Abstract:
Auxiliary multi-pulse setting circuit  130  set candidates of pulse positions so that the pulse positions to which no pulse is located are selected in auxiliary multi-pulse searching circuit  131  prior to the pulse positions at which pulses have already been encoded in multi-pulse searching circuit  110.  Auxiliary multi-pulse searching circuit  131  generates an auxiliary multi-pulse signal according to the candidates of pulse positions set in auxiliary multi-pulse setting circuit  130  and encodes the auxiliary multi-pulse signal so that difference between the reproduced audio signal which is obtained by driving a linear predictive synthesis filter with the auxiliary multi-pulse signal and an input audio signal is minimized similarly to multi-pulse searching circuit  110.

Description:
BACKGROUND OF THE INVENTION 
     1. Field of the Invention 
     The present invention relates to an audio encoding apparatus and audio decoding apparatus which adopt a hierarchical encoding/decoding method. 
     2. Description of the Prior Art 
     Heretofore, the aim of introducing an audio encoding apparatus and decoding apparatus which adopt the hierarchical encoding method which enables decoding audio signals from a part of a bitstream of encoded signals as well as all of it, is to cope with the case that a part of the packets of encoded audio signals are lost in a packet transmission network. An example of such apparatus based on the CELP (Code Excited Linear Prediction) encoding method comprises excitation signal encoding blocks in a multistage connection. This is disclosed in “Embedded CELP coding for variable bit-rate between 6.4 and 9.6 kbit/s” by R. Drog in proceedings of ICASSP, pp. 681-684, 1991 and “Embedded algebraic CELP coders for wideband speech coding” by A. Le Guyader, et. al. in proceedings of EUSIPCO, signal processing VI, pp. 527-530, 1992. 
     With reference to FIGS. 2A and 2B, the operation of an example of the prior art will be explained. Although only two excitation signal encoding blocks are connected in the example for simplicity, the following explanation can be extended to the structure of three or more stages. 
     Frame dividing circuit  101  divides an input signal into frames and supplies the frames to sub-frame dividing circuit 
     Sub-frame dividing circuit  102  divides the input signal in a frame into sub-frames and supplies the sub-frames to linear-predictive analysis circuit  103  and psychoacoustic weighting signal generating circuit  105 . 
     Linear predictive analyzing circuit  103  applies linear predictive analysis to each sub-frame of the input from sub-frame dividing circuit  102  and supplies linear predictor coefficients a(i) (i=1,2,3, . . . , Np) to linear predictor coefficient quantizing circuit  104 , psychoacoustic weighting signal generating circuit  105 , psychoacoustic weighting signal reproducing circuit  106 , adopt ive codebook searching circuit  109 , multi-pulse searching circuit  110 , and auxiliary multi-pulse searching circuit  112 . Number Np in the former sentence represents the degree of linear predictive analysis and, for example may take a value of  10 . The correlation method and the covariance method are two examples of linear predictive analysis and they are explained in detail in chapter five of “Digital Audio Processing” published by Tohkai University Press in Japan. 
     Linear predictor coefficient quantizing circuit  104  quantizes the linear predictor coefficients for each frame instead of sub-frame. In order to decrease bitrate, it is common to adopt the method in which only the last sub-frame in the present frame is quantized and the rest of the sub-frames in the frame are interpolated using the quantized linear predictor coefficients of the present frame and the preceding frame. The quantization and interpolation are executed after converting linear predictor coefficients to line spectrum pairs (LSP). The conversion from linear predictor coefficients to LSP is explained in “Speech data Compression by LSP Speech Analysis-Synthesis Technique” in Journal of the Institute of Electronics, Information and Communication Engineers, J64-A, pp. 599-606, 1981. Well-known methods can be used for quantizing LSP. One example of such methods is explained in Japanese Patent Laid-open 4-171500. 
