now , detailed description of the present invention follows referring to the attached figures . fig1 is an exemplary block diagram of a general convolutional encoder in which 11 and 12 denote memories , and 13 and 14 denote adders . referring to fig1 the convolutional encoder shown in the figure has a simple structure with the code rate being 1 / 2 and the constraint length being 3 . as shown in fig1 the convolutional encoder outputs 2 encoded bits each time an information bit enters , as the code rate of the encoder is 1 / 2 . the constraint length denotes the length that an information bit affects the encoded output bits , which depends on the number of memories 11 , 12 inside the encoder . since the structure and operation of the convolutional encoder with code rate 1 / 2 and constraint length 3 is well known , detailed description is omitted here except the procedure of state transition of the trellis . in general , the number of trellis states is determined according to the number of memories 11 , 12 . a code rate 1 / 2 convolutional encoder with constraint length 3 has 2 memories 11 , 12 . as binary numbers can be stored in the memories 11 , 12 , it has 2 2 (= 4 ) trellis states . that is , as an information bit is input , the adders 13 , 14 add it to the bits input previously and stored in the memories 11 , 12 , and concurrently output two encoded bits . then , the currently input bit is shifted into memories 11 and 12 and the same procedure is repeated . the trellis diagram of the convolutional encoder is shown in fig2 . fig2 is an explanatory diagram of the trellis structure of fig1 . fig2 is a trellis diagram of a simple convolutional encoder with code rate being 1 / 2 and constraint length being 3 . in this figure , solid lines denote input bit 0 and dotted lines denote input bit 1 . state transitions at each state of the trellis shown in fig2 is determined by the new information bits inputted to the memories 11 , 12 . as the information bit is inputted bit by bit , that is with two possible values , there are two branches to the next state . referring to fig2 each node denoted by a black dot in the trellis diagram shows the state of the encoder at certain time . the line connecting a node and a node is called a branch , which denotes a transition from the state of the encoder at the current time point to the state of the following time point . each time point of the trellis ( that is , x axis ) is called a level of the trellis and the line composed of branches connecting nodes is called a path . as a result , the paths denote code words . in the viterbi decoding scheme , metrics for all paths ( i . e ., code words ) existing in the trellis is computed for the inputted bits , and the path with the smallest metric value is determined as a code word . the metric value is euclidean metric in this embodiment . fig3 is a flow chart which shows the entire flow of the complexity reduction method according to the present invention . the present invention utilizes the fact that in a decoder which uses the trellis decoding scheme like viterbi decoding , almost alike performance to the maximum likelihood decoder can be achieved with only arbitrary a paths which is less than the total number of paths s and the fact that the probability distribution of path metric values at each level of the trellis is an almost gaussian distribution . thus , to select good a paths out of s paths at each level of the entire trellis , the present invention reduces the number of paths based on mean and standard deviation of the path metric values at each level . hence it can reduce the complexity of the decoder by reducing the number of paths without any additional large computations . for example , the present invention make it possible to utilize an additional coding gains due to soft - decision decoding of a trellis decoder with a large amount of computations . that is , it can reduce the complexity of a decoder using statistics of path metric values even for the viterbi decoder for reed - solomon codes , the complexity thereof being extremely high , or for the viterbi decoder for convolutional codes with a large constraint length , the complexity thereof being too high . as any other linear block code as well as convolutional code can be expressed with the trellis , the trellis decoding technique like viterbi decoding can be applied to them . so the soft - decision decoding can easily be applied to them achieving additional coding gain . as shown in fig3 the complexity reduction method of the present invention first initializes the level of the trellis and a flag ( i . e ., level = 0 , flag = 0 )( step 301 ). then , as the reliability of the received signal can be determined based on the soft - decision information , it determines the reliability by checking the soft - decision information for the received signal at the current level ( step 302 ). the reliability here is a value denoting the reliability of the hard - decisioned value and the reliability value is determined by the soft - decisioned value . if the flag is 1 or the reliability of the received signal is the smallest value ( step 303 ), it extends paths to take into account all possible cases ( step 304 ), and it computes and stores the information for all possible paths ( step 305 ). if the reliability of the received signal is larger than the smallest value and if the flag is 0 , the decoder only keeps the most likely paths and neglects the rest of them ( step 306 ), and it computes and stores the selected information for the most likely path ( step 305 ). thus , if there is little noise in the received signal , the reliability of the received signal is high and the number of paths to be considered is very small . on the contrary , if there is lot of noise in the received signal , the reliability gets low making the number of paths to be considered is increased . if the number of paths which satisfy the current conditions gets 0 ( i . e ., flag = 1 ) while decoding is continued this way , paths are extended to take into account all possible cases ( step 304 ), information for all paths is computed and saved ( step 305 ). then , it analyzes if the total number of paths at the current level of the entire trellis is larger than the maximum number of paths a to be maintained ( step 307 ). if the total number of paths is found not to be larger than the maximum number of paths a as a result of the analysis , it checks if the total number of paths at the current level of the entire trellis is larger than 0 ( step 308 ). if the total number of paths is found not to be larger than 0 as a result of the checking , it makes the level to 0 and sets the flag to 1 ( step 311 ), it checks the soft - decision information for the received signal at the current level to measure the reliability ( step 302 ). if the