Abstract:
Provided is an encoder which can decode a high-quality stereo signal while keeping the amount of information in the bit allocation information to a minimum when a scalable coding technique is used for a stereo signal. In the encoder, a principal component analysis (PCA) converter converts the left signal and the right signal of the stereo signal and generates the main signal of the first layer and the sub-signal of the first layer. In the first layer to the M-th layer (where M is a natural number, 2 or greater), an adaptive residual encoder compares the importance of the main signal of the m-th layer, where m is a natural number from 1 to M, and the importance of the sub-signal of the m-th layer, selects the signal having the higher importance, encodes the selected signal, and generates the encoded data of the m-th layer. From the first layer to the M−1-st layer, the adaptive residual encoder generates the signal obtained by subtracting the decoded signal of the encoded data of the m-th layer from the selected signal as the main signal of the m+1-st layer, and generates the unselected signal as the sub-signal of the m+1-st layer.

Description:
TECHNICAL FIELD 
     The present invention relates to an encoding apparatus, decoding apparatus, and encoding and decoding methods adopting a principal component analysis transformation. 
     BACKGROUND ART 
     In conventional speech communication systems, monaural speech signals are transmitted under the constraint of a limited transmission band. With broadbandization of communication networks, user&#39;s expectation on speech communication has risen from mere intelligibility to stereo image and naturalness, and a trend to deliver stereo speech has emerged. Therefore, a coding scheme for transmitting stereo speech efficiently is desired. 
     To achieve the above goal, encoding methods using PCA (Principal Component Analysis) have been studied as a method of encoding a stereo signal (i.e. two channels) or a plurality of channels (see Non-Patent Literature 1 and Non-Patent Literature 2). In an encoding method using PCA, an input signal is transformed by PCA (PCA-transformation) and each transformed signal is encoded independently. PCA transformation refers to linear transformation that achieves energy concentration in an input signal according to the distribution of eigenvalues obtained from the co-variance matrix of the input signal. 
     For example, a PCA-transformed stereo signal is transformed into a principal signal corresponding to principal components of the stereo signal (e.g. audio signal components or dominant speech components), and a secondary signal corresponding to the rest of the components other than the principal signal of the stereo signal. That is, the energy of the stereo signal is concentrated on the principal signal. By this means, with an encoding method using PCA, it is possible to remove the redundancy in an input signal by encoding signals in which energy is concentrated, so that it is possible to improve the efficiency of coding. Also, the principal signal and the secondary signal of a stereo signal are mutually uncorrelated, so that it is possible to further remove the redundancy in an input signal. 
       FIG. 1  and  FIG. 2  are block diagrams showing a general encoding apparatus and decoding apparatus of stereo signal codec using PCA. In the encoding apparatus shown in  FIG. 1 , PCA transformation section  11  transforms left signal L(n) and right signal R(n) of a stereo signal into primary signal P(n) and secondary signal A(n) (equation 1).
     [1]
 
 P ( n )= v   1   ×L ( n )+ v   2   ×R ( n )
 
 A ( n )=− v   2   ×L ( n )+ v   1   ×R ( n )  (Equation 1)
   

     Here, v 1  and v 2  refer to the PCA transformation parameters to use to transform left signal L(n) and right signal R(n) into primary signal P(n) and secondary signal A(n). Encoding section  12  and encoding section  13  encode primary signal P(n) and secondary signal A(n) independently (e.g. scalar quantization or vector quantization), and output encoded data of primary signal P(n) and encoded data of secondary signal A(n) to multiplexing section  15 . Also, quantizing section  14  quantizes PCA transformation parameters v 1  and v 2  obtained in PCA transformation section  11 , and generates quantized codes of the PCA transformation parameters. Multiplexing section  15  multiplexes the encoded data of primary signal P(n), the encoded data of secondary signal A(n) and the quantized codes of the PCA transformation parameters, and generates bit streams. 
     Upon decoding a stereo signal in a decoding apparatus shown in  FIG. 2 , demultiplexing section  21  demultiplexes bit streams into encoded data of primary signal P(n), encoded data of secondary signal A(n) and quantized codes of PCA transformation parameters. Then, decoding section  22  decodes the encoded data of primary signal P(n) and obtains decoded primary signal P{tilde over ( )}(n). Also, decoding section  23  decodes the encoded data of secondary signal A(n) and obtains decoded secondary signal A{tilde over ( )}(n). Also, dequantizing section  24  dequantizes the quantized codes of PCA transformation parameters and obtains PCA transformation parameters v{tilde over ( )} 1  and v{tilde over ( )} 2 . Inverse PCA transformation section  25  performs an inverse PCA transformation of primary signal P{tilde over ( )}(n) and secondary signal A{tilde over ( )}(n) using PCA transformation parameters v{tilde over ( )} 1  and v{tilde over ( )} 2 , and generates left signal L{tilde over ( )}(n) and right signal R{tilde over ( )}(n) of a stereo signal (equation 2).
     [2]
 
 {tilde over (L)} ( n )= {tilde over (v)}   1   ×{tilde over (P)} ( n )− {tilde over (v)}   2   ×Ã ( n )
 
 {tilde over (R)} ( n )= {tilde over (v)}   2   ×{tilde over (P)} ( n )+ {tilde over (v)}   1   ×Ã ( n )  (Equation 2)
   

     Also, according to speech communication systems, in speech data communication on IP networks, speech coding providing a scalable configuration is demanded to realize traffic control on networks and multicast communication. A scalable configuration refers to a configuration in which the receiving side can decode speech data even from partial encoded data. As a speech encoding technique providing a scalable configuration, scalable encoding (layer encoding) techniques integrating a plurality of encoding techniques in a layered manner have been studied. In scalable encoding techniques, the transmitting side performs layered coding processing of input speech signals and transmits encoded data layered in a plurality of encoded layers. 
     Also, in speech communication systems, there is a demand to compress speech signals at a low bit rate and transmit the results for efficient use of radio resources. Under a low bit rate constraint, when stereo signal coding is performed using the above PCA, it is difficult to encode both the primary signal and the secondary signal in high quality. Consequently, it is necessary to adequately allocate limited bits to the primary signal and the secondary signal. For example, Non-Patent Literature 1 and Non-Patent Literature 2 disclose a bit allocation method in stereo signal coding using PCA. 
     Non-Patent Literature 1 discloses a method of applying parametric coding to a secondary signal in stereo signal coding processing. That is, in a primary signal and a secondary signal, the secondary signal is represented as a parameter (parametric coding parameter) based on the difference between the characteristic of primary signal encoded data and the characteristic of the secondary signal. By applying parametric coding to the secondary signal, the redundancy of the secondary signal is removed, which decreases the bit rate of the secondary signal. By this means, primary signal encoded data and parametric coding parameter (secondary signal) with a low bit rate are allocated to limited bits. 
     Non-Patent Literature 2 discloses a bit allocation method of adaptively allocating bits according to the energy of each of a plurality of channels obtained by applying PCA transformation to an input signal. For example, in stereo signal coding processing, bits are adaptively allocated according to the energy of each of a primary signal and a secondary signal obtained by applying PCA transformation to a stereo signal (i.e. two channels). By this means, it is possible to preferentially transmit the channel of higher energy among a plurality of channels after PCA transformation. Also, under a low bit rate constraint, it is possible to discard the channel of lower energy among a plurality of channels forming a stereo signal. This transmission method is referred to as “channel scalability transmission method.” 
     CITATION LIST 
     Non-Patent Literature 
     
         
         [NPL 1] 
         Manuel Briand, David Virette and Nadine Martin “Parametric coding of stereo audio based on principal component analysis”, Proc of the 9 th  International Conference on Digital Audio Effects, Montreal, Canada, Sep. 18-20, 2006. 
         [NPL 2] 
         Dai Yang, Hongmei Ai, Chris Kyriakakis and C.-C. Jay Kuo “High-fidelity multichannel audio coding with Karhunen Lóeve Transform”, IEEE transactions on speech and audio processing, Vol. 11, No. 4, July 2003. 
       