     After converting quantized LSPs to quantized linear predictor coefficients a′(i) (i=1,2,3, . . . , Np), linear predictive coefficient quantizing circuit  104  supplies the quantized linear predictor coefficients to psychoacoustic weighting signal reproducing circuit  106 , adaptive codebook searching circuit  109 , multi-pulse searching circuit  110 , and auxiliary multi-pulse searching circuit  112  and supplies indices representing quantized LSPs to multiplexer  114 . 
     Psychoacoustic weighting signal generating circuit  105  drives the psychoacoustically weighting filter Hw(z) represented by equation (1) by input signal in a sub-frame to generate psychoacoustically weighted signal which is supplied to target signal generating circuit  108 :                  Hw        (   z   )       =       1   -       ∑     i   =   1       N   p              a        (   i   )            R   2   i          z     -   i               1   -       ∑     i   =   1       N   p              a        (   i   )            R   1   i          z     -   i                 ,           (   1   )                                
     where R 1  and R 2  are weighting coefficients which control the amount of psychoacoustic weighting. For example, R 1 =0.6 and R 2 =0.9. 
     Psychoacoustic weighting signal reproducing circuit  106  drives a psychoacoustically weighting synthesis filter by excitation signal of the preceding sub-frame which is supplied via sub-frame buffer  107 . The psychoacoustic weighting synthesis filter consists of a linear predictive synthesis filter represented by equation (2) and psychoacoustically weighting filter Hw(z) in cascade connection whose coefficients are of the preceding sub-frame and have been held therein:                  H   s          (   z   )       =       1     1   -       ∑     i   =   1       N   p                a   ′          (   i   )            z     -   i               .             (   2   )                                
     After the driving, psychoacoustic weighting signal reproducing circuit  106  drives the psychoacoustically weighting synthesis filter by a series of zero signals to calculate the response to zero inputs. The response is supplied to target signal generating circuit  108 . 
     Target signal generating circuit  108  subtracts the response to zero inputs from the psychoacoustic weighting signal to get target signals X(n) (n=0,1,2, . . . , N−1) . Number N in the former sentence represents the length of a sub-frame. Target signal generating circuit  108  supplies the target signals to adaptive codebook searching circuit  109 , multi-pulse searching circuit  110 , gain searching circuit  111 , auxiliary multi-pulse searching circuit  112 , and auxiliary gain searching circuit  113 . 
     Using excitation signal of the preceding sub-frame supplied through sub-frame buffer  107 , adaptive codebook searching circuit  109  renews an adaptive codebook which has held past excitation signals. Adaptive vector signal Ad(n) (n=0,1,2, . . . , N−1) corresponding to pitch  d  is a signal delayed by pitch  d  which has been stored in the adaptive codebook. Here, if pitch  d  is longer than the length of a sub-frame N, adaptive codebook searching circuit  109  detaches  d  samples just before the present sub-frame and repeatedly connects the detached samples until the number of the samples reaches the length of a sub-frame N. Adaptive codebook searching circuit  109  drives the psychoacoustic weighting synthesis filter which is initialized for each sub-frame (hereinafter referred to as a psychoacoustic weighting synthesis filter in zero-state) by the generated adaptive code vector Ad(n) (n=0,1,2, . . . , N−1) to generate reproduced signals SAd(n) (n=0,1,2, . . . , N−1) and selects pitche d′ which minimizes error E(d), which is the difference between target signals X(n) and SAd(n), from a group of  d  within a predetermined searching range, for example d=17, . . . , 144. Hereinafter the selected pitch d′ will be referred to as  d  for simplicity.                E        (   d   )       =         ∑     n   =   1     N            X        (   n   )       2       -         (       ∑     n   =   1     N            X        (   n   )            SAd        (   n   )           )     2         ∑     n   =   1     N            SAd        (   n   )       2                   (   3   )                                
     Adaptive codebook searching circuit  109  supplies the selected pitch  d  to multiplexer  114 , the selected adaptive code vector Ad (n) to gain searching circuit  111 , and the regenerated signals SAd(n) to gain searching circuit  111  and multi-pulse searching circuit  110 . 
