first , in which circumstances the accumulated rounding errors as described in the “ related art ” occur must be considered . an example of an image sequences encoded by coding methods which can perform both unidirectional prediction and bidirectional prediction such as in mpeg . 1 , mpeg . 2 and h . 263 is shown in fig5 . an image 501 is a frame - coded by means of intraframe coding and is referred to as an i frame . in contrast , images 503 , 505 , 507 , 509 are called p frames and are coded by unidirectional interframe coding by using the previous i or p frame as the reference image . accordingly , when for instance encoding image 505 , image 503 is used as the reference image and interframe prediction is performed . images 502 , 504 , 506 and 508 are called b frames and bidirectional interframe prediction is performed utilizing the previous and subsequent i or p frame . the b frame is characterized by not being used as a reference image when interframe prediction is performed . since motion compensation is not performed in i frames , the rounding error caused by motion compensation will not occur . in contrast , not only is motion compensation performed in the p frames but the p frame is also used as a reference image by other p or b frames so that it may be a cause leading to accumulated rounding errors . in the b frames on the other hand , motion compensation is performed so that the effect of accumulated rounding errors appears in the reconstructed image . however , due to the fact that b frames are not used as reference images , b frames cannot be a source of accumulated rounding errors . thus , if accumulated rounding errors can be prevented in the p frame , then the bad effects of rounding errors can be alleviated in the overall image sequence . in h . 263 a frame for coding a p frame and a b frame exists and is called a pb frame ( for instance , frames 503 and 504 can both be encoded as a pb frame ). if the combined two frames are viewed as separate frames , then the same principle as above can be applied . in other words , if countermeasures are taken versus rounding errors for the p frame part within a pb frame , then the accumulation of errors can be prevented . rounding errors occur during interpolation of intensity values when a value obtained from normal division ( division whose operation result is a real number ) is a half ( ½ ) integer ( 0 . 5 added to an integer ) and this result is then rounded up to the next integer in the direction away from zero . for instance , when dividing by 4 to find an interpolated intensity value is performed , the rounding errors for the cases when the residual is 1 and 3 have equal absolute values but different signs . consequently , the rounding errors caused by these two cases are canceled when the expectation for the rounding errors is calculated ( in more general words , when dividing by a positive integer d ′ is performed , the rounding errors caused by the cases when the residual is t and d ′− t are cancelled ). however , when the residual is 2 , in other words when the result of normal division is a half integer , the rounding error cannot be canceled and leads to accumulated errors . to solve this problem , a method that allows the usage of two rounding methods can be used . the two rounding methods used here are : a rounding method that rounds half ( ½ ) integers away from zero ( 0 ); and a rounding method that rounds half ( ½ ) integers towards zero ( 0 ). by combining the usage of these two rounding methods , the rounding errors can be canceled . hereafter , the rounding method that rounds the result of normal division to the nearest integer and rounds half integer values away from 0 is called “ positive rounding ”. additionally , the rounding method that rounds the result of normal division to the nearest integer and rounds half ( ½ ) integer values towards zero ( 0 ) is called “ negative rounding ”. the process of positive rounding used in block matching with half ( ½ ) pixel accuracy is shown in equation 3 . when negative rounding is used instead , this equation can be rewritten as shown below . hereafter motion compensation methods that performs positive and negative rounding for the synthesis of interframe prediction images are called “ motion compensation using positive rounding ” and “ motion compensation using negative rounding ”, respectively . furthermore , for p frames which use block matching with half ( ½ ) pixel accuracy for motion compensation , a frame that uses positive rounding is called a “ p + frame ” and a frame that uses negative rounding is called a “ p − frame ” ( under this definition , the p frames in h . 263 are all p + frames ). the expectation for the rounding errors in p + and p − frames have equal absolute values but different signs . accordingly , the accumulation of rounding errors can be prevented when p + frames and p − frames are alternately located along the time axis . in the example in fig5 , if the frames 503 and 507 are set as p + frames and the frames 505 and 509 are set as p − frames , then this method can be implemented . the alternate occurrence of p + frames and p − frames leads to the usage of a p + frame and a p − frame in the bidirectional prediction for b frames . generally , the average of the forward prediction image ( i . e . the prediction image synthesized by using frame 503 when frame 504 in fig5 is being encoded ) and the backward prediction image ( i . e . the prediction image synthesized by using frame 505 when frame 504 in fig5 is being encoded ) is frequently used for synthesizing the prediction image for b frames . this