repeatedly performed so that it is possible to decrease the computation amount of the coding of the data between the nodes for thereby generating an optimal path the procedure for determining the optimal path between two stages will be explained based on the optimal path tracing method using a trellis based adaptive quantizer according to the present invention first the length of the code based on the run level is defined as shown in table 1 as shown in the above table 1 u201c 0 u201d and u201c 1 u201d represent the coded values the levels with respect to each code value are 1 2 3 the length of the code is defined the number of bits increased as the level is increased using a monotonic increase characteristics with respect to each level the end of block eob means the coding end of the data and is defined as has seven bits the procedure for tracing the optimal path with respect to the two stages will be explained based on the above table with reference to fig8 fig8 a illustrates the run and level with respect to two stages s 1 and s 2 and 1 2 and 0 6 represent quantizing coefficients with respect to the stages s 1 and s 2 when coding to u201c 0 u201d if the level of the coding value is 1 the nodes.