     Multi-pulse searching circuit  110  searches for  P  pieces of non-zero pulse which constitute a multi-pulse signal. Here, the position of each pulse is limited to the pulse position candidates which were determined in advance. The pulse position candidates for a different non-zero pulse are different from one another. The non-zero pulses are expressed only by polarity. Therefore, the coding the multi-pulse signal is equivalent to selecting index  j  which minimizes error E(j) in equation (4):                  E        (   j   )       =         ∑     n   =   1     N              X   ′          (   n   )       2       -         (       ∑     n   =   1     N              X   ′          (   n   )              SC   j          (   n   )           )     2         ∑     n   =   1     N              SC   j          (   n   )       2             ,           (   4   )                                
     where SCj (n) (n=0,1,2, . . . , N−1) is a reproduced signal obtained by driving the psychoacoustic weighting synthesis filter in zero-state by multi-pulse signals Cj (n=0, 1,2, . . . , N−1) which is constituted for index  j  ( j =0,1,2, . . . , J−1) which represents one of J pieces of combination of the pulse position candidate and the polarity, and X′ (n) (n=0,1,2, . . . , N−1) is a signal obtained by orthogonalizing the target signal X(n) by the reproduced signal SAd(n) of the adaptive code vector signal and given by equation (5):                  X   ′          (   n   )       =       X        (   n   )       -           ∑     n   =   1     N            X        (   n   )            SAd        (   n   )               ∑     n   =   1     N            SAd        (   n   )       2                SAd        (   n   )       .                 (   5   )                                
     This method is explained in detail in “Fast CELP coding 10 based on algebraic codes” in proceedings of ICASSP, pp. 1957-1960, 1987. 
     Index  j  representing the multi-pulse signal can be transmitted with          ∑     p   =   0       P   -   1            (     1   +       log   2          M        (   p   )           )                            
     bits where M(p)(p=0,1,2, . . . , P−1) is the number of the pulse position candidates for the p-th pulse. For example, the number of bits necessary to transmit index  j  is 20 provided that sampling rate is 8 kHz, the length of a sub-frame is 5 msec (N =40 samples), the number of pulses P is five, the number of the pulse position candidates M(p)=8, p=0,1,2, . . . , P-1, and the number of the pulse position candidates is, for simplicity, constant. 
     Multi-pulse searching circuit  110  supplies selected multi-pulse signal Cj (n) and the reproduced signal SCj (n) for the multi-pulse signal to gain searching circuit  111  and corresponding index  j  to multiplexer  114 . 
     Gain searching circuit  111  searches for the optimum gain consisting of GA(k) and GE(K) (k=0,1,2, . . . , K−1) for a pair of the adaptive code vector signal and the multi pulse signal from again codebook of size K. Index  k  of the optimum gain is selected so as to minimize error E(k) in equation (6):                  E        (   k   )       =       ∑     n   =   1     N            [       X        (   n   )       -       GA        (   k   )            SAd        (   n   )         -       GE        (   k   )            SCj        (   n   )           ]     2         ,           (   6   )                                
     where X(n) is the target signal, SAd(n) is the reproduced adaptive code vector, and SCj (n) is the reproduced multi-pulse signal. 
     Gain searching circuit  111  also generates excitation signal D(n) (n=0,1,2, . . . , N−1) using the selected gain, the adaptive code vector, and the multi-pulse pulse signal. Excitation signal D(n) is supplies to sub-frame buffer  107  and auxiliary multi-pulse searching circuit  112 . Moreover, gain searching circuit  111  drives the psychoacoustic weighting filter in zero-state by excitation signal D(n) to generate reproduced excitation signal SD(n) (n=0,1,2, . . . , N−1) which is supplied to auxiliary multi-pulse searching circuit  112 , auxiliary gain searching circuit  113 , and multiplexer  114 . 