    
     SUMMARY OF INVENTION 
     Technical Problem 
     However, in scalable coding systems using a scalable coding technique for stereo signals, if the above bit allocation method is adopted, the amount of information (the number of bits) of bit allocation information to be reported from the encoding apparatus to the decoding apparatus increases, and therefore the efficiency of coding degrades. 
     To be more specific, if the bit allocation method disclosed in Non-Patent Literature 1 is applied to a scalable coding system, a parametric coding parameter based on a principal signal subjected to scalable coding needs to be updated in each coding layer of scalable coding. Also, this parametric coding parameter requires a predetermined number of bits in each coding layer. That is, the encoding apparatus needs to report, to the decoding apparatus, bit allocation information indicating the amount of information (number of bits) of the parametric coding parameter that varies between coding layers, and therefore the efficiency of coding degrades. 
     Also, if the bit allocation method disclosed in Non-Patent Literature 2 is applied to a scalable coding system, the number of bits allocated to the primary signal and secondary signal of a stereo signal varies between coding layers. Consequently, the encoding apparatus needs to report, to the decoding apparatus, bit allocation information indicating the number of bits allocated to the primary signal and the secondary signal, and therefore the efficiency of coding degrades. 
     Thus, in a scalable coding system, when bits are allocated to the primary signal and secondary signal obtained by applying PCA transformation to a stereo signal, it is necessary to report bit allocation information of predetermined bits every coding layer, which increases the amount of bit allocation information to be reported to decoded signals. 
     It is therefore an object of the present invention to provide an encoding apparatus, decoding apparatus, and encoding and decoding methods for minimizing the amount of bit allocation information and generating stereo signals of high quality upon using a scalable coding technique for stereo signals. 
     Solution to Problem 
     The encoding apparatus of the present invention employs a configuration having: a transformation section that performs principal component analysis transformation of a first channel signal and a second channel signal of an input stereo signal, to generate a first layer primary signal and a first layer secondary signal; an m-th layer selecting section that compares importance of an m-th layer primary signal (where m is a natural number equal to or greater than 1 and equal to or less than M) and importance of an m-th layer secondary signal in a first layer to an M-th layer (where M is a natural number equal to or greater than 2), and selects a signal of higher importance; an m-th layer encoding section that encodes the signal selected in the m-th layer selecting section, to generate m-th layer encoded data in the first layer to the M-th layer; an m-th layer decoding section that decodes the m-th encoded data to generate an m-th layer decoded signal in the first layer to an (M−1)-th layer; a subtracting section that generates a signal obtained by subtracting the m-th layer decoded signal from the signal selected in the m-th layer selecting section, and a signal that is not selected in the m-th layer selecting section, as an (m+1)-th layer primary signal and an (m+1)-th layer secondary signal, in the first layer to the (M−1)-th layer; and a transmitting section that transmits encoded data of the first layer to the M-th layer and signal information indicating signals selected in selecting sections in the first layer to the M-th layer. 
     Advantageous Effects of Invention 
     According to the present invention, upon using a scalable coding technique for stereo signals, the encoding apparatus encodes only the signal of the higher importance between two signals of a primary signal and a secondary signal obtained by applying PCA transformation to a stereo signal in each coding layer, so that it is possible to minimize the amount of bit allocation information while the decoding side can generate stereo signals of high quality. 
    
    
     
       BRIEF DESCRIPTION OF DRAWINGS 
         FIG. 1  is a block diagram showing a configuration of a general encoding apparatus using PCA; 
         FIG. 2  is a block diagram showing a configuration of a general decoding apparatus using PCA; 
         FIG. 3  is a block diagram showing a configuration of an encoding apparatus according to Embodiment 1 of the present invention; 
         FIG. 4  is a block diagram showing a configuration inside a PCA transformation section according to Embodiment 1 of the present invention; 
         FIG. 5  is a block diagram showing a configuration inside an adaptive residue encoding section according to Embodiment 1 of the present invention; 
         FIG. 6  is a block diagram showing a configuration inside a selecting section according to Embodiment 1 of the present invention; 
         FIG. 7  is a block diagram showing a configuration of a decoding apparatus according to Embodiment 1 of the present invention; 
         FIG. 8  is a block diagram showing a configuration of an encoding apparatus according to Embodiment 2 of the present invention; 
         FIG. 9  is a block diagram showing a configuration inside a band division encoding section according to Embodiment 2 of the present invention; 
         FIG. 10  shows a signal formed in a band division encoding section according to Embodiment 2 of the present invention; 
         FIG. 11  is a block diagram showing a configuration of a decoding apparatus according to Embodiment 2 of the present invention; 
         FIG. 12  is a block diagram showing a configuration inside a band division decoding section according to Embodiment 2 of the present invention; 
         FIG. 13  is a block diagram showing a configuration of a selecting section in a case of performing another selecting processing, according to the present invention; 
         FIG. 14  is a block diagram showing a configuration of an encoding apparatus that performs processing of dividing a signal, which is obtained by applying an MDCT to an LPC residual signal, into a plurality of subbands, according to the present invention; 
         FIG. 15  is a block diagram showing a configuration of another encoding apparatus according to the present invention; 
         FIG. 16  is a block diagram showing a configuration of another decoding apparatus according to the present invention; and 
         FIG. 17  is a block diagram showing a configuration of a decoding apparatus that performs processing of combining signals divided into a plurality of subbands, according to the present invention. 
     
    
    
