value,
• wherein the coding process of the sign code is performed independently of the first arithmetic coding and the second arithmetic coding,
• wherein the number of the plurality of first probability tables is the same as the number of the plurality of second probability tables, and the switching of the first probability table can be performed in a different timing from the switching of the second probability table,
• wherein, in the switching of the first probability table, the switching between the plurality of first probability tables is performed in one direction such that the first probability table, which has been used before the new first probability table, is not used after switching to the new first probability table,
• wherein, in the switching of the second probability table, the switching between the plurality of second probability tables is performed in one direction such that the second probability table, which has been used before the new second probability table, is not used after switching to the new second probability table,
• wherein the picture decoding apparatus includes:
• a decoding unit operable to, for each of non-zero coefficients of a second block, (i) perform a decoding process on a sign code of the non-zero coefficient, (ii) perform first arithmetic decoding on a first bit of binary data corresponding to an absolute value of the non-zero coefficient, and (iii) perform second arithmetic decoding on a bit other than the first bit of the binary data corresponding to the absolute value of the non-zero coefficient;
• a combining unit operable to, for each of the non-zero coefficients of the second block, (i) combine the first bit of the binary data and the bit other than the first bit of the binary data into the absolute value of the non-zero coefficient and (ii) combine the absolute value of the non-zero coefficient and the sign code of the non-zero coefficient into a value of the non-zero coefficient;
• and
• a coefficient arranging unit operable to arrange, on a block basis, the values of the non-zero coefficients into the two-dimensional array of frequency components,
• wherein the first arithmetic decoding on the first bit of the binary data is performed on a block basis according to a predetermined scanning order starting at a high frequency component toward a low frequency component by switching a plurality of third probability tables,
• wherein the second arithmetic decoding on a bit other than the first bit of the binary data is performed on a block basis according to the predetermined scanning order starting at a high frequency component toward a low frequency component by switching a plurality of fourth probability tables,
• wherein the switching of the plurality of third probability tables includes switching a third probability table to a new third probability table based on a result of a comparison between an absolute value of a target non-zero coefficient to be decoded and a predetermined threshold value,
• wherein the switching of the plurality of fourth probability tables includes switching a fourth probability table to a new fourth probability table based on a result of a comparison between an absolute value of a target non-zero coefficient to be decoded and the predetermined threshold value,
• wherein the switching of the plurality of third probability tables includes switching between the plurality of third probability tables in one direction such that the third probability table, which has been used before the new third probability table, is not used after switching to the new third probability table, and
• wherein the switching of the plurality of fourth probability tables includes switching between the plurality of fourth probability tables in one direction such that the fourth probability table, which has been used before the new fourth probability table, is not used after switching to the new fourth probability table.