     Similarly to multi-pulse searching circuit  110 , auxiliary multi-pulse searching circuit  112  generates auxiliary multi-pulse signal Cm(n) (n=0,1,2, . . . , N−1) and regenerated auxiliary multi-pulse signal SCm(n) (n=0,1,2, . . . , N−1) and selects m which minimizes error E(m) in equation (7):                  E        (   m   )       =         ∑     n   =   1     N              X   ″          (   n   )       2       -         (       ∑     n   =   1     N              X   ″          (   n   )            SCm        (   n   )           )     2         ∑     n   =   1     N            SCm        (   n   )       2             ,           (   7   )                                
     where X″ (n) (n  32  0,1,2, . . . , N−1) is a signal obtained by orthogonalizing target signal X(n) by reproduced signal SD(n) of the excitation signal and given by equation (8):                  X   ″          (   n   )       =       X        (   n   )       -           ∑     n   =   1     N            X        (   n   )            SD        (   n   )               ∑     n   =   1     N            SD        (   n   )       2                SD        (   n   )       .                 (   8   )                                
     Index  m  representing multi-pulse signal C(m) can be transmitted with          ∑     p   =   0         p   ′     -   1            (     1   +       log   2            M   ′          (   p   )           )                            
     bits where P′ is the number of auxiliary multi-pulse signals and M′ (p) (p  32  0,1,2, . . . , P′−1) is the number of the pulse position candidates for p-th pulse. For example, the number of bits necessary to transmit index  m  is 20 provided that the number of pulses P′ is five, the number of the pulse position candidates for each pulse M′ (p) is 8, p=0,1,2, . . . , P′−1, and the number of the pulse position candidates is, for simplicity, constant. 
     Auxiliary multi-pulse searching circuit  112  also supplies regenerated signal SCm(n) to auxiliary gain searching circuit  113  and corresponding index m to multiplexer  114 . 
     Auxiliary gain searching circuit  113  searches for the optimum gain consisting of GEA(l) and GEC(l) (l=0,1,2, . . . , K′−1) for a pair of the excitation signal and the auxiliary multi-pulse signal from a gain codebook of size K′. Index  l  of the optimum gain is selected so as to minimize error E(l) in equation (9)                  E        (   l   )       =       ∑     n   =   1     N            [       X        (   n   )       -       GEA        (   l   )            Sd        (   n   )         -       GEC        (   l   )            SCm        (   n   )           ]     2         ,           (   9   )                                
     where X(n) is the target signal, SD(n) is the reproduced excitation signal, and SCm(n) is the reproduced auxiliary multi-pulse signal. 
     Selected index  l  is supplied to multiplexer  114 . 
     Multiplexer  114  converts indices, which correspond to the quantized LSP, the adaptive code vector, the multi-pulse signal, the gains, the auxiliary multi-pulse signal and the auxiliary gains, into a bitstream which is supplied to first output terminal  115 . 
     Bitstream from second input terminal  117  is supplied to demultiplexer  117 . Demultiplexer  117  converts the bitstream into the indices which correspond to the quantized LSP, the adaptive code vector, the multi-pulse signal, the gains, the auxiliary multi-pulse signal and the auxiliary gains. Demultiplexer  117  also supplies the index of the quantized LSP to linear predictor coefficient decoding circuit  118 , the index of the pitch to adaptive codebook decoding circuit  119 , the index of the multi-pulse signal to multi-pulse decoding circuit  120 , the index of the gains to gain decoding circuit  121 , the index of the auxiliary multi-pulse signal to auxiliary multi-pulse decoding circuit  124 , and the index of the auxiliary gains to auxiliary gain decoding circuit  125 . 
     Linear predictor coefficient decoding circuit  118  docodes the index of the quantized LSP to quantized linear predictor coefficients a′ (i) (i=1,2,3, . . . , Np) which is supplied to first signal reproducing circuit  122  and second signal reproducing circuit  126 . 