     DESCRIPTION OF EMBODIMENTS 
     Now, embodiments of the present invention will be explained using the accompanying drawings. 
     (Embodiment 1) 
       FIG. 3  is a block diagram showing the configuration of an encoding apparatus according to the present embodiment, and  FIG. 7  is a block diagram showing the configuration of a decoding apparatus according to the present embodiment. As an example, a scalable configuration of M layers will be explained as the configurations of the encoding apparatus and decoding apparatus according to the present embodiment. That is, in the following explanation, assume that the number of coding layers is M (M is a natural number equal to or greater than 2) in scalable coding processing. In encoding apparatus  100  shown in  FIG. 3 , adaptive residue encoding sections  102 - 1  to  102 -M support the first layer to the M-th layer, respectively. Similarly, in decoding apparatus  200  shown in  FIG. 7 , decoding sections  202 - 1  to  202 -M support the first layer to the M-th layer, respectively. Also, in the following explanation, the left signal and the right signal of a stereo signal are divided every NB samples (NB is a natural number), and NB samples form one frame. Here, the left signal and the right signal are represented by left signal L(n) and right signal R(n), respectively. Also, n represents the (n+1)-th signal element in a signal divided every NB samples, and n equals to numbers between 0 to NB−1. 
     In encoding apparatus  100  shown in  FIG. 3 , PCA transformation section  101  receives as input left signal L(n) and right signal R(n) of a stereo signal. PCA transformation section  101  performs a PCA transformation of input left signal L(n) and right signal R(n) according to equation 1, to generate first layer primary signal P 1 (n) and first layer secondary signal A 1 (n). Then, PCA transformation section  101  outputs first layer primary signal P 1 (n) and first layer secondary signal A 1 (n) to adaptive residue encoding section  102 - 1 . Further, PCA transformation section  101  outputs PCA transformation parameters v 1  and v 2  calculated upon PCA transformation processing, to quantizing section  103 . 
     Adaptive reissue encoding sections  102 - 1  to  102 -M adaptively each select one of the two signals based on the importance of the primary signal and the importance of the secondary signal in the corresponding coding layer, and encode the selected signal (i.e. adaptive residue encoding). To be more specific, in the first layer to the M-th layer, adaptive residue encoding section  102 -m (m is a natural number equal to or greater than 1 and equal to or less than M) compares the importance of the m-th layer primary signal and the importance of the m-th layer secondary signal, selects the signal of the higher importance and generates m-th layer encoded data (bit sequence) by encoding the selected signal. Also, in the first layer to the (M−1)-th layer, adaptive residue encoding section  102 -m generates a residual signal obtained by subtracting a decoded signal of encoded data from the selected signal, and the other signal than the selected signal, as the (m+1)-th layer primary signal and the (m+1)-th layer secondary signal, respectively. Also, in the first layer to the M-th layer, adaptive residue encoding section  102 -m generates an indicator representing signal information to indicate an encoded signal (primary signal or secondary signal). For example, if a signal indicated by the indicator is a primary signal, an encoded signal is the m-th layer primary signal, and, if a signal indicated by the indicator is a secondary signal, an encoded signal is the m-th layer secondary signal. That is, an indicator is generated as bit allocation information to indicate a signal allocated to the bit sequence for encoded data set in each coding layer. 
     For example, adaptive residue encoding section  102 - 1 , which supports the lowest layer (i.e. first layer), applies adaptive residue encoding processing to first layer primary signal P 1 (n) and first layer secondary signal A 1 (n) received as input from PCA transformation section  101 , and generates first layer encoded data C 1 . Also, adaptive residue encoding section  102 - 1  generates a residual signal obtained by subtracting a decoded signal of encoded data C 1  from the encoded signal (the selected signal) in the input signals (first layer primary signal P 1 (n) and first layer secondary signal A 1 (n)) and generates the other signal (i.e. the signal that is not selected) than the encoded signal (i.e. the selected signal) in the input signals (first layer primary signal P 1 (n) and first layer secondary signal A 1 (n)), as second layer primary signal P^ 2 (n) and second layer secondary signal A^ 2 (n). Also, adaptive residue encoding section  102 - 1  generates indicator F 1  indicating a signal encoded in the first layer (i.e. first layer primary signal P 1 (n) or first layer secondary signal A 1 (n)). Then, adaptive residue encoding section  102 - 1  outputs second layer primary signal P^ 2 (n) and second layer secondary signal A^ 2 (n) to adaptive residue encoding section  102 - 2  supporting the next coding layer (i.e. a second layer), and outputs indicator F 1  and encoded data C 1  to multiplexing section  104 . 
     Similarly, adaptive residue encoding section  102 - 2  receives second layer primary signal P^ 2 (n) and second layer secondary signal A^ 2 (n) as input from adaptive residue encoding section  102 - 1 . Then, in the same way as in adaptive residue encoding section  102 - 1 , adaptive residue encoding section  102 - 2  generates second layer encoded data C 2 , third layer primary signal P^ 3 (n), third layer secondary signal A^ 3 (n) and indicator F 2 . Then, adaptive residue encoding section  102 - 2  outputs third layer primary signal P^ 3 (n) and third layer secondary signal A^ 3 (n) to adaptive residue encoding section  102 - 3  supporting the next coding layer (i.e. a third layer), and outputs indicator F 2  and encoded data C 2  to multiplexing section  104 . The same applies to adaptive residue encoding sections  102 - 3  to  102 -M. Here, adaptive residue encoding section  102 -M supporting the highest layer (i.e. M-th layer) does not output coding residual signals as the primary signal and secondary signal of the next coding layer. That is, only in the first layer to the (M−1)-th layer, that is, only adaptive residue encoding sections  102 - 1  to  102 -(M−1) generate a coding residual signal obtained by subtracting a decoded signal of encoded data from a selected signal, and a signal that is not selected, as the (m+1)-th layer primary signal and the (m+1)-th layer secondary signal, respectively. 
     Quantizing section  103  quantizes PCA transformation parameters v 1  and v 2  received as input from PCA transformation section  101 , and generates quantized codes of the PCA transformation parameters. Then, quantizing section  103  outputs the quantized codes of PCA transformation parameters to multiplexing section  104 . 
     Multiplexing section  104  multiplexes encoded data C m  and indicators F m  individually received as input from adaptive residue encoding sections  102 - 1  to  102 -M, and the quantized codes received as input from quantizing section  103 , and generates bit streams. The resulting bit streams are transmitted to decoding apparatus  200  ( FIG. 7 ) via the communication path. 
       FIG. 4  is a block diagram showing the configuration inside PCA transformation section  101 . Co-variance matrix calculating section  1011  calculates a co-variance matrix using left signal L(n) and right signal R(n) in frame units of a stereo signal, and outputs the calculated co-variance matrix to eigenvector calculating section  1012 . 
