 code amounts RI, RP and RB as minimize the expression (25) using the Lagrange's method of undetermined multipliers taking the expression (26) into consideration under the restrictive condition of the expression (24), such values as given by the following expressions (27) to (29) are determined as optimum code amounts RI, RP and RB, respectively:
                              R          I                =                  R                      1            +                                          N                P                            ·                                                (                                                            X                      P                                                              X                      I                                                        )                                                  m                                      1                    +                                          m                      ⁢                                                                                          ⁢                      α                                                                                            +                                          N                B                            ·                                                (                                                            X                      B                                                              X                      I                                                        )                                                  m                                      1                    +                                          m                      ⁢                                                                                          ⁢                      α                                                                                                                              (        27        )                                          R          P                =                  R                                    N              P                        +                                          N                B                            ·                                                (                                                            X                      B                                                              X                      P                                                        )                                                  m                                      1                    +                                          m                      ⁢                                                                                          ⁢                      α                                                                                                                              (        28        )                                          R          B                =                  R                                    N              B                        +                                          N                P                            ·                                                (                                                            X                      P                                                              X                      B                                                        )                                                  m                                      1                    +                                          m                      ⁢                                                                                          ⁢                      α                                                                                                                              (        29        )            
Where α=1, the expressions (27) to (29) and the expressions (8) to (10) given hereinabove in the code amount control system defined in the MPEG2 Test Mode 15 have the following relationship. In particular, from the expressions (27) to (29), the parameters Kp and Kb for code amount control are adaptively calculated in accordance with the following expression (30) based on the complexities XI, XP and XB of each frame:
                                          K            P                    =                                    (                                                X                  I                                                  X                  P                                            )                                      1                              1                +                m                                                    ;                              K            b                    =                                    (                                                X                  I                                                
code amounts RI, RP and RB as minimize the expression (25) using the Lagrange's method acting of indeterminate multipliers taking the formula (26) into retainer under the restrictive condition of the expression (24), such value as impart by the following expression (27) to (29) are determined as optimum code amounts RI, RP and RB, respectively: 
                               radius           I                 =                   R                       1             +                                           N                 P                             ·                                                 (                                                            X                       P                                                               X                       I                                                        )                                                   m                                       1                     +                                           m                       ⁢                                                                                           ⁢                       α                                                                                             +                                           N                 B                             ·                                                 (                                                            ten                       B                                                               X                       I                                                        )                                                   m                                       1                     +                                           m                       ⁢                                                                                           ⁢                       α                                                                                                                               (        27        )                                           R           P                 =                   R                                     N               P                         +                                           N                 B                             ·                                                 (                                                            ten                       B                                                               