means that using a p + frame ( which has a positive value for the expectation of the rounding error ) and a p − frame ( which has a negative value for the expectation of the rounding error ) in bidirectional prediction for a b frame is effective in canceling out the effects of rounding errors . just as related above , the rounding process in the b frame will not be a cause of error accumulation . accordingly , no problem will occur even if the same rounding method is applied to all the b frames . for instance , no serious degradation of decoded images is caused even if motion compensation using positive rounding is performed for all of the b frames 502 , 504 , 506 , and 508 in fig5 . preferably only one type of rounding is performed for a b frame , in order to simplify the b frame decoding process . a block matching section 1600 of an image encoder according to the above described motion compensation method utilizing multiple rounding methods is shown in fig1 . numbers identical to those in other drawings indicate the same part . by substituting the block matching section 116 of fig1 with 1600 , multiple rounding methods can be used . motion estimation processing between the input image 101 and the decoded image of the previous frame is performed in a motion estimator 1601 . as a result , motion information 120 is output . this motion information is utilized in the synthesis of the prediction image in a prediction image synthesizer 1603 . a rounding method determination device 1602 determines whether to use positive rounding or negative rounding as the rounding method for the frame currently being encoded . information 1604 relating to the rounding method that was determined is input to the prediction image synthesizer 1603 . in this prediction image synthesizer 1603 , a prediction image 117 is synthesized and output based on the rounding method determined by means of information 1604 . in the block matching section 116 in fig1 , there are no items equivalent to 1602 , 1604 of fig1 , and the prediction image is synthesized only by positive rounding . also , the rounding method 1605 determined at the block matching section can be output , and this information can then be multiplexed into the bit stream and be transmitted . a prediction image synthesizer 1700 of an image decoder which can decode bit streams generated by a coding method using multiple rounding methods is shown in fig1 . numbers identical to those in other drawings indicate the same part . by substituting the prediction image synthesizer 211 of fig2 by 1700 , multiple rounding methods can be used . in the rounding method determination device 1701 , the rounding method appropriate for prediction image synthesis in the decoding process is determined . in order to carry out decoding correctly , the rounding method selected here must be the same as the rounding method that was selected for encoding . for instance the following rule can be shared between the encoder and decoder : when the current frame is a p frame and the number of p frames ( including the current frame ) counted from the most recent i frame is odd , then the current frame is a p + frame . when this number is even , then the current frame is a p − frame . if the rounding method determination device on the encoding side ( for instance , 1602 in fig1 ) and the rounding method determination device 1701 conform to this common rule , then the images can correctly be decoded . the prediction image is synthesized in the prediction image synthesizer 1703 using motion information 202 , decoding image 210 of the prior frame , and information 1702 related to the rounding method determined as just described . this prediction image 212 is output and then used for the synthesis of the decoded image . as an alternative to the above mentioned case , a case where the information related to the rounding method is multiplexed in the transmitted bit stream can also be considered ( such bit stream can be generated at the encoder by outputting the information 1605 related to the rounding method from the block matching section depicted in fig1 ). in such case , the rounding method determiner device 1701 is not used , and information 1704 related to the rounding method extracted from the encoded bit stream is used at the prediction image synthesizer 1703 . besides the image encoder and the image decoder utilizing the custom circuits and custom chips of the conventional art as shown in fig1 and fig2 , this invention can also be applied to software image encoders and software image decoders utilizing general - purpose processors . a software image encoder 600 and a software image decoder 700 are shown in fig6 and fig7 . in the software image encoder 600 , an input image 601 is first stored in the input frame memory 602 and the general - purpose processor 603 loads information from here and performs encoding . the program for driving this general - purpose processor is loaded from a storage device 608 which can be a hard disk , floppy disk , etc . and stored in a program memory 604 . this general purpose processor also uses a process memory 605 to perform the encoding . the encoding information output by the general - purpose processor is temporarily stored in the output buffer 606 and then output as an encoded bit stream 607 . a flowchart for the encoding software ( recording medium readable by computer ) is shown in fig8 . the process starts in 801 , and the value 0 is assigned to variable n in 802 . next , in 803 and 804 , the value 0 is assigned to n when the value for n is 100 . n is a counter for the number of frames . 