     Eigenvector calculating section  1012  calculates a co-variance matrix eigenvector using the co-variance matrix received as input from co-variance matrix calculating section  1011 . Here, the elements of the eigenvector calculated in eigenvector calculating section  1012  are PCA transformation parameters v 1  and v 2 . Then, eigenvector calculating section  1012  outputs the calculated eigenvector (PCA transformation parameters) to PCA transformation matrix forming section  1013  and quantizing section  103  shown in  FIG. 3 . 
     PCA transformation matrix forming section  1013  forms a PCA transformation matrix using the eigenvector received as input from eigenvector calculating section  1012 , and outputs the formed PCA transformation matrix to transformation section  1014 . 
     Transformation section  1014  transforms left signal L(n) and right signal R(n) of a stereo signal into first layer primary signal P 1 (n) and first layer secondary signal A 1 (n), using the PCA transformation matrix received as input from PCA transformation matrix forming section  1013 . Here, P 1 (n)=P(n) and A 1 (n)=A(n)). 
     Next, as an example of adaptive residue encoding processing in adaptive residue encoding sections  102 - 1  to  102 -M, the configuration inside adaptive residue encoding section  102 -m supporting the m-th layer will be explained using  FIG. 5 .  FIG. 5  is a block diagram showing the configuration inside adaptive residue encoding section  102 -m. Adaptive residue encoding section  102 -m shown in  FIG. 5  receives m-th layer primary signal P^ m (n) and m-th layer secondary signal A^ m (n) as input from adaptive residue encoding section  102 -(m−1) supporting the (m−1)-th layer, which is lower by one. To be more specific, selecting section  1021 -m and encoding section  1022 -m shown in  FIG. 5  receive m-th layer primary signal P^ m (n) and m-th layer secondary signal A^ m (n) as input. Also, subtractor  1024 -m shown in  FIG. 5  receives m-th layer primary signal P^ m (n) as input, and subtractor  1025 -m receives m-th layer secondary signal A^ m (n) as input. Here, adaptive residue encoding section  102 -m supporting the first layer shown in  FIG. 5  receives first layer primary signal P 1 (n) and first layer secondary signal A 1 (n) as input from PCA transformation section  101 . Also, adaptive residue encoding section  102 -M supporting the highest layer (i.e. M-th layer) includes only selecting section  1021 -m and encoding section  1022 -m shown in  FIG. 5 , and does not include decoding section  1023 -m, subtractor  1024 -m and subtractor  1025 -m. That is, adaptive residue encoding section  102 -M outputs only indicator F m  and encoded data C m . 
     In adaptive residue encoding section  102 -m shown in  FIG. 5 , selecting section  1021 -m compares the energy of input m-th layer primary signal P^ m (n) and the energy of input m-th layer secondary signal A^ m (n), and selects the signal of the higher energy. Then, selecting section  1021 -m outputs indicator F m  indicating the selected signal (primary signal or secondary signal) to encoding section  1022 -m, decoding section  1023 -m and multiplexing section  104  shown in  FIG. 3 . 
     In m-th layer primary signal P^ m (n) and m-th layer secondary signal A^ m (n) received as input, encoding section  1022 -m encodes a signal indicated by indicator F m  received as input from selecting section  1021 -m, that is, a signal selected in selecting section  1021 -m, to generate m-th layer encoded data C m . To be more specific, encoding section  1022 -m encodes m-th layer primary signal P^ m (n) when the signal indicated by indicator F m  is the primary signal, or encodes m-th layer secondary signal A^ m (n) when the signal indicated by indicator F m  is the secondary signal. Then, encoding section  1022 -m outputs generated m-th layer encoded data C m  to decoding section  1023 -m and multiplexing section  104  shown in  FIG. 3 . 
     Decoding section  1023 -m specifies encoded data C m  received as input from encoding section  1022 -m based on indicator F m  received as input from selecting section  1021 -m and generates an m-th layer decoded signal by decoding encoded data C m . Here, decoding section  1023 -m makes a decoded signal of the other signal than the signal indicated by indicator F m  “0.” Then, in m-th layer decoded signals generated, decoding section  1023 -m outputs the decoded signal of the primary signal to subtractor  1024 -m and the decoded signal of the secondary signal to subtractor  1025 -m. To be more specific, when the signal indicated by indicator F m  is the primary signal, decoding section  1023 -m decodes m-th layer primary signal P^ m (n) using m-th layer encoded data C m . Then, decoding section  1023 -m outputs decoded signal P{tilde over ( )} m (n) of the primary signal to subtractor  1024 -m while outputting “0” to subtractor  1025 -m as decoded signal A{tilde over ( )} m (n) of the secondary signal. By contrast with this, when the signal indicated by indicator F m  is the secondary signal, decoding section  1023 -m decodes m-th layer secondary signal A^ m (n) using encoded data C m . Then, decoding section  1023 -m outputs decoded signal A{tilde over ( )} m (n) of the secondary signal to subtractor  1025 -m while outputting “0” to subtractor  1024 -m as decoded signal P{tilde over ( )} m (n) of the primary signal. 
     Subtractor  1024 -m generates, as (m+1)-th layer primary signal P^ m+1 (n), a coding residual signal obtained by subtracting decoded signal P{tilde over ( )} m (n) of the primary signal received as input from decoding section  1023 -m, from m-th layer primary signal P^ m (n) of an input signal. Then, subtractor  1024 -m outputs (m+1)-th layer primary signal P^ m+1 (n) to adaptive residue encoding section  102 -(m+1) supporting the (m+1)-th layer, which is the next coding layer. 
     Subtractor  1025 -m generates, as (m+1)-th layer secondary signal A^ m+1 (n), a coding residual signal obtained by subtracting decoded signal A{tilde over ( )} m (n) of the secondary signal received as input from decoding section  1023 -m, from m-th layer secondary signal A^ m (n) of an input signal. Then, subtractor  1025 -m outputs (m+1)-th layer secondary signal A^ m + 1 (n) to adaptive residue encoding section  102 -(m+1). 
     For example, when the primary signal is selected in selecting section  1021 -m, subtractor  1024 -m generates, as (m+1)-th layer primary signal P^ m+1 (n), a coding residual signal obtained by subtracting a decoded signal of encoded data C m  from m-th layer primary signal P^ m (n). Also, subtractor  1025 -m generates m-th layer secondary signal A^ m (n) as (m+1)-th layer secondary signal A^ m+1 (n). In contrast, when the secondary signal is selected in selecting section  1021 -m, subtractor  1025 -m generates, as (m+1)-th layer secondary signal A^ m+1 (n), a coding residual signal obtained by subtracting a decoded signal of encoded data C m  from m-th layer secondary signal A^ m (n). Also, subtractor  1024 -m generates m-th layer primary signal P^ m (n) as (m+1)-th layer primary signal P^ m+1 (n). 
     Next, the configuration inside selecting section  1021 -m will be explained using  FIG. 6 .  FIG. 6  is a block diagram showing the configuration inside selecting section  1021 m. 
     In selecting section  1021 -m shown in  FIG. 6 , energy calculating section  1201 -m calculates energy E P^m  of m-th layer primary signal P^ m (n) according to equation 3. Then, energy calculating section  1201 -m outputs calculated energy E P^m  to comparison section  1203 -m. 
     