     Adaptive codebook decoding circuit  119  decodes the index of the pitch to adaptive code vector Ad(n) which is supplied to gain decoding circuit  121 . Multi-pulse decoding circuit  120  decodes the index of the multi-pulse signal to multi-pulse signal Cj(n) which is supplied to gain decoding circuit  121 . Gain decoding circuit  121  decodes the index of the gains to gains GA(k) and GC(k) and generates a first excitation signal using gains GA(k) and GC(k), adaptive code vector Ad(n), multi-pulse signal Cj(n) and gains GA(k) and GC(k). The first excitation signal is supplied to first signal reproducing circuit  122  and auxiliary gain decoding circuit  125 . 
     First signal reproducing circuit  122  generates a first reproduced signal by driving linear predictive synthesis filter Hs(z) with the first excitation signal. The first reproduced signal is supplied to second output terminal  123 . 
     Auxiliary multi-pulse decoding circuit  124  decodes the index of the auxiliary multi-pulse signal to auxiliary multi-pulse signal Cm(n) which is supplied to auxiliary gain decoding circuit  125 . Auxiliary gain decoding circuit  125  decodes the index of the auxiliary gains to auxiliary gains GEA(l) and GEC (l) and generates a second excitation signal using the first excitation signal, auxiliary multi-pulse signal Cm(n) and auxiliary gains GEA(l) and GEC(l). 
     Second signal reproducing circuit  126  generates a second reproduced signal by driving linear predictive synthesis filter Hs(z) with the second excitation signal. The second reproduced signal is supplied to third output terminal  127 . 
     The conventional method explained above has a disadvantage that coding efficiency of a multi-pulse signal in the second stage and following stages is not sufficient because there is a possibility that each stage locates pulses in the same positions with those of pulses encoded in former stages. Because a multi-pulse signal is represented by positions and polarities of pulses, the same multi-pulse is formed when plural pulses are located in the same position and when one pulse is located therein. Therefore, coding efficiency is not improved when plural pulses are located in the same position. 
     SUMMARY OF THE INVENTION 
     An object of the present invention is to provide an audio encoding apparatus which efficiently encodes a multi-pulse in multiple stages and a corresponding audio decoding apparatus. 
     According to an aspect of the present invention, there is provided an audio encoding apparatus for encoding in multiple stages a multi-pulse signal representing excitation signal of a reproduced audio signal by plural pulses so that difference between the reproduced audio signal and an input audio signal is minimized, the reproduced audio signal being obtained by driving a linear predictive synthesis filter by means of the excitation signal, which comprises between the stages a multi-pulse setting circuit which sets pulse positions so that positions to which no pulse is located are selected prior to positions at which pulses have been already encoded in preceding stages, wherein each of the multi stages encodes pulses of the multi-pulse signal which are in the pulse positions set by the multi-pulse setting circuit. 
     According to another aspect of the present invention, there is provided an audio decoding apparatus for reproducing an audio signal by driving a linear predictive synthesis filter by means of an excitation signal, coefficients of the linear predictive synthesis filter being reproduced from data encoded in a encoding apparatus, the excitation signal being represented by plural pulses reproduced in multiple stages from data encoded in corresponding multiple stages in the encoding apparatus, which comprises between the stages a multi-pulse setting circuit which sets pulse positions so that position to which no pulse is located are selected prior to positions at which pulses have been already decoded in preceding stages, wherein each of the multi stages decodes pulses of the multi-pulse signal which is in the pulse positions set by the multi-pulse setting circuit. 
     According to the present invention, the multi-pulse setting circuit (an auxiliary multi-pulse setting circuit) sets candidates for pulse positions so that the pulse positions to which no pulse has been located are selected prior to the pulse positions at which pulses have been already encoded, and a multi-pulse searching circuit following the multi-pulse setting circuit selects pulse positions from the candidates and encodes the selected pulse positions. Thus, the multi-pulse searching circuit encodes the information concerning the selected pulse positions among candidates of pulse positions from which positions of already encoded pulses are excluded, whereby required number of bits for the encoding can be reduced. 