1 is added for each one frame whose processing is complete , and values from 0 to 99 are allowed when performing coding . when the value for n is 0 , the current frame is an i frame . when n is an odd number , the current frame is a p + frame , and when an even number other than 0 , the current frame is a p − frame . when the upper limit for the value of n is 99 , it means that one i frame is coded after 99 p frames ( p + frames or p − frames ) are coded . by always inserting one i frame in a certain number of coded frames , the following benefits can be obtained : ( a ) error accumulation due to a mismatch between encoder and decoder processing can be prevented ( for instance , a mismatch in the computation of dct ); and ( b ) the processing load for acquiring the reproduced image of the target frame from the coded data ( random access ) is reduced . the optimal n value varies when the encoder performance or the environment where the encoder is used are changed . it does not mean , therefore , that the value of n must always be 100 . the process for determining the rounding method and coding mode for each frame is performed in 805 and the flowchart with details of this operation is shown in fig9 . first of all , whether n is a zero ( 0 ) or not is checked in 901 . if n is 0 , then ‘ i ’ is output as distinction information of the prediction mode , to the output buffer in 902 . this means that the image to be coded is will be coded as an i frame . here , “ output to the output buffer ” means that after being stored in the output buffer , the information is output to an external device as a portion of the coded bit stream . when n is not 0 , then whether n is an odd or even number is identified in 904 . when n is an odd number , ‘+’ is output to the output buffer as the distinction information for the rounding method in 905 , and the image to be coded will be coded as a p + frame . on the other hand , when n is an even number , ‘−’ is output to the output buffer as the distinction information for the rounding method in 906 , and the image to be coded will be coded as a p − frame . the process again returns to fig8 , where after determining the coding mode in 805 , the input image is stored in the frame memory a in 806 . the frame memory a referred to here signifies a portion of the memory zone ( for instance , the memory zone maintained in the memory of 605 in fig6 ) of the software encoder . in 807 , it is checked whether the frame currently being coded is an i frame . when not identified as an i frame , motion estimation and motion compensation is performed in 808 . the flowchart in fig1 shows details of this process performed in 808 . first of all , in 1001 , motion estimation is performed between the images stored in frame memories a and b ( just as written in the final part of this paragraph , the decoded image of the prior frame is stored in frame memory b ). the motion vector for each block is found , and this motion vector is sent to the output buffer . next , in 1002 , whether or not the current frame is a p + frame is checked . when the current frame is a p + frame , the prediction image is synthesized in 1003 utilizing positive rounding and this prediction image is stored in frame memory c . on the other hand , when the current frame is a p − frame , the prediction image is synthesized in 1004 utilizing negative rounding and this prediction image is stored in the frame memory c . next , in 1005 , the differential image between frame memories a and c is found and stored in frame memory a . here , the process again returns to fig8 . prior to starting the processing in 809 , the input image is stored in frame memory a when the current frame is an i frame , and the differential image between the input image and the prediction image is stored in frame memory a when the current frame is a p frame ( p + or p − frame ). in 809 , dct is applied to the image stored in frame memory a , and the dct coefficients calculated here are sent to the output buffer after being quantized . in 810 , inverse quantization is performed to the quantized dct coefficients and inverse dct is applied . the image obtained by applying inverse dct is stored in frame memory b . next in 811 , it is checked again whether the current frame is an i frame . when the current frame is not an i frame , the images stored in frame memory b and c are added and the result is stored in frame memory b . the coding process of a frame ends here , and the image stored in frame memory b before going into 813 is the reconstructed image of this frame ( this image is identical with the one obtained at the decoding side ). in 813 , it is checked whether the frame whose coding has just finished is the final frame in the sequence . if this is true , the coding process ends . if this frame is not the final frame , 1 is added to n in 814 , and the process again returns to 803 and the coding process for the next frame starts . a software decoder 700 is shown in fig7 . after the coded bit stream 701 is temporarily stored in the input buffer 702 , this bit stream is then loaded into the general - purpose processor 703 . the program for driving this general - purpose processor is loaded from a storage device 708 which can be a hard disk , floppy disk , etc . and stored in a program memory 704 . this general - purpose processor also uses a process memory 605 to perform the decoding . the decoded image obtained by the decoding process is temporarily stored in the output frame memory 706 and then sent out as the output image 707 . a flowchart of the decoding software for the software decoder 700 shown in fig7 is shown in fig1 . the process starts in 1101 , and it is checked in 1102 whether input information is present . if there is no input information , the decoding process ends in 1103 . when input information is present , distinction information of the prediction mode is input in 1104 . the word “ input ” used here means that the information stored in the input buffer ( for instance 702 of fig7 ) is loaded by the general - purpose processor . in 1105 , it is checked whether the encoding mode distinction information is “ i ”. when not “ i ”, the distinction information for the rounding method is input and synthesis of the interframe prediction image is performed in 1107 . a flowchart showing details of the operation in 1107 is shown in fig1 . in 1201 , a motion vector is input for each block . then , in 1202 , it is checked whether the distinction information for the rounding method loaded in 1106 is a “+”. when this information is “+”, the frame currently being decoded is a p + frame . in this case , the prediction image is synthesized using positive rounding in 1203 , and the prediction image is stored in frame memory d . here , frame memory d signifies a portion of the memory zone of the software decoder ( for instance , this memory zone is obtained in the processing memory 705 in fig7 ). when the distinction information of the rounding method is not “+”, the current frame being decoded is a p − frame . the prediction image is synthesized using negative rounding in 1204 and this prediction image is stored in frame memory d . at this point , if a p + frame is decoded as a p − frame due to some type of error , or conversely if a p − frame is decoded as a p + frame , the correct prediction image is not synthesized in the decoder and the quality of the decoded image deteriorates . after synthesizing the prediction image , the operation returns to fig1 and the quantized dct coefficients is input in 1108 . inverse quantization and inverse dct is then applied to these coefficients and the resulting image is stored in frame memory e . in 1109 , it is checked again whether the frame currently being decoded is an i frame . if the current frame is not an i frame , images stored in frame memory d and e are added in 1110 and the resulting sum image is stored in frame memory e . the image stored in frame memory e before starting the process in 1111 is the reconstructed image . this image stored in frame memory e is output to the output frame memory ( for instance , 706 in fig7 ) in 1111 , and then output from the decoder as the reconstructed image . the decoding process for a frame is completed here and the process for the next frame starts by returning to 1102 . when a software based on the flowchart shown in fig8 - 12 is run in the software image encoders or decoders , the same effect as when custom circuits and custom chips are utilized are obtained . a storage media ( recording media ) with the bit stream generated by the software encoder 601 of fig6 being recorded is shown in fig1 . it is assumed that the algorithms shown in the flowcharts of fig8 - 10 is used in the software encoder . digital information is recorded concentrically on a recording disk 1301 capable of recording digital information ( for instance magnetic disks , optical disk , etc .). a portion 1302 of the information recorded on this digital disk includes : prediction mode distinction information 1303 , 1305 , 1308 , 1311 , and 1314 ; rounding method distinction information 1306 , 1309 , 1312 , and 1315 ; and motion vector and dct coefficient information 1304 , 1307 , 1310 , 1313 , and 1316 . information representing ‘ i ’ is recorded in 1303 , ‘ p ’ is recorded in 1305 , 1308 , 1311 , and 1314 , ‘+’ is recorded in 1306 , and 1312 , and ‘−’ is recorded in 1309 , and 1315 . in this case , ‘ i ’ and ‘+’ can be represented by a single bit of zero ( 0 ), and ‘ p ’ and ‘−’ can be represented by a single bit of one ( 1 ). using this representation , the decoder can correctly interpret the recorded information and the correct reconstructed image is synthesized . by storing a coded bit stream in a storage media using the method described above , the accumulation of rounding errors is prevented when the bit stream is read and decoded . a storage media with the bit stream of the coded data of the image sequence shown in fig5 being recorded is shown in fig1 . the recorded bit stream includes information related to p +, p −, and b frames . in the same way as in 1301 of fig1 , digital information is recorded concentrically on a record disk 1501 capable for recording digital information ( for instance , magnetic disks , optical disks , etc .). a portion 1502 of the digital information recorded on this digital disk includes : prediction mode distinction information 1503 , 1505 , 1508 , 1510 , and 1513 ; rounding method distinction information 1506 , and 1512 ; and motion vector and dct coefficient information 1504 , 1507 , 1509 , 1511 , and 1514 . information representing ‘ i ’ is recorded in 1503 , ‘ p ’ is recorded in 1505 , and 1510 , ‘ b ’ is recorded in 1508 , and 1513 , ‘+’ is recorded in 1505 , and ‘−’ is recorded in 1511 . in this case , ‘ i ’, ‘ p ’ and ‘ b ’ can be represented respectively by two bit values 00 , 01 , and 10 , and ‘+’ and is ‘−’ can be represented respectively by one bit values 0 and 1 . using this representation , the decoder can correctly interpret the recorded information and the correct reconstructed is synthesized . in fig1 , information related to frame 501 ( i frame ) in fig5 is 1503 and 1504 , information related to 502 ( b frame ) is 1508 and 1509 , information related to frame 503 ( p + frame ) is 1505 and 1507 , information related to frame 504 ( b frame ) is 1513 and 1514 , and information related to frame 505 ( p − frame ) is 1510 and 1512 . when coding image sequences are coded using b frames , the transmission order and display order of frames are usually different . this is because the previous and subsequent reference images need to be coded before the prediction image for the b frame is synthesized . consequently , in spite of the fact that the frame 502 is displayed before frame 503 , information related to frame 503 is transmitted before information related to frame 502 . as described above , there is no need to use multiple rounding methods for b frames since motion compensation in b frames do not cause accumulation of rounding errors . therefore , as shown in this example , information that specifies rounding methods ( e . g . ‘+’ and ‘−’) is not transmitted for b frames . thus for instance , even if only positive rounding is applied to b frames , the problem of accumulated rounding errors does not occur . by storing coded bit streams containing information related to b frames in a storage media in the way described above , the occurrence of accumulated rounding errors can be prevented when this bit stream is read and decoded . specific examples of coders and decoders using the coding method described in this specification is shown in fig1 . the image coding and decoding method can be utilized by installing image coding and decoding software into a computer 1401 . this software is recorded in some kind of storage media ( cd - rom , floppy disk , hard disk , etc .) 1412 , loaded into a computer and then used . additionally , the computer can be used as an image communication terminal by connecting the computer to a communication lines . it is also possible to install the decoding method described in this specification into a player device 1403 that reads and decodes the coded bit stream recorded in a storage media 1402 . in this case , the reconstructed image signal can be displayed on a television monitor 1404 . the device 1403 can be used only for reading the coded bit stream , and in this case , the decoding device can be installed in the television monitor 1404 . it is well known that digital data transmission can be realized using satellites and terrestrial waves . a decoding device can also be installed in a television receiver 1405 capable of receiving such digital transmissions . also , a decoding device can also be installed inside a set top box 1409 connected to a satellite / terrestrial wave antenna , or a cable 1408 of a cable television system , so that the reconstructed images can be displayed on a television monitor 1410 . in this case , the decoding device can be incorporated in the television monitor rather than in the set top box , as in the case of 1404 . the layout of a digital satellite broadcast system is shown in 1413 , 1414 and 1415 . the video information in the coded bit stream is transmitted from a broadcast station 1413 to a communication or broadcast satellite 1414 . the satellite receives this information , sends it to a home 1415 having equipment for receiving satellite broadcast programs , and the video information is reconstructed and displayed in this home using devices such as a television receiver or a set top box . digital image communication using mobile terminals 1406 has recently attracted considerable attention , due to the fact that image communication at very low bit rates has become possible . digital portable terminals can be categorized in the following three types : a transceiver having both an encoder and decoder ; a transmitter having only an encoder ; and a receiver having only a decoder . an encoding device can be installed in a video camera recorder 1407 . the camera can also be used just for capturing the video signal and this signal can be supplied to a custom encoder 1411 . all of the devices or systems shown in this drawing can be equipped with the coding and / or decoding method described in this specification . by using this coding and / or decoding method in these devices or systems , images of higher quality compared with those images obtained using conventional technologies can be obtained . the following variations are clearly included within the scope of this invention . ( i ) a prerequisite of the above described principle was the use of block matching as a motion compensation method . however , this invention is further capable of being applied to all image sequence coding and decoding methods in which motion compensation is performed by taking a value for the vertical and horizontal components of the pixel motion vector that is other than an integer multiple of the sampling period in the vertical and horizontal directions of the pixel , and then finding by interpolation , the intensity value of a position where the sample value is not present . thus for instance , the global motion compensation listed in japanese patent application no . 8 - 60572 published as japanese patent application laid - open no . 9 - 252470 and the warping prediction listed in japanese patent application no . 8 - 249601 published as japanese patent application laid - open no . 10 - 98729 are applicable to the method of this invention . ( ii ) the description of the invention only mentioned the case where a value integral multiple of ½ was taken for the horizontal and vertical components of the motion vector . however , this invention is also generally applicable to methods in which integral multiples of 1 / d ( d is a positive integer and also an even number ) are allowed for the horizontal and vertical components of the motion vector . however , when d becomes large , the divisor for division in bilinear interpolation ( square of “ d ”, see equation 2 ) also becomes large , so that in contrast , the probability of results from normal division reaching a value of 0 . 