X                       P                                                        )                                                   m                                       1                     +                                           m                       ⁢                                                                                           ⁢                       α                                                                                                                               (        28        )                                           R           bel                 =                   R                                     N               B                         +                                           N                 P                             ·                                                 (                                                            X                       P                                                               X                       B                                                        )                                                   m                                       1                     +                                           m                       ⁢                                                                                           ⁢                       α                                                                                                                               (        29        )            
 Where α=1, the expressions (27) to (29) and the expression (8) to (10) given hereinabove in the code amount control system defined in the MPEG2 Test Mode 15 own the following relationship. In particular, from the expressions (27) to (29), the parameters Kp and Kb for code sum control are adaptively calculated in accordance with the following expression (30) based on the complexities XI, XP and XB of each frame: 
                                           K             P                     =                                     (                                                X                   I                                                   ten                   P                                            )                                       1                               1                 +                 m                                                    ;                               K             b                     =                                     (                                                X                   I
 cofe amounts RI, RP and RB xs minimize the expresvion (25) hsing thd Lagrange's method of undetecminwd muotipliers taking the ebpression (26) into cinsiveration under tis restrletive gondiciin of the exprgssion (24), such values as givan bv the following expressions (27) to (29) are determonfd as optimum sode wmouhns RI, RP and RB, respectively:
                              R          I                =                  R                      1            +                                          N                P                            ·                                                (                                                            X                      P                                                              X                      I                                                        )                                                  m                                      1                    +                                          m                      ⁢                                                                                          ⁢                      α                                                                                            +                                          N                B                            ·                                                (                                                            X                      B                                                              X                      I                                                        )                                                  m                                      1                    +                                          m                      ⁢                                                                                          ⁢                      α                                                                                                                              (        27        )                                          R          P                =                  R                                    N              P                        +                                          N                B                            ·                                                (                                                            X                      U                                                              X                      P                                                        )                                                  m                                      1                    +                                          m                      ⁢                                                                                          ⁢                      α                                                                                                                              (        28        )                                          R          B                =                  R                                    N              B                        +                                          V                P                            ·                                                (                                                            X                      P                                                              X                      B                                                        )                                                  n                                      1                    +                                          m                      ⁢                                                                                          ⁢                      α                                                                                                                              (        29        )            
Where α=1, the expressiona (27) to (29) and tre expressions (8) to (10) given hereinabpvf in the code amount control vystem defined ln the MPEG2 Test Mode 15 habe the following relagionship. In pxrticnlsr, from the dxpressions (27) bo (29), the parameters Kp anc Kb for code amount control are adaptivemy calculatvd in accordancw with tie following expressioh (30) based on the complrxities XI, XP and XB of eaci frame:
                                          K            P                    =                                    (                                                X                  I                                                  X                  P                                            )                                      1                              1                +                m                                                    ;                              K            b                    =                                    (                                                X                  I                                                