    
    
     These and other objects, features and advantages of the present invention will become more apparent in light of the following detailed description of the best mode embodiments thereof, as illustrated in the accompanying drawings. 
     BRIEF DESCRIPTION OF THE DRAWINGS 
     FIG. 1A shows an audio encoding apparatus according to one embodiment of the present invention; 
     FIG. 1B shows an audio decoding apparatus according to one embodiment of the present invention; 
     FIG. 2A shows an audio encoding apparatus in the prior art; and 
     FIG. 2B shows an audio decoding apparatus in the prior art. 
    
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT 
     A preferred embodiment according to the present invention will be explained with reference to the accompanying drawings. 
     FIGS. 1A and 1B show an audio encoding apparatus and an audio decoding apparatus according to one embodiment of the present invention. 
     Although only two excitation signal encoding blocks are connected in the apparatuses for simplicity, the following explanation can be extended to the structure of three or more stages. 
     Differences between the apparatuses according to this embodiment and the prior art are the addition of multi-pulse setting circuits  130  and  132 , replacement of auxiliary multi-pulse searching circuit  112  by auxiliary multi-pulse searching circuit  131 , and replacement of auxiliary multi-pulse decoding circuit  124  by auxiliary multi-pulse decoding circuit  133 . Therefore, only the differences will be explained, as follows. 
     Auxiliary multi-pulse setting circuit  130  sets candidates for pulse positions so that pulse positions to which no pulse has been assigned are selected in auxiliary multi-pulse searching circuit  131  prior to those of pulses already encoded in multi-pulse searching circuit  110 . For example, auxiliary multi-pulse setting circuit  130  operates as follows: Auxiliary multi-pulse setting circuit  130  divides each sub-frame into  O  pieces of sub-areas. One pulse is assigned to each sub-area. Candidates for the position of each pulse is the sub-area. Auxiliary multi-pulse setting circuit  130  selects a limited number of sub-areas from the top of the ascending order of the number of pulses already encoded therein, and outputs the indices of the selected sub-areas. The indices may be called the indices of pulses because the pulses and the sub-areas are connected biuniquely. Auxiliary multi-pulse setting circuit  130  has candidates for pulse positions X(q, r) (q=0,1,2, . . . , Q-1; r=0,1,2, . . . , M″(q)−1) for  O  pieces of pulse in advance, where  O  represents the number of pulses,  q  represents pulse number, M″(q) represents the total number of candidates for pulse positions corresponding to pulse  q  , and  r  represents serial number of a candidate of a pulse position. Here, the number of pulses Q, for example,  10 , is different from the number of pulses of the multi-pulse signal, for example, five which is the same as the prior art. In this embodiment, M″(q) is constant and four, which is quotient of division of the length of sub-frame  40  by the number of pulses  10 , for all the values of  q  . A candidate for a pulse position X(q,r) for a certain pair of  q  and  r  is different from that for another pair of  q  and  r  . Auxiliary multi-pulse setting circuit  130  comprises counters Ctr(q) (q=0,1,2, . . . , Q−1) corresponding to  O  pieces of pulses. The initial values of counters Ctr(q) are zero. Pulse number  q  is extracted by searching for one candidate of which position is the same as that of a pulse of the multi-pulse signal supplied from multi-pulse searching circuit  110  from candidates for pulse positions X(q,r). The counter Ctr(q) corresponding to the extracted pulse number  q  is incremented. The same operation is repeated for all the pulses supplied from multi-pulse searching circuit  110 . Subsequently, Q′, for example, five, pieces of counters are selected from the top in ascending order of count values. Serial numbers of selected counters are represented by s(t) (t=0,1,2, . . . , Q′−1). Therefore, s(t) indicates one of pulse numbers ranging from zero to Q-1. In this meaning, s(t) may be called pulse number. In the selection, if plural counters take the same count value, for example the counter with minimum  q  is selected. Moreover, auxiliary multi-pulse setting circuit  130  supplies Q′ pieces of selected pulse number s(t) (t=0,1,2, . . . , Q′−1) to auxiliary multi-pulse searching circuit  131 . 