5 become low . accordingly , when performing only positive rounding , the absolute value of the expectation for rounding errors becomes small and the bad effects caused by accumulated errors become less conspicuous . also applicable to the method of this invention , is a motion compensation method where for instance , the d value is variable , both positive rounding and negative rounding are used when d is smaller than a fixed value , and only positive rounding or only negative rounding is used when the value of d is larger than a fixed value . ( iii ) as mentioned in the “ related art ” section , when dct is utilized as an error coding method , the adverse effects from accumulated rounding errors are prone to appear when the quantized step size of the dct coefficient is large . however a method is also applicable to the invention , in which , when the quantization step size of dct coefficients is larger than a threshold value then both positive rounding and negative rounding are used . when the quantization step size of the dct coefficients is smaller than the threshold value then only positive rounding or only negative rounding is used . ( iv ) in cases where error accumulations occur on the luminance plane and cases where error accumulations occur on the chrominance plane , the bad effects on the reconstructed images are generally more serious in the case of error accumulations on the chrominance plane . this is due to the fact that rather than cases where the image darkens or lightens slightly , cases where overall changes in the image color happen are more conspicuous . however , a method is also applicable to this invention in which both positive rounding and negative rounding are used for the chrominance signal , and only positive rounding or negative rounding is used for the luminance signal . as described in the “ related art ” section , ¼ pixel accuracy motion vectors obtained by halving the ½ pixel accuracy motion vectors are rounded to ½ pixel accuracy in h . 263 . however by adding certain changes to this method , the absolute expectation value for rounding errors can be reduced . in h . 263 that was mentioned in the related art , a value which is half the horizontal or vertical components of the motion vector for the luminance plane is expressed as r + s / 4 ( r is an integer , s is an integer less than 4 and not smaller than 0 ), and when s is 1 or 3 , a rounding operation is performed to obtain a 2 . this operation can be changed as follows : when s is 1 , a rounding operation is performed to obtain a zero “ 0 ”, and when s is 3 a 1 is be added to r to make s a “ 0 ”. by performing these operations , the number of times that the intensity values at positions 406 - 408 in fig4 is definitely reduced ( probability that horizontal and vertical components of motion vector will be an integer become high ) so that the absolute expectation value for the rounding error becomes small . however , even if the size of the error occurring in this method can be limited , the accumulation of errors cannot be completely prevented . ( v ) the invention described in this specification is applicable to a method that obtains the final interframe prediction image by averaging the prediction images obtained by different motion compensation methods . for example , in the method described in japanese patent application no . 8 - 3616 published as japanese patent application laid - open no . 9 - 200763 , interframe prediction images obtained by the following two methods are averaged : block matching in which a motion vector is assigned to each 16 × 16 pixel block ; and block matching in which a motion vector is assigned to each 8 × 8 pixel blocks . in this method , rounding is also performed when calculating the average of the two prediction images . when only positive rounding is continuously performed in this averaging operation , a new type of rounding error accumulates . this problem can be solved by using multiple rounding methods for this averaging operation . in this method , negative rounding is performed in the averaging operation when positive rounding is performed in block matching . conversely , positive rounding is used for the averaging when negative rounding is used for block matching . by using different rounding methods for averaging and block matching , the rounding errors from two different sources is cancelled within the same frame . ( vi ) when utilizing a method that alternately locates p + frames and p − frames along the time axis , the encoder or the decoder needs to determine whether the currently processed p frame is a p + frame or a p − frame . the following is an example of such identification method : a counter counts the number of p frames after the most recently coded or decoded i frame , and the current p frame is a p + frame when the number is odd , and a p − frame when the number is even ( this method is referred to as an implicit scheme ). there is also a method for instance , that writes into the header section of the coded image information , information to identify whether the currently coded p frame at the encoder is a p + frame or a p − frame ( this method is referred to as an explicit scheme ). compared with the implicit method , this method is well able to withstand transmission errors , since there is no need to count