total number of paths exceeds 0 , it moves to the next level ( step 310 ). then it checks the soft - decision information for the received signal at the next level to measure the reliability ( step 302 ). if the total number of paths is found to exceed the maximum number of paths a to be maintained as a result of the analysis , the method computes the statistics of path metric values and obtains the reference path metric , then it reduces the number of paths using them ( step 309 ). the method then moves to the next level ( step 310 ) and checks the soft - decision information for the received signal at the next level to measure the reliability ( step 302 ). multiple paths always exists at each level of the trellis . the number of paths at a level generally increases as the error - correction capability of the code gets high . also , as the number of paths increases the probability distribution of the path metrics at each level gets close to gaussian . the distribution of the number of path metrics at an arbitrary level for various decoding schemes are shown in fig4 a and fig4 b . fig4 a shows the path matric distribution of the viterbi decoder for a convolutional code having total 256 paths at each level . fig4 b shows the path matric distribution of the viterbi decoder for a reed - solomon code having total 65536 paths at each level . referring to fig4 a and fig4 b , it can be seen that the probability distribution of the path metric almost follows gaussian distribution . thus , as it is known that the probability distribution of the path metric follows gaussian distribution , if only a paths out of a total of s paths are to be maintained at the decoding stage , the maximum metric value of a paths can be obtained if mean and standard deviations of the path metric are known . metric values of these a paths are larger than the reference path metric pmr , which can be expressed as equation 1 . a s i =  ∫ p m n ∞  1 2  πσ pmi  exp  [ - ( x - m pmi ) 2 2  σ pmi 2 ]    x   if   a / s i & gt ; 0 . 5 =  1 - ∫ pm n ∞  1 2  πσ pmi  exp  [ - ( x - m pmi ) 2 2  σ pmi 2 ]    x   if   a / s i & lt ; 0 . 5 where , a is the maximum number of paths to be maintained at each level , s i is the total number of paths at the i th level , m pmi is the mean of path metric values at the i th level , σ pmi is the standard deviation value of the path metric at the i th level , and pm ri is the reference path metric at the i th level . the decoder simply computes the reference path metric pmr and eliminates the paths having path metrics larger than the reference path metric to select the best a paths . for practical systems , it could be easily implemented by normalizing the integral value into a table with mean being 0 and standard deviation being 1 . to help understanding , the above mentioned technique will be explained with an example of a code rate 1 / 2 convolutional code with constraint length 7 . there are 64 total paths at each level for the above coding scheme . assuming that only 12 of these paths are always to be maintained , the number of paths starts with 2 and increases to 4 , 8 , and 16 , thereby exceeding the required 12 paths . at this time , a / s i becomes 0 . 75 and the reference metric pm ri is computed from equation 1 using m pmi and σ pmi for the entire 16 paths . then , paths with path metrics values larger than pm ri are removed . at the next level then only 24 paths ( double of 12 ) rather than 32 paths ( double of 16 ) exist . here , the same procedure is applied to them to reduce the number of paths . fig5 is a detailed flow chart of an embodiment for the path reduction procedure using statistics of the path metric of fig3 . as shown in fig5 the reduction method of the number of paths ( step 309 ) using the statistics of path metrics according to the present invention starts with obtaining the statistics of path metrics ( step 501 ). that is , it calculates a total number s i of paths extended at the current level , the mean m pmi and the standard deviation σ pmi of the path metrics . then , it calculates the maximum number of paths a to be maintained in the decoder by using the statistics of path metrics and the ratio a / s i which is the ratio of the maximum number of paths a to be maintained in the decoder to the total number of paths s i extended at the current level ( step 502 ). next , it calculates the reference path metric pmr using equation 1 ( step 503 ). paths with larger path metric values than the reference path metric are removed ( step 504 ). let &# 39 ; s take a look at the gain attainable when the present invention is applied with an example of viterbi decoding for ( 15 , 11 ) reed - solomon code . there are approximately 1 . 7 × 105 paths to be extended in average for an information bit . but only 1024 paths might be maintained at each level to obtain similar performance . in this case the number of paths that should be extended for an information bit is approximately 1600 . if the method suggested here is applied then further complexity reduction can be achieved . fig6 and fig7 show respectively the bit error rate performance and complexity comparison when the complexity reduction method of the embodiment of the present invention is applied to the viterbi decoding scheme for the ( 15 , 11 ) reed - solomon code . referring to fig6 it can be seen that the bit error rate performance curves when the present invention is applied to the viterbi decoding scheme for the ( 15 , 11 ) reed - solomon code are similar for the case 6 a when about 1024 paths is maintained at each level and the case 6 b when all possible paths have been extended ( that is , viterbi decoding ). referring to fig7 it can be seen that similar number of paths 7 c in the case when only the step 309 in fig5 of path reduction using the statistics of path metric ( 7 c ) is used is maintained to the number of path extension which is calculated theoretically ( 7 b ). here , 7 a denotes the number of path extension in the case of viterbi decoding . it can be seen , therefore , that the path reduction procedure using the statistics of path metric values suggested by the present invention is very effective and accurate . furthermore , in the case 7 d when both the path reduction procedure 309 and complexity reduction procedure according to the present invention in fig3 ( i . e ., other procedures except the path reduction procedure 309 ) are applied at the same time , the complexity has been further reduced , and it gets more effective when signal to noise ratio increases . while the invention has been particularly shown and described with reference to preferred embodiments thereof , it will be understood by those skilled in the art that the foregoing and other changes in form and details can be made therein without departing from the spirit and scope of the invention .