       
         
           
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     Energy calculating section  1202 -m calculates energy E A^m , of m-th layer secondary signal A^ m (n) according to equation 4. Then, energy calculating section  1202 -m outputs calculated energy E A^m  to comparison section  1203 -m. 
     
       
         
           
             
               
                 
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     Comparison section  1203 -m compares energy E P^m  received as input from energy calculating section  1201 -m and energy E A^m  received as input from energy calculating section  1202 -m. Then, comparison section  1203 -m selects the signal of the higher energy (i.e. primary signal or secondary signal) as a signal to encode in the m-th layer. For example, when energy E P^m  is equal to or higher than energy E A^m , comparison section  1203 -m selects the primary signal (i.e. m-th layer primary signal P^ m (n)) as the signal to encode in the m-th layer. By contrast, when energy E P^m  is lower than energy E A^m , comparison section  1203 -m selects the secondary signal (i.e. m-th layer secondary signal A^ m (n)) as the signal to encode in the m-th layer. Then, comparison section  1203 -m generates indicator F m  indicating the selected signal, that is, the signal (primary signal or secondary signal) encoded in the m-th layer. 
     As described above, encoding apparatus  100  according to the present embodiment encodes only one of the primary signal and the secondary signal every coding layer. Therefore, the amount of information (the number of bits) of an indicator, which is bit allocation information in each coding layer, requires only one bit to distinguish between the primary signal and the secondary signal. 
     Also, selecting section  1021 -m described above may calculate the energy of a primary signal and secondary signal in the logarithmic domain. Also, selecting section  1021 -m may use left signal L(n) and right signal R(n) to calculate the energy of the primary signal and the secondary signal, and, for example, may use the energy of left signal L(n) and right signal R(n). Also, selecting section  1021 -m may calculate the energy of the primary signal and the secondary signal taking into account masking. 
     Next, decoding apparatus  200  shown in  FIG. 7  will be explained. Decoding section  200  receives bit streams transmitted from encoding apparatus  100  via the communication path. In decoding apparatus  200  shown in  FIG. 7 , demultiplexing section  201  demultiplexes the bit streams into encoded data C m  and indicator F m  for respective coding layers of the first layer to the M-th layer, and quantized codes of PCA transformation parameters. Then, demultiplexing section  201  outputs encoded data C m  and indicator F m  for each coding layer to decoding sections  202 - 1  to  202 -M respectively supporting the first layer to the M-th layer. Further, demultiplexing section  201  outputs the quantized codes of PCA transformation parameters to dequantizing section  205 . 
     Decoding sections  202 - 1  to  202 -M each decodes encoded data received as input from demultiplexing section  201 , based on indicator F m  received as input from demultiplexing section  201 . For example, when the signal indicated by indicator F m  is the primary signal, decoding section  202 -m decodes the primary signal using encoded data C m . Then, decoding section  202 -m outputs decoded signal P{tilde over ( )} m (n) to adder  203 . In contrast, when the signal indicated b indicator F m  is the secondary signal, decoding section  202 -m decodes the secondary signal using encoded data C m . Then, decoding section  202 -m outputs decoded signal A{tilde over ( )} m (n) to adder  204 . Also, decoding section  202 -m outputs “0” to adder  203  or adder  204  as a decoded signal of the other signal than the signal indicated by indicator F m . 
     Adder  203  adds decoded signals P{tilde over ( )} m (n) received as input from decoding sections  202 - 1  to  202 -M. Then, adder  203  outputs decoded primary signal P{tilde over ( )}(n), which is obtained by adding decoded signals of all coding layers (the first layer to the M-th layer), to inverse PCA transformation section  206 . 
     Adder  204  adds decoded signals A{tilde over ( )} m (n) received as input from decoding sections  202 - 1  to  202 -M. Then, adder  204  outputs decoded secondary signal A{tilde over ( )}(n), which is obtained by adding decoded signals of all coding layers (the first layer to the M-th layer), to inverse PCA transformation section  206 . 
     Also, depending on, for example, the communication path condition, a case is possible where part of bit streams is discarded. For example, if bit streams include only encoded data up to the m-th layer (m&lt;M), decoding sections up to the first to M-th layers perform operations and adders  203  and  204  supporting these coding layers perform operations to obtain decoded primary signal P{tilde over ( )}(n) and decoded secondary signal A{tilde over ( )}(n), and these decoded primary signal P{tilde over ( )}(n) and decoded secondary signal A{tilde over ( )}(n) are outputted to inverse PCA transformation section  206 . 
     Dequantizing section  205  dequantizes quantized codes received as input from demultiplexing section  201  and outputs resulting PCA transformation parameters v{tilde over ( )} 1  and v{tilde over ( )} 2  to inverse PCA transformation section  206 . 
     Inverse PCA transformation section  206  receives decoded primary signal P{tilde over ( )}(n) as input from adder  203 , receives decoded secondary signal A{tilde over ( )}(n) as input from adder  204  and receives PCA transformation parameters v{tilde over ( )} 1  and v{tilde over ( )} 2  as input from dequantizing section  205 . According to equation 2, inverse PCA transformation section  206  applies inverse PCA transformation to decoded primary signal P{tilde over ( )}(n) and decoded secondary signal A{tilde over ( )}(n) using PCA transformation parameters v{tilde over ( )} 1  and v{tilde over ( )} 2 , and obtains left signal L{tilde over ( )}(n) and right signal R{tilde over ( )}(n) of a stereo signal. 
     Thus, according to the present embodiment, encoding apparatus  100  ( FIG. 3 ) selects the signal of the higher energy between the primary signal and the secondary signal in each coding layer, as the coding target. As a result, the signal encoded in each coding layer is only one of the primary signal and the secondary signal, and, consequently, the amount of information (the number of bits) of an indicator indicating an encoded signal (i.e. a signal allocated to a bit sequence) requires only one bit. That is, encoding apparatus  100  can minimize bit allocation information of encoded data in each coding layer. 
     Also, in scalable coding, coding residual signals in a lower coding layer are received as the input primary signal and secondary signal in each coding layer. Consequently, the energy of input signals in each coding layer changes depending on the coding result in a lower coding layer. Therefore, encoding apparatus  100  ( FIG. 3 ) can adaptively select the signal of the higher energy (i.e. the signal of the higher importance) in each coding layer, according to the coding result in a lower coding layer. By this means, decoding apparatus  200  ( FIG. 7 ) can decode stereo signals of high quality. 
     (Embodiment 2) 
     Although adaptive residue coding processing is applied to the primary signal and the secondary signal in the first layer of the lowest layer in Embodiment 1, with the present embodiment, band division coding processing is applied to the primary signal in the first layer for further dividing the first layer into layers and performing coding in division frequency band units. 
     As a method of scalable coding in division frequency band units, studies are underway on, for example, a method of realizing scalable coding by dividing an input signal into a plurality of bands and performing coding in divided band signal units (e.g. see US Patent Application Publication No. 2008/004883, specification), and a method of realizing scalable coding by performing coding in subband units on MDCT coefficients in coding after layer 4 of ITU-T recommendation G.729.1 (i.e. TDAC (Time-Domain Aliasing Cancellation)), and transmitting encoded data preferentially from the subband of the highest energy (see ITU-T recommendation G.729.1 (2006)). 
     In scalable coding based on band division coding, when an encoded error signal (coding residual signal) of a band signal of the coding target in a lower layer is large, the influence given from the coding residual signal to perceptual decoding quality is larger than the influence given from a band signal of the coding target in a higher layer to perceptual decoding quality. 
     Therefore, in a coding layer of the band division coding target, the present embodiment adaptively decides whether or not to encode the coding residual signal in a lower layer than each coding layer. 
       FIG. 8  is a block diagram showing the configuration of an encoding apparatus according to the present embodiment. Also, in  FIG. 8 , the same components as in encoding apparatus  100  shown in  FIG. 3  will be assigned the same reference numerals and their explanation will be omitted. 
     In encoding apparatus  500  shown in  FIG. 8 , PCA transformation section  101  outputs first layer primary signal P 1 (n) to band division encoding section  501  and outputs first layer secondary signal A 1 (n) to adaptive residue encoding section  102 - 2  as second layer secondary signal A^ 2 (n). 
     Band division encoding section  501  divides primary signal P 1 (n) received as input from PCA transformation section  101  into a plurality of bands, and encodes divided band unit signals in a layered manner. Here, when band division encoding section  501  performs coding from the first layer to the L-th layer (L is a natural number equal to or greater than 2), adaptive residue encoding sections  102 - 2  to  102 -M perform coding after the (L+1)-th layer in order. Then, band division encoding section  501  outputs encoded data C S  including encoded data generated in each of coding layers up to the L-th layer, and indicator F S  including the decision result generated in each of bands (subbands) dividing the first layer coding target band, to multiplexing section  104 . Further, band division encoding section  501  outputs a coding residual signal encoded to adaptive residue encoding section  102 - 2  as input signal P^ 2 (n) of adaptive residue encoding section  102 - 2 . 
       FIG. 9  is a block diagram showing the components related to input signal forming processing for the components related to first layer coding processing and second layer coding processing, in the configuration inside band division encoding section  501  shown in  FIG. 8 . 
     In band division encoding section  501  shown in  FIG. 9 , band dividing section  551  divides first layer primary signal P 1 (n) received as input from PCA transformation section  101  ( FIG. 8 ), into first band signal S 1 , which is the first band signal of the first layer coding target, and signal S″ 1  different from first band signal S 1 . For example, band dividing section  551  uses the signal from a lower band to a predetermined frequency band in the frequency band of first layer primary signal P 1 (n), as first band signal S 1 . Then, band dividing section  551  outputs first band signal S 1  to subband dividing section  552  and encoding section  553 , and outputs signal S″ 1  different from the first band signal, to signal forming section  558 . 
     Subband dividing section  552  divides first band signal S 1  received as input from band dividing section  551 , into a plurality of subband signals S 1,sb  (sb=1, 2, . . . , Nsb, Nsb, which represents the number of subband divisions). Then, subband dividing section  552  outputs divided subband signals S 1,sb  to evaluating section  556  and residue calculating section  557 . 
     Encoding section  553  encodes first band signal S 1  received as input from band dividing section  551  at a coding bit rate set in advance, and generates first layer encoded data. Then, encoding section  553  outputs generated first layer encoded data to decoding section  554  and multiplexing section  104  ( FIG. 8 ). 
     Decoding section  554  decodes the first layer encoded data received as input from encoding section  553  and generates first layer decoded signal S{tilde over ( )} 1 . Then, decoding section  554  outputs generated first layer decoded signal S{tilde over ( )} 1  to subband dividing section  555 . 
     Similar to subband dividing section  552 , subband dividing section  555  divides first layer decoded signal S{tilde over ( )} 1  received as input from decoding section  554 , into a plurality of subband signals S{tilde over ( )} 1,sb . Then, subband dividing section  555  outputs divided subband signals S{tilde over ( )} 1,sb  to evaluating section  556  and residue calculating section  557 . 
     Evaluating section  556  decides whether or not the residue energy in each subband is lower than a predetermined threshold, using subband signals S 1,sb  received as input from subband dividing section  552  and subband signals S{tilde over ( )} 1,sb  received as input from subband dividing section  555 . To be more specific, first, evaluating section  556  calculates the evaluation value related to coding performance in each subband of the first layer, using subband signals S 1,sb  and subband signals S{tilde over ( )} 1,sb . For example, evaluating section  556  uses the SNR (Signal to Noise Ratio) for the coding residual signal in each subband, as an evaluation value. To be more specific, evaluating section  556  calculates SNR sb  in the sb-th subband according to equation 5. Here, assume that the number of samples of a subband signal in the sb-th subband is P 1,sb . 
     
       
         
           
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     Further, evaluating section  556  decides whether or not the residue energy is lower than a predetermined threshold, based on the calculated evaluation value (SNR) related to coding performance in each subband. To be more specific, evaluating section  556  compares SNR sb  of each subband and predetermined threshold SNR thr , and generates following decision result F 1,sb  in the following sb-th subband.
 