the number of p frames . additionally , the explicit method has the following advantages : as described in the “ related art ” section , past encoding standards ( such as mpeg - 1 or mpeg - 2 ) use only positive rounding for motion compensation . this means for instance that the motion estimation / motion compensation devices ( for example equivalent to 106 in fig1 ) for mpeg - 1 / mpeg - 2 on the market are not compatible with coding methods that use both p + frames and p − frames . it is assumed that there is a decoder which can decode bit streams generated by a coding method that uses p + frames and p − frames . in this case if the decoder is based on the above mentioned implicit method , then it will be difficult to develop an encoder that generates bit streams that can be correctly decoded by the above mentioned decoder , using the above mentioned motion estimation / compensation device for mpeg - 1 / mpeg - 2 . however , if the decoder is based on the above mentioned explicit method , this problem can be solved . an encoder using an mfeg - 1 / mpeg - 2 motion estimation / motion compensation device can continuously send p + frames , by continuously writing rounding method distinction information indicating positive rounding into the frame information header . when this is performed , a decoder based on the explicit method can correctly decode the bit stream generated by this encoder . of course , it should be more likely in such case that the accumulation of rounding errors occurs , since only p + frames are present . however , error accumulation is not a serious problem in cases where the encoder uses only small values as the quantization step size for the dct coefficients ( an example for such coders is a custom encoder used only for high rate coding ). in addition to this interoperability between past standards , the explicit method further have the following advantages : ( a ) the equipment cost for high rate custom encoders and coders not prone to rounding error accumulation due to frequent insertion of i frames can be reduced by installing only positive or negative rounding as the pixel value rounding method for motion compensation ; and ( b ) the above encoders not prone to rounding error accumulation have the advantage in that there is no need to decide whether to code the current frame as a p + or p − frame , and the processing is simplified . ( vii ) the invention described in this specification is applicable to coding and decoding methods that applies filtering accompanying rounding to the interframe prediction images . for instance , in the international standard h . 261 for image sequence coding , a low - pass filter ( called a “ loop filter ”) is applied to block signals whose motion vectors are not zero ( 0 ) in interframe prediction images . also , in h . 263 , filters can be used to smooth out discontinuities on block boundaries ( blocking artifacts ). all of these filters perform weighted averaging to pixel intensity values and rounding is then performed on the averaged intensity values . even for these cases , selective use of positive rounding and negative rounding is effective for preventing error accumulation . ( viii ) besides i p + p − p + p − . . . , various methods for mixing p + frames and p − frames such as i p + p + p − p − p + p + . . . , or i p + p − p − p + p + . . . are applicable to the method of this invention . for instance , using a random number generator that outputs 0 and 1 both at a probability of 50 percent , the encoder can code a p + and p − frame when the output is 0 and 1 , respectively . in any case , the less the difference in probability that p + frames and p − frames occur in a certain period of time , the less the rounding error accumulation is prone to occur . further , when the encoder , is allowed to mix p + frames and p − frames by an arbitrary method , the encoder and decoder must operate based on the explicit method and not with the implicit method described above . accordingly , the explicit method is superior when viewed from the perspective of allowing flexibility configuration for the encoder and decoder . ( ix ) the invention described in this specification does not limit the pixel value interpolation method to bilinear interpolation . interpolation methods for intensity values can generally be described by the following equation : where , r and s are real numbers , h ( r , s ) is a function for interpolating the real numbers , and t ( z ) is a function for rounding the real number z . the definitions of r ( x , y ), x , and y are the same as in equation 4 . motion compensation utilizing positive rounding is performed when t ( z ) is a function representing positive rounding , and motion compensation utilizing negative rounding is performed when the function representing negative rounding . this invention is applicable to interpolation methods that can be described using equation 5 . for instance , bilinear interpolation can be described by defining h ( r , s ) as shown below . then an interpolation method different from bilinear interpolation is implemented but the invention is still applicable . ( x ) the invention described in this specification does not limit the coding method for error images to dct ( discrete cosine transform ). for instance , wavelet transform ( for example , n . antonioni , et . al , “ image coding using wavelet transform ” ieee trans . image processing , vol . 1 , no . 2 , april 1992 ) and walsh - hadamard transform ( for example , a . n . netravalli and b . g . haskell , “ digital pictures ”, plenum press , 1998 ) are also applicable to this invention .