Variable length coding method and variable length decoding method

1. A coding method for performing variable-length coding on two-dimensional coefficients of a block which are obtained by performing frequency transformation on picture data of the block that has a predetermined size of pixels, the method comprising:

scanning the two-dimensional coefficients of the block in a predetermined order starting from a low frequency component toward a high frequency component so as to obtain scanned coefficients;

performing variable-length coding on the scanned coefficients from a high frequency component toward a low frequency component using a plurality of variable length code tables;

wherein each of the plurality of variable length code tables includes a plurality of variable length codes which correspond to the coefficients,

wherein said performing variable-length coding comprises:

coding a first coefficient using a first variable length code table of the plurality of variable length code tables;

determining whether or not an absolute value of the first coefficient exceeds a first threshold value by comparing the absolute value of the first coefficient to the first threshold value;

switching to a second variable length code table of the plurality of variable length code tables only when it is determined that the absolute value of the first coefficient exceeds the first threshold value;

coding a second coefficient using the second variable length code table of the plurality of variable length code tables;

determining whether or not an absolute value of the second coefficient exceeds a second threshold value by comparing the absolute value of the second coefficient to the second threshold value, the second threshold value being greater than the first threshold value;

switching to a third variable length code table of the plurality of variable length code tables only when it is determined that the absolute value of the second coefficient exceeds the second threshold value;

coding a third coefficient using the third variable length code table of the plurality of variable length code tables;

determining whether or not an absolute value of the third coefficient exceeds a third threshold value by comparing the absolute value of the third coefficient to the third threshold value, the third threshold value being greater than the second threshold value;

switching to a fourth variable length code table of the plurality of variable length code tables only when it is determined that the absolute value of the third coefficient exceeds the third threshold value; and

coding a fourth coefficient using the fourth variable length code table of the plurality of variable length code tables,

wherein each of the first threshold value, the second threshold value, and the third threshold value is determined based on a rate of change in code length of the variable length codes included in each of the variable length code tables, and

wherein the switching of the variable length code tables is performed in only one direction.

2. A coding apparatus that performs variable-length coding on two-dimensional coefficients of a block which are obtained by performing frequency transformation on picture data of the block that has a predetermined size of pixels, the apparatus comprising:

a scanning unit operable to scan the two-dimensional coefficients of the block in a predetermined order starting from a low frequency component toward a high frequency component so as to obtain scanned coefficients;

a variable length coding unit operable to perform variable-length coding on the scanned coefficients from a high frequency component toward a low frequency component using a plurality of variable length code tables;

wherein each of the plurality of variable length code tables includes a plurality of variable length codes which correspond to the coefficients,

wherein said variable length coding unit is operable to:

code a first coefficient using a first variable length code table of the plurality of variable length code tables;

determine whether or not an absolute value of the first coefficient exceeds a first threshold value by comparing the absolute value of the first coefficient to the first threshold value;

switch to a second variable length code table of the plurality of variable length code tables only when it is determined that the absolute value of the first coefficient exceeds the first threshold value;

code a second coefficient using the second variable length code table of the plurality of variable length code tables;

determine whether or not an absolute value of the second coefficient exceeds a second threshold value by comparing the absolute value of the second coefficient to the second threshold value, the second threshold value being greater than the first threshold value;

switch to a third variable length code table of the plurality of variable length code tables only when it is determined that the absolute value of the second coefficient exceeds the second threshold value;

code a third coefficient using the third variable length code table of the plurality of variable length code tables;

determine whether or not an absolute value of the third coefficient exceeds a third threshold value by comparing the absolute value of the third coefficient to the third threshold value, the third threshold value being greater than the second threshold value;

switch to a fourth variable length code table of the plurality of variable length code tables only when it is determined that the absolute value of the third coefficient exceeds the third threshold value; and

code a fourth coefficient using the fourth variable length code table of the plurality of variable length code tables,

wherein each of the first threshold value, the second threshold value, and the third threshold value is determined based on a rate of change in code length of the variable length codes included in each of the variable length code tables, and

wherein the switching of the variable length code tables is performed in only one direction.