F 1,sb =1 if SNR sb &lt;SNR thr  
 
F 1,sb =0 else
 
     That is, evaluating section  556  provides “1” as decision result F 1,sb  when the evaluation value (SNR) in each subband is lower than a predetermined threshold (i.e. when the residue energy is higher than a predetermined threshold), or provides “0” as decision result F 1,sb  when the evaluation value (SNR) is equal to or higher than a predetermined threshold (i.e. when the residue energy is equal to or lower than a predetermined threshold). Here, evaluating section  556  may set SNR thr  in advance, set SNR thr  based on the characteristic of the input signal, or set SNR thr  every subband. Then, evaluating section  556  outputs decision result F 1,sb  in each subband to residue calculating section  557  and multiplexing section  104  ( FIG. 8 ). 
     Residue calculating section  557  calculates the coding residue signal in each subband based on decision result F 1,sb  received as input from evaluating section  556 . To be more specific, in the sb-th subband in which decision result F 1,sb  is “1,” residue calculating section  557  calculates a coding residual signal in the sb-th subband by subtracting subband signals S{tilde over ( )} 1,sb , received as input from subband dividing section  555 , from subband signals S 1,sb  received as input from subband dividing section  552 . By contrast, in the sb-th subband in which decision result F 1,sb  is “0,” residue calculating section  557  does not calculate a coding residual signal. Then, residue calculating section  557  outputs coding residual signal S r1  of the entire first band including a coding residual signal only in subbands in which decision result F 1,sb  is “1,” to signal forming section  558 . 
     Signal forming section  558  forms signal S′ 1  by adding coding residual signal S r1  received as input from residue calculating section  557  and signal S″ 1  received as input from band dividing section  551 . That is, in the frequency band of first layer primary signal P 1 (n), signal S′ 1  has coding residual signal S r1  in the first band and signal S″ 1  in the frequency band different from the first band. Then, signal forming section  558  outputs generated signal S′ 1  to components (not shown) related to second layer coding processing. 
     Also, band division encoding section  501  uses signal S′ 1  outputted from signal forming section  558 , as an input signal to the second layer. Then, in the second layer, similar to the first layer, band division encoding section  501  divides the input signal into a second band signal of the second layer coding target and a signal different from the second band signal, and encodes the second band signal at a coding bit rate set in advance. Also, band division encoding section  501  uses the signal different from the second band signal, as an input signal in the third layer. Here, band division encoding section  501  uses a frequency band including part of the first band, as the second band. Therefore, band division encoding section  501  preferentially encodes a frequency band signal corresponding to part of the first band in the second band signal. To be more specific, band division encoding section  501  preferentially encodes coding residual signals in part or all of subbands in which subband decision result F 1,sb  is “1.” The same applies to a third layer or later. Then, band division encoding section  501  outputs, to multiplexing section  104 , encoded data C S  including encoded data in all coding layers and indicator F S  including decision result F 1,sb  in each subband of the first band. 
     Next, signal S′ 1  formed in signal forming section  558  is shown in  FIG. 10 . As shown in  FIG. 10 , in the first band of the first layer coding target, a coding layer residual signal is present only in subbands in which decision result F 1,sb  is “1.” For example, as shown in  FIG. 10 , a coding residual signal (S 1,1 -S{tilde over ( )} 1,1 ) is present in the first subband (sb=1), in which decision result F 1,1  is “1,” and a coding residual signal (S 1,3 -S{tilde over ( )} 1,3 ) is present in a third subband (sb=3), in which decision result F 1,3  is “1.” In contrast, a coding residual signal is not present in a second subband (sb=2), in which decision result F 1,2  is “0,” and in a fourth subband (sb=4) in which decision result F 1,4  is “0.” Also, in the band different from the first layer coding target, signal S″ 1  of the frequency band different from the first band in first layer primary signal P 1 (n), is present as is. 
     By this means, among subbands of the first band, band division encoding section  501  outputs coding residual signals of subbands in which the residue energy is higher than a threshold, to a higher layer as an input signal. Therefore, among coding residual signals obtained in a lower layer, band division encoding section  501  can adaptively select only signals of higher residue energy (i.e. signals of higher importance) as coding residual signals to encode in a higher layer. 
     Next, the decoding apparatus according to the present embodiment will be explained.  FIG. 11  is a block diagram showing the configuration of decoding apparatus  600 . Here, in  FIG. 11 , the same components as in decoding apparatus  200  shown in  FIG. 7  will be assigned the same reference numerals and their explanation will be omitted. 
     In decoding apparatus  600  shown in  FIG. 11 , band division decoding section  601  receives as input encoded data C S  including encoded data of each coding layer generated in band division encoding section  501  of encoding apparatus  500 , and indicator F S  including decision results F 1,sb  in a plurality of subbands of the first layer. Band division decoding section  601  decodes encoded data C s  based on decision results F 1,sb . To be more specific, band division decoding section  601  decodes encoded data of each coding layer received as input from demultiplexing section  201 , adds generated decoded signals and decoded signals generated in a higher layer, and thereby generates the decoded signal of each coding layer. Then, as decoded signal P{tilde over ( )} 1 (n), band division decoding section  601  outputs, to adder  203 , a decoded signal in the first layer, which is the lowest layer among coding layers to which band division encoding processing is applied. 
       FIG. 12  is a block diagram showing the components related to decoding processing of generating decoded signal P{tilde over ( )} 1 (n) in the first layer of the lowest layer, using second layer decoded signal S{tilde over ( )}′ 1 , in the configuration inside band division decoding section  601  shown in  FIG. 11 . 
     In band division decoding section  601  shown in  FIG. 12 , decoding section  651  decodes first layer encoded data included in encoded data C S  received as input from demultiplexing section  201  ( FIG. 11 ). Then, decoding section  651  outputs first layer decoded signal S{tilde over ( )} 1  to band decoded signal forming section  653 . 
     Based on decision result F 1,sb  received as input from demultiplexing section  201 , residual signal separating section  652  separates second layer decoded signal S{tilde over ( )}′ 1  received as input from components (not shown) related to second layer decoding processing (i.e. a signal decoded in the second layer to the L-th layer), to decoded residual signal S{tilde over ( )} r1  of the first band and decoded signal S{tilde over ( )}″ 1  of the different frequency band from the first band. Then, residual signal separating section  652  outputs decoded residual signal S{tilde over ( )} r1  of the first band to band decoded signal forming section  653  and decoded signal S{tilde over ( )}″ 1  of the different frequency band from the first band, to decoded signal forming section  654 . 
     Based on decision result F 1,sb  received as input from demultiplexing section  201 , band decoded signal forming section  653  forms the first band decoded signal by adding decoded signal S{tilde over ( )} 1  received as input from decoding section  651  and decoded residual signal S{tilde over ( )} r1  received as input from residual signal separating section  652 . To be more specific, band decoded signal forming section  653  adds decoded signal S{tilde over ( )} 1  and decoded signals of subbands in which decision result F 1,sb  is “1” in decoded residual signal S{tilde over ( )} r1 . Then, band decoded signal forming section  653  outputs a formed first band decoded signal to decoded signal forming section  654 . 
     Decoded signal forming section  654  forms decoded signal P{tilde over ( )} 1 (n) using the first band decoded signal received as input from band decoded signal forming section  653  and decoded signal S{tilde over ( )}″ 1  of the frequency band different from the first band received as input from residual signal separating section  652 . Then, decoded signal forming section  654  outputs formed decoded signal P{tilde over ( )} 1 (n) to adder  203  ( FIG. 11 ). 
     Thus, according to the present embodiment, encoding apparatus  500  ( FIG. 8 ) applies scalable coding based on band division coding to primary signal P 1 (n) and adaptively selects and encodes a signal of a perceptually important frequency band (lower band in particular) in stereo coding, so that it is possible to reduce coding distortion. Therefore, decoding apparatus  600  ( FIG. 11 ) can improve decoded sound quality. 
     Also, according to the present embodiment, among subbands of the first band of the first layer coding target, only subbands in which the evaluation value (SNR) is less than a predetermined threshold, that is, only subbands in which the residue energy is higher than a predetermined amount, are used as a coding target signal in a higher layer. That is, only signals of the subbands of higher energy in each coding layer (i.e. signals of the subbands of higher perceptual importance) are received as input in a higher layer. Therefore, in each coding layer in band division encoding section  501 , encoding apparatus  500  adaptively encodes signals of higher residue energy (i.e. a signal of higher importance) according to a coding result in a lower layer, so that decoding apparatus  600  ( FIG. 11 ) can generate stereo signals of high quality. 
     Also, according to the present embodiment, the coding target signal in each coding layer may be a time domain signal or a frequency domain signal (e.g. coefficients after MDCT transform). 
     Also, a case has been described above with the present embodiment where band division coding processing is applied to a lower coding layer than a coding layer to which adaptive residue coding processing is applied. However, according to the present invention, a coding layer to which band division coding processing is applied is not limited to a lower coding layer than a coding layer to which adaptive residue coding processing is applied. For example, an encoding apparatus may apply band division coding processing to a coding layer in the middle of a plurality of coding layers to which adaptive residue coding processing is applied. 
     Also, a case has been described above with the present embodiment where band division coding processing is applied to a PCA-transformed primary signal. However, according to the present invention, a signal to which adaptive division coding processing is applied is not limited to a PCA-transformed primary signal. For example, an encoding apparatus may apply band division coding processing to a coding residual signal in a coding layer in the middle of a plurality of coding layers to which adaptive residue coding processing is applied, or an arbitrary input signal different from a PCA-transformed signal. Also, an encoding apparatus may apply band division coding processing alone, without combining band division coding processing and adaptive residue coding processing. 
     Also, a case has been described above with the present embodiment where, in a band division encoding section, a frequency band set in advance from a lower band to a predetermined band in an input signal, is used as the coding target frequency band in each coding layer. However, according to the present invention, it is possible to adaptively set, for example, a frequency band based on the characteristic of an input signal as the coding target frequency band in each coding layer. 
     Also, a case has been described above with the present embodiment where an encoding apparatus determines whether or not to calculate the coding residual signal in each subband of the first band based on decision result F 1,sb . However, according to the present invention, it is equally possible to calculate coding residual signals in all subbands of the first band, regardless of decision result F 1,sb . 
     Embodiments of the present invention have been described above. 
     Also, cases have been described above with embodiments where signal energy is used as an index of signal importance. However, according to the present invention, the signal importance is not limited to the signal energy, and, for example, signal&#39;s SNR (Signal to Noise Ratio) may be used. The configuration inside selecting section  3021 -m of adaptive residue encoding section  102 -m in a case where the SNR is used as an index of signal importance, will be explained using the block diagram of  FIG. 13 . In selecting section  3021 -m shown in  FIG. 13 , encoding section  3201 -m generates encoded data by encoding m-th layer primary signal P^ m (n), and decoding section  3202 -m generates decoded signal P{tilde over ( )} m (n) of the m-th layer primary signal by decoding encoded data of m-th layer primary signal P^ m (n). Then, subtractor  3203 -m generates (m+1)-th layer primary signal P^ m+1 (n) by subtracting decoded signal P{tilde over ( )} m (n) of the m-th layer primary signal from m-th layer primary signal P^ m (n). Inverse PCA transformation section  3204 -m obtains left signal L^ m1 (n) and right signal R^ m1 (n) by applying inverse PCA transformation to (m+1)-th layer primary signal P^ m+1 (n) and m-th layer secondary signal A^ m (n). That is, encoding section  3201 -m, decoding section  3202 -m, subtractor  3203 -m and inverse PCA transformation section  3204 -m generate output stereo signals (left signal L^ m1 (n) and right signal R^ m1 (n)) in decoding apparatus  200  in a case where m-th layer primary signal P^ m (n) is encoded (i.e. where selecting section  3021 -m selects the primary signal). Then, measurement value calculating section  3205 -m calculates quantitative measurement value M 1  (i.e. SNR) using left signal L^ m1 (n) and right signal R^ m1 (n) (equation 6). 
     