     Similarly to auxiliary multi-pulse setting circuit  130 , auxiliary multi-pulse searching circuit  131  comprises candidates for pulse positions X(q,r) (q=0,1,2, . . . , Q-1; r=0,1,2, . . . , M″(q)−1) for  O  pieces of pulse in advance. Auxiliary multi-pulse searching circuit  131  searches for Q′ pieces of non-zero pulse constituting an auxiliary multi-pulse signal. 
     Here, the position of the each pulse is limited within candidates for pulse position X(s(t),r) (r=0,1,2, . . . , M″(s(t))−1) in accordance with Q′ pieces of pulse number s(t) (t=0,1,2, . . . , Q′−1). Moreover, the amplitudes of the pulses are represented only by polarity. Therefore, encoding of the auxiliary multi-pulse is performed by constituting auxiliary multi-pulse signals Cm(n) (n=0,1,2, . . . , N−1) for index m which represents one of all the combinations of candidates for pulse position and polarities, driving the psychoacoustic weighting synthesis filter in zero-state with auxiliary multi-pulse signals Cm(n) so as to generate reproduced signals SCm(n) (n=0,1,2, . . . , N−1), and selecting index m which minimizes error E(m) represented by equation (7). Selected index m can be encoded and transmitted with          ∑     t   =   0         Q   ′     -   1            (     1   +       log   2            M   ″          (     s        (   t   )       )           )                            
     bits. For example, substituting Q′=5 and M″ (s(t))=4 for the equation, the number of bit is 15. That is, the number of bit required to encode an auxiliary multi-pulse signal is 15. The corresponding number in the prior art is 20. Therefore, the number of bit is reduced by five. Auxiliary multi-pulse searching circuit  131  supplies reproduced auxiliary multi-pulse signal SCm(n) to auxiliary gain searching circuit  113  and corresponding index  m  to multiplexer  114 . 
     Auxiliary multi-pulse setting circuit  132  in the audio decoding apparatus operates in the same way as auxiliary multi-pulse setting circuit  130  in the audio encoding apparatus. That is, auxiliary multi-pulse setting circuit  132  selects pulse numbers s(t) (t=0,1,2, . . . , Q′−1) for Q′ pieces of pulse in a multi-pulse supplied from multi-pulse decoding circuit  120 , and supplies selected pulse numbers s(t) to auxiliary multi-pulse decoding circuit  133 . 
     Auxiliary multi-pulse decoding circuit  133  reproduces the auxiliary multi-pulse signal using the index of the auxiliary multi-pulse signal supplied from demultiplexer  117  and pulse number s(t) (t=0,1,2, . . . , Q′−1) selected in auxiliary multi-pulse setting circuit  132  and referring to candidates for each pulse position X(s(t),r) (r=0,1,2, . . . , M″), and supplies the auxiliary multi-pulse signal to auxiliary gain decoding circuit  125 . 
     As explained above, according to the audio encoding apparatus and the audio decoding apparatus of the present invention, the efficiency of encoding a multi-pulse signal in a second stage and following stages in multistage connection can be improved because plural pulses constituting the multi-pulse signal are scarcely located in the same position and the number of bits required for encoding can be reduced without deteriorating coding quality. 
     Although the present invention has been shown and explained with respect to the best mode embodiments thereof, it should be understood by those skilled in the art that the foregoing and various other changes, omissions, and additions in the form and detail thereof may be made therein without departing from the spirit and scope of the present invention.