Variable length coding method and variable length decoding method

A decoding apparatus which performs arithmetic decoding, on a block basis, on coefficients of a two-dimensional array of frequency components, the coefficients being generated by frequency transformation performed on picture data of a block which has a 4×4 size of pixels, the decoding apparatus comprising:

• a decoding unit operable to, for each of non-zero coefficients of a 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;
• and
• a combining unit operable to, for each of the non-zero coefficients of the 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 first probability tables,
• wherein the second arithmetic coding 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 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 decoded 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 decoded and the predetermined threshold value,
• wherein the switching of the plurality of first probability tables includes switching between the plurality of first probability tables 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, and
• wherein the switching of the plurality of second probability tables includes switching between the plurality of second probability tables 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.