       
         
           
             
               
                 
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     Similarly, encoding section  3206 -m, decoding section  3207 -m, subtractor  3208 -m and inverse PCA transformation section  3209 -m generate output stereo signals (left signal L^ m2 (n) and right signal R^ m2 (n)) in decoding apparatus  200  in a case where m-th layer secondary signal A^ m (n) is encoded (i.e. where selecting section  3021 -m selects the secondary signal). Then, measurement value calculating section  3210 -m calculates quantitative measurement value M 2  (i.e. SNR) using left signal L^ m2 (n) and right signal R^ m2 (n) (equation 7). 
     
       
         
           
             
               
                 
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     Comparison section  3211 -m compares quantitative measurement value M 1  and quantitative measurement value M 2 , selects the signal of the higher quantitative measurement value (i.e. primary signal or secondary signal) as the signal to be encoded, and outputs indicator F m  to indicate the selected signal. That is, selecting section  3021 -m generates an output stereo signal obtained in decoding apparatus  200  upon encoding the primary signal and an output stereo signal obtained in decoding apparatus  200  upon encoding the secondary signal, in selecting section  3021 -m. By this means, selecting section  3021 -m can calculate the SNR in decoding apparatus  200  as a quantitative measurement value. Therefore, selecting section  3021 -m selects the signal of the higher SNR in decoding apparatus  200 , so that, similar to the above embodiments, it is possible to minimize the amount of information for reporting bit allocation information and improve the efficiency of coding. Here, the quantitative measurement value to indicate signal importance is not limited to the SNR calculated in equations 6 and 7, and it is equally possible to use, for example, an MNR (Mask to Noise Ratio). For example, when an MNR is used as stereo signal importance, it is possible to obtain the MNR through processing including psychoacoustic modeling of left signal L(n) and right signal R(n) in the stereo signal. 
     Also, cases have been described above with embodiments where the present invention is applied to time domain stereo signals. However, the present invention is not limited to time domain signals, but is applicable to stereo signals in other domains. For example, it is possible to apply the present invention to stereo signals in the MDCT (Modified Discrete Cosine Transform) domain or LPC (Linear Prediction Coefficient) residual signals obtained by applying an LPC analysis to stereo signals. Also, the present invention is applicable to LPC residual signals in the MDCT domain. 
     Also, in a case where the encoding apparatus according to the present invention divides an input signal band into a plurality of subbands, the present invention is applicable to subband signals, each of which is the signal of each subband of the input signal. For example, left signal L(n) and right signal R(n) of a stereo signal of an input signal are divided into K subbands to obtain subband signals L k (n) (k=1 to K) of left signal L(n) and subband signals R k (n) (k=1 to K) of right signal R(n). 
     For example, in a stereo signal, a case will be explained with  FIG. 14  to  FIG. 17 , where an LPC residual signal in the MDCT domain is divided into a plurality of subband signals. Here,  FIG. 14  shows configuration  300  in the encoding apparatus, relating to processing of dividing an MDCT-domain LPC residual signal into a plurality of subband signals, and  FIG. 15  shows configuration  350  in the encoding apparatus, relating to coding processing according to the present invention. Similarly,  FIG. 16  shows configuration  400  in the decoding apparatus, relating to decoding processing according to the present invention, and  FIG. 17  shows configuration  450  in the decoding apparatus, relating to processing of generating a stereo signal by combining a plurality of subband signals dividing an MDCT-domain LPC residual signal. Here, in  FIG. 14  to  FIG. 17 , the same components as in encoding apparatus  100  shown in  FIG. 3  and decoding apparatus  200  shown in  FIG. 7  will be assigned the same reference numerals and their explanation will be omitted. 
     In  FIG. 14 , LPC analyzing section  301  performs a linear predictive analysis using left signal L(n) of a stereo signal and obtains LPC parameter (Linear predictive parameter) A L (z) to indicate the spectral outline of left signal L(n). Quantizing section  302  quantizes LPC parameter A L (z) and obtains quantized code I qL . Dequantizing section  303  dequantizes quantized code I qL  of the LPC parameter and obtains decoded LPC parameter A dL (z). Inverse filter  304  applies inverse filtering (LPC inverse filtering) to left signal L(n) using decoded LPC parameter A dL (z), and thereby obtains filtered left signal L e (n) from which a feature of the spectral outline is removed. T/F section  305  performs an MDCT (i.e. time/frequency domain transform) of inverse-filtered left signal L e (n) and obtains MDCT-domain (frequency-domain) left signal L e (f) from time-domain left signal L e (n). That is, LPC residual signal L e (f) in the MDCT domain of the left signal is obtained. 
     Band dividing section  306  divides LPC residual signal L e (f) in the MDCT domain of the left signal into a plurality of subbands (K subbands in this case), and generates subband signals L e1 (f) to L eK (f) of left signal L e (f). 
     In contrast, analyzing section  307 , quantizing section  308 , dequantizing section  309 , inverse filter  310 , T/F section  311  and band dividing section  312  generate subband signals R e1 (f) to R eK (f) of right signal R e (f), by applying, to right signal R(n), the same sequential processing as in from LPC analyzing section  301  to band dividing section  306 . 
     Here, for example, a case will be explained where the present invention is applied only to subband signal L e1 (f) and subband signal R e1 (f) among subband signals L e1 (f) to L eK (f) of left signal L e (f) and subband signals R e1 (f) and R eK (f) of right signal R e (f). As shown in  FIG. 15 , PCA transformation section  351  PCA-transforms subband signal L e1 (f) and subband signal R e1 (f) and obtains primary signal P(f) and secondary signal A(f) in the MDCT domain. Then, in the same way as in the above embodiments, adaptive residue encoding sections  352 - 1  to  352 -M apply adaptive residue coding processing to primary signal P(f) and secondary signal A(f). Multiplexing section  313  multiplexes encoded data C m  and indicator F m  received as input from adaptive residue encoding sections  352 - 1  to  352 -M and LPC parameter quantized codes I qL  and I qR  received as input from quantizing section  302  and quantizing section  308 . 
     In contrast, demultiplexing section  401  of the decoding apparatus shown in  FIG. 16  outputs encoded data C m  and indicator F m  multiplexed in bit streams, to decoding sections  402 - 1  to  402 -M. Also, demultiplexing section  401  outputs LPC parameter quantized codes I qL  and I qR  to dequantizing section  451  and dequantizing section  455  shown in  FIG. 17 . In the same way as in the above embodiments, decoding sections  402 - 1  to  402 -M each decode encoded data and obtain MDCT-domain decoded signal P{tilde over ( )} m (f) and MDCT-domain decoded signal A{tilde over ( )} m (f). Inverse PCA transformation section  403  obtains subband signal L{tilde over ( )} e1  of the left signal and subband signal R{tilde over ( )} e1  of the right signal using decoded primary signal P{tilde over ( )} m (f) and decoded secondary signal A{tilde over ( )} m (f). Subband signal L{tilde over ( )} e1  of the left signal is outputted to band combining section  452  shown in  FIG. 17  and subband signal R{tilde over ( )} e1  of the right signal is outputted to band combining section  456  shown in  FIG. 17 . 