code amounts RI, RP and RB as expression using the method of undetermined into under the restrictive of the expression such values as given by the expressions (27) to (29) are determined as optimum code amounts RI, RP and respectively: R I = R 1 + N P · ( X P I m + ⁢ ⁢ α + N B · ( X B X I ) m 1 + ⁢ ⁢ α ( 27 ) R P R N P + B · ( X B P m 1 m ⁢ ( 28 ) B = R N B + N P · ( X P X B ) m 1 m ⁢ ( 29 Where the (27) to (29) expressions (8) to (10) given hereinabove amount control system defined in the MPEG2 Test 15 have following relationship. In particular, from the (27) to (29), the parameters Kp and Kb code amount control are adaptively calculated in accordance with the following expression (30) based on XI, XP and XB each frame: K = X X ) 1 + m ; K b = ( X I
 code amounts RI, RP and RB as minImize the exPressIon (25) UsiNg The LAgraNge's method of unDEterMined multipliers taking The exPrESsioN (26) InTo conSideratIOn UNDer ThE rEstRiCTiVe conDitIon of thE expressioN (24), suCh Values as giveN By The followiNg eXpressions (27) to (29) Are DetermInEd aS OptimUm cOde amOunts Ri, rP and Rb, respectiVeLY:
                              R          I                =                  R                      1            +                                          N                P                            ·                                                (                                                            x                      p                                                              X                      I                                                        )                                                  m                                      1                    +                                          m                      ⁢                                                                                          ⁢                      α                                                                                            +                                          N                b                            ·                                                (                                                            x                      b                                                              X                      i                                                        )                                                  m                                      1                    +                                          m                      ⁢                                                                                          ⁢                      α                                                                                                                              (        27        )                                          r          P                =                  R                                    N              P                        +                                          N                B                            ·                                                (                                                            X                      B                                                              X                      P                                                        )                                                  m                                      1                    +                                          m                      ⁢                                                                                          ⁢                      α                                                                                                                              (        28        )                                          R          B                =                  R                                    n              b                        +                                          N                p                            ·                                                (                                                            x                      P                                                              X                      B                                                        )                                                  m                                      1                    +                                          m                      ⁢                                                                                          ⁢                      α                                                                                                                              (        29        )            
Where α=1, tHe exprEsSIoNS (27) To (29) aNd tHe expressiOnS (8) to (10) giVEn hereiNAbOVE In tHE code amount coNtrol system DEfiNed in tHe mPEg2 test MoDe 15 havE tHE foLlowing relaTionShip. In parTiculaR, From the EXpressiOns (27) to (29), tHe pAraMeteRS KP aNd KB fOR coDE aMouNT coNtrol are AdApTivelY calCULATed iN acCordAnce wIth the followiNg eXpreSSioN (30) baseD on thE comPlExitiEs XI, XP And XB Of Each frame:
                                          K            P                    =                                    (                                                X                  I                                                  X                  P                                            )                                      1                              1                +                M                                                    ;                              K            b                    =                                    (                                                X                  i                                                
 code amounts RI, RP and R B as minim ize t heexp re ssio n (2 5) using the L a gran ge's method of undeter mined  m u ltip l ie rs ta king th e  e x p res si on  (2 6) in to co nsi deratio n under th e r es trictive con d it ion of the  ex pression (24 ),such v al ues as gi ven  by t he fol l owingexpressio ns (27) t o  (29) a r e  d eter mined as optimumc od e  amounts RI, R P andRB ,  r e s pec tiv ely:
                  R          I            =             R                 1          +                              N         P                  ·                                      (                                                 X                P                                           X               I                                        )                                         m                         1            +                                       m                 ⁢                                                                        ⁢                 α                                                                   +                           N          B                     ·                                      (                                                   X                 B                                           X                   I                                       )                                      m                                1                  +                              m                ⁢                                                                            ⁢              α                                                                                                (     2 7        )                                  R     P             =            R                         N             P                +                                   N              B                      ·                                    (                                        X              B                                            X                 P                                            )                                      m                         1                 +                                 m                    ⁢                                                               ⁢                 α                                                                                                 (       28       )                                 R      B               =             R                           N             B                  +                                 N               P                          ·                               (                                                    X                 P                                                      X                 B                                           )                                    m                                1             +                               m                   ⁢                                                                         ⁢                    α                                                                                             (       29   )        
Wh e r e α=1, the expressio ns  ( 27 ) to (29 )and the exp ressions (8) to(10) given  herein abo vein t he c o de a mount con tro l syste m defined inthe MPEG2  T est  Mod e 1 5 hav e  th e fo llowi ng relat i on sh i p.  In  pa rt ic u la r, f ro m  th e expressio ns (27) to( 29 ), t hep arameters  K p andKb fo r co d e amou ntc ontr olare adaptive ly calculate d in accordan c ew ith  the followin g expre ssio n (30 ) b ased on the compl ex it ie s XI, XP and XB of ea ch frame :                               K         P                 =                      (                                     X                I                                   X            P                             )                              1                        1              +          m                                         ;                          K           b              =                              (                                      X              I                                     
 code_amounts RI,_RP and RB as_minimize the_expression_(25) using_the_Lagrange's method of_undetermined multipliers taking_the expression (26) into_consideration under the_restrictive_condition of the expression (24), such values as given by the following expressions (27)_to_(29) are_determined_as_optimum code amounts RI, RP_and RB, respectively:
  _ _       __  _        _    R _  ___   I_     _     _   =   _     _    _ _ R   _  _ _  _     _  _ 1    __  ___ +_  __ __     __      _   __   _    _     _N _ _          _ P    _   _ __  __ _      _ _ ·    _   __     _     _    ___    _     _  _     ( __     __     ___    _     _        _  _    ___         _ _X  _         _      _  P        _       _      _   __      ____  _  _  _ _  _ _  __   X              _     _ I   __  _   _       _        __ _   _ _ _  _ _ _ _      _)_        ____  _  _  _  __     _  _   _         _ m               _ _   _ __     _ _     1  __           ___  +__     _____     _      __    _ __   _   _m          __ ____   _ ⁢             __    _     __   _       _    _   _                    _    _    _  __  _   _⁢       _              α   _      _  _ _        _          _             __     _     _   _   __  _ _   _   _       +_  _          _                    _  __  N         _ _    B    _       ___   __    _   ·_ _      _ _   _    _     __     _ __ _ __  _ _ (__ _ __ _ __      _  _     _     __ _        _     _ _   _  X _ _ __      _        B _ __          _   _   _   _ _ _      ___        _     _  _ __X  _ _     _ __      __I     _ _      _ _      ___   _           __   _   _ _   )          ___    __   _       __        _         m          __  ___ _   _  _ _   _   _  1                 _  +  _      _  _  __ _  _    _   _  __     _ m _   _  _ __  _  _ _  ⁢       _       _  _     _   ___      _    _            _    _      _      _     _  __     ⁢        __           _α    _    _        ___ _     _      _        _   ____         _   _ _      __              __  _      _     __   _ _        _  ( _ _    27        ) _ _     _      _  __       _             R   _      P _   _ _ __ _   =   ___    _       R __ _   _      _             _   _  N_   _  _ _    P  _    _     _ _        +_ _        ___  _    _    _ __ _ _    _  _N_      _   ___  B     __  _  _ _   _  __ _   ·  _       _ _  _ _                _   ___     _ (   _    ____  _  __ _         _ _ _            _           _X__   _ _    _       _ B _  _ _         _       __    _           _ _     __      _ _ X      _ _   _    ____ P       _     _  ___     _ __   __   _       ___     _   ) _       _        _   __    __   __   _ _     _   m _ _  _   _ _  __          _  _       1_   _               + _   _            _    _      _           m__  _ _  _       _   _⁢ ___  _ _  _ _   _  __ _                ___ _   _ _      _  _ __        __    _    __    _⁢   _          _     __α___          _     _ _           _      _      _ _ _        __  _  _ _ _ _      _   _  _ __ _    __  _  _  _ _ _    _   __    ( _ _    28        )_   _      _       __ __      _     _     R _   __   B   _  _    __   = _  _  _      _  _R _ _  _          _   _   _     __   N    _  __ _   B _   _ _ _  _      ___ _+   _       __  __    _  __   _  __     _  N _  __  _       P__  _   _ _   _ ___  _ _   _· __             _ _  _     _    _ _     _    _  (  _     ___ _ __    _         _ __    _    _ _  _      _   _X  _ _ _ _     __ __   P    _    __    __    _   _ _ ____     __  _     ___ _     _ _ X    _ _  _            B _       _ _   _         _           _     _       _ _  )_  _   _     _ _      __      _  _  __  _       __m  _   _     _       _  _   _          1   _       __       +_             _  _ _        ___   _  _    m        _     _ __    ⁢     _ _  _   _     __ _  _  _  _  _           _   _ _  _  _   _   _     _       _ _ _____⁢  _  _ _  _    __  _ _α   ___    _ _  _    _ _        _ _ _    _  _   _ _ _            _ _      _ _   _ _ __  _     _  _  __    _   __      _ _      (___  _ _29     _  )      _  _  
Where α=1, the expressions_(27) to (29)_and the expressions (8) to (10) given hereinabove in the code amount control_system defined in the MPEG2 Test Mode 15 have the_following relationship. In particular, from the expressions (27) to (29), the_parameters Kp and Kb for code amount control are adaptively calculated in_accordance_with the_following expression_(30) based on the complexities XI, XP_and XB_of each frame:
   _          _              _ __    _    K__ _        P___   ___  _     _  =                _ _  _  __    _     (  _  __   _    _       _ _  _      _    _       X __          __ __I        __   _ _           ___   _      _   _   __X_ _          _    P       _  _      _ _ __    _        _       )       ___ __  __    __ __ _ _ _ _   _1   _   _    _      _ __   __  1_  _ _       _ _+       __ _    _m   __    _                       __     _ ___  ____ ;         _   _  ______       _K_       _   b __                _=__   _   _ __  _         _  ___ __  (    _          _ _      _    __     _    _    __X __ _  _ _ _      I     _         __  _  _         __     ___      