     Dequantizing section  451  shown in  FIG. 17  dequantizes LPC parameter quantized code I qL  and obtains LPC parameter A dL (z). Band combining section  452  combines subband signals L e1 (f) to L eK (n) of left signal L e (f) and obtains MDCT-domain left signal L{tilde over ( )} e (f). F/T section  453  performs an inverse MDCT (i.e. frequency/time domain transform) of MDCT-domain left signal L{tilde over ( )} e (f) and obtains time-domain left signal L{tilde over ( )} e (n). Synthesis filter  454  applies a synthesis filter to time-domain left signal L{tilde over ( )} e (n) using LPC parameter A dL (z) and obtains left signal L{tilde over ( )}(n). 
     In contrast, dequantizing section  455 , band combining section  456 , F/T section  457  and synthesis filter  458  generate right signal R{tilde over ( )}(n) by applying the same processing as in dequantizing section  451 , band combining section  452 , F/T section  453  and synthesis filter  454 , to quantized code I qR  and subband signals R e1 (f) to R eK (n) of right signal R e (f). 
     Thus, by transforming an LPC residual signal of a stereo signal into the MDCT domain, dividing the MDCT-domain signal into a plurality of subbands and applying PCA transformation or adaptive residue coding to the divided band signals, it is possible to perform efficient coding suitable to each subband. 
     Also, cases have been described above with embodiments where, when a stereo signal is PCA-transformed, PCA transformation parameters before quantization (i.e. elements of the co-variance matrix eigenvector calculated from a stereo signal) are used. However, according to the present invention, it is equally possible to use quantized PCA transformation parameters as PCA transformation parameters to use upon PCA transformation. 
     Also, cases have been described above with embodiments where adaptive residue coding processing is performed in coding layers from the first layer to the M-th layer. However, according to the present invention, it is possible to omit adaptive residue coding processing in the first layer of the lowest layer. For example, the primary signal is more important information than the secondary signal in the first layer, so that the encoding apparatus can omit adaptive residue coding processing in the first layer and always select the primary signal. In this case, the encoding apparatus transmits indicators in the second layer to the M-th layer. That is, the indicator in the first layer needs not be transmitted, so that it is possible to reduce bit allocation information by one bit. Also, a case is possible where the encoding apparatus encodes both the primary signal and the secondary signal in the first layer and the present invention is applied to the second layer or later coding layers. 
     Also, cases have been described above with embodiments where adaptive residue coding processing is performed in coding layers from the first layer to the M-th layer. However, according to the present invention, for example, it is equally possible to omit adaptive residue coding processing in the first layer of the lowest layer to a predetermined coding layer. For example, in the first layer to the (i−1)-th layer (i is a natural number equal to or greater than 2), the encoding apparatus may omit adaptive residue coding processing and always select the primary signal. That is, the present invention is applicable to the i-th layer to the M-th layer in the encoding apparatus. Also, a case is possible where the encoding apparatus encodes both the primary signal and the secondary signal in the first layer to the (i−1)-th layer and the present invention is applied in the i-th layer to the M-th layer. 
     Also, cases have been described above with embodiments where adaptive residue coding processing is performed in coding layers from the first layer to the M-th layer. However, the present invention is applicable to at least one arbitrary coding layer among the first layer to the M-th layer. 
     Also, PCA transformation may be referred to as KLT (Karhunen Loeve Transform). 
     Also, example cases have been described with the above embodiments where the decoding apparatus according to the above embodiments receives and processes bit streams transmitted from the encoding apparatus according to the above embodiments. However, the present invention is not limited to this, and an essential requirement is that bit streams received and processed in the decoding apparatus according to the above embodiments are transmitted from an encoding apparatus that can generate bit streams that can be processed in the decoding apparatus according to the above embodiments. 
     Also, the above explanation is an example of the best mode for carrying out the present invention, and the scope of the present invention is not limited to this. The present invention is applicable to any systems as long as these systems include an encoding apparatus and decoding apparatus. 
     Also, for example, as a speech encoding apparatus and a speech decoding apparatus, the encoding apparatus and the decoding apparatus according to the present invention can be mounted on a communication terminal apparatus and base station apparatus in a mobile communication system, so that it is possible to provide a communication terminal apparatus, base station apparatus and mobile communication system having the same operational effects as above. 
     Although example cases have been described with the above embodiments where the present invention is implemented with hardware, the present invention can be implemented with software. For example, by describing the algorithm according to the present invention in a programming language, storing this program in a memory and running this program by an information processing section, it is possible to realize the same function as the encoding apparatus according to the present invention. 
     Furthermore, each function block employed in the description of each of the aforementioned embodiments may typically be implemented as an LSI constituted by an integrated circuit. These may be individual chips or partially or totally contained on a single chip. 
     “LSI” is adopted here but this may also be referred to as “IC,” “system LSI,” “super LSI,” or “ultra LSI” depending on differing extents of integration. 
     Further, the method of circuit integration is not limited to LSI&#39;s, and implementation using dedicated circuitry or general purpose processors is also possible. After LSI manufacture, utilization of an FPGA (Field Programmable Gate Array) or a reconfigurable processor where connections and settings of circuit cells in an LSI can be reconfigured is also possible. 
     Further, if integrated circuit technology comes out to replace LSI&#39;s as a result of the advancement of semiconductor technology or a derivative other technology, it is naturally also possible to carry out function block integration using this technology. Application of biotechnology is also possible. 
     The disclosures of Japanese Patent Application No. 2008-143863, filed on May 30, 2008, and Japanese Patent Application No. 2008-160954, filed on Jun. 19, 2008, including the specifications, drawings and abstracts, are incorporated herein by reference in their entireties. 
     Industrial Applicability 
     For example, the encoding apparatus and the decoding apparatus according to the present invention are suitably used for mobile phones, IP telephones and television conference, and so on.