JP2009094666A - Multiple vector quantization method, device, program, and recording medium - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide a high-speed multiple vector quantization technology where an operation amount has been reduced. <P>SOLUTION: Values of cross items cross (j, m) regarding a pair of representative output vectors (x_j, y_m) selected respectively from a code book X storage part 31 and a code book Y storage part 32 are calculated in advance and stored by a cross table storage part 6. The cross items are defined regardless of an input vector (u) among definition equations of a second distance measure d (j, m). The second distance measure calculation part 5 refers to the cross table storage part 6 to find a value of a cross item cross (j, m) needed when finding the second distance measure d (j, m). <P>COPYRIGHT: (C)2009,JPO&INPIT

Description

  The present invention relates to a multi-vector quantization method, apparatus, program, and recording medium for encoding a signal sequence such as sound and image with a small amount of information.

  Patent Document 1 calculates a distortion between an average vector of a set of representative output vectors and an input vector selected one by one from a plurality of codebook storage units for an average vector of a set of different representative output vectors. A multi-vector quantization method is described in which a set of representative output vectors giving the smallest distortion is a quantized value of the input vector.

Details of the multi-vector quantization method described in Patent Document 1 will be described with reference to FIG. First, symbols are defined as follows.
X, Y: code book u: input vector x_j: j-th representative output vector in code book X y_m: representative output vector of vector number m in code book Y K: representative output vector in code books X, Y Number of dimensions (number of elements)
N: number of representative output vectors stored in each codebook X, Y x (i, j): i-th element of representative output vector x_j of codebook X y (i, m): representative of codebook Y I-th element of output vector y_m u (i): i-th element of input vector u Codebook X corresponds to codebook X storage unit 1020, and codebook Y corresponds to codebook Y storage unit 1030. Yes.

The distance calculation unit 1010 is a distance between an average vector of a set of representative output vectors selected from the code book X storage unit 1020 and the code book Y storage unit 1030, respectively, and the input vector u input from the input terminal 1001. The scale d (j, m) is calculated for all representative output vectors based on the following formula (1).

  The minimum distance determining unit 1050 determines a set of representative output vectors that minimizes the distance measure d (j, m) calculated by the above formula (1), and the index (j of the determined set of representative output vectors) , M) is output as a quantized value for the input vector.

Patent Document 1 also proposes a technique for reducing the amount of calculation of the above multivector quantization method. In order to reduce the amount of calculation, a square term F (j, m) defined by the following equation (2) is calculated in advance for a plurality of different square terms F (j, m), and a square term table storage unit 1060 is obtained. Remember it.

このように、二乗項Ｆ（ｊ，ｍ）を予め計算しておくことにより、同じ二乗項Ｆ（ｊ，ｍ）を何度も計算する手間を省くことができる（例えば、特許文献１参照。）。 The distance calculation unit 1010 calculates the first term on the right side of the following formula (3), and adds the calculated value and F (j, m) obtained by referring to the square term table storage unit 1060 to measure the distance scale. d (j, m) is obtained.

Thus, by calculating the square term F (j, m) in advance, it is possible to save the trouble of calculating the same square term F (j, m) many times (for example, see Patent Document 1). ).

On the other hand, in Patent Document 2, in order to reduce the amount of calculation, first, a representative plurality of representative output vectors are preliminarily selected from each codebook storage unit to narrow down representative output vector candidates. A multi-vector quantization method is described in which the most effective representative output vector combination among the representative output vectors is selected (see, for example, Patent Document 2).
JP-A-1-205638 JP 11-191739 A

  There is a problem that the amount of calculation cannot be further reduced by applying the method described in Patent Document 1 to the vector quantization method for performing the preliminary selection and the main selection described in Patent Document 2. This is because the square term F (j, m) does not appear in the vector quantization method described in Patent Document 2.

  It is an object of the present invention to provide a multi-vector quantization method, apparatus, program, and recording medium that further reduce the amount of vector quantization for performing preliminary selection and main selection.

  According to the first aspect of the present invention, a predetermined number of representative output vectors are registered in each of the plurality of codebooks, and the first distance measure for a certain vector is the vector and the input vector. It is the first index that expresses the distance, and is defined using the inner product of the vector and the input vector and the sum of squares of the components of the vector, and the second distance measure for the average vector of a set of vectors is , A second index representing the distance between the average vector of the set of vectors and the input vector. A first distance measure is calculated for each representative output vector registered in each codebook. For each codebook, predetermined by selecting a representative output vector that minimizes the first distance measure from the smallest of the first distance measures or from each of a plurality of groups of representative output vectors. A number of representative output vectors (hereinafter referred to as candidate representative output vectors) are respectively determined. A second distance measure for the average vector of a set of candidate representative output vectors selected one by one from each codebook is calculated for each of a plurality of sets of different candidate representative output vectors. A set of candidate representative output vectors that minimizes the second distance measure is determined, and an index indicating a set of representative output vectors corresponding to the set of candidate representative output vectors is output. In the power table, the value of the sum of squares of the components of each representative output vector registered in each codebook is registered in advance, and the square of the component of the representative output vector necessary for calculating the first distance measure is stored in advance. The sum value is obtained with reference to the power table.

  According to the second aspect of the present invention, a predetermined number of representative output vectors are registered in each of the plurality of codebooks, and the first distance measure for a certain vector is the vector and the input vector. The first index that represents the distance, and the second distance measure for the average vector of a set of vectors is the second index that represents the distance between the average vector of the set of vectors and the input vector. It is defined using a respective first distance measure for each vector constituting the set and a cross term defined using the inner product of the pair of vectors constituting the vector set. A first distance measure is calculated for each representative output vector registered in each codebook. For each codebook, predetermined by selecting a representative output vector that minimizes the first distance measure from the smallest of the first distance measures or from each of a plurality of groups of representative output vectors. A number of representative output vectors (hereinafter referred to as candidate representative output vectors) are respectively determined. A second distance measure for the average vector of a set of candidate representative output vectors selected one by one from each codebook is calculated for each of a plurality of sets of different candidate representative output vectors. A set of candidate representative output vectors that minimizes the second distance measure is determined, and an index indicating a set of representative output vectors corresponding to the set of candidate representative output vectors is output. In the cross table, values of cross terms defined using inner products of representative output vector pairs each selected from two different codebooks are registered in advance for a plurality of different representative output vector pairs. The value of the cross term for the candidate representative output vector pair necessary for calculating the second distance measure is obtained with reference to the cross table.

  According to the third aspect of the present invention, a predetermined number of representative output vectors are registered in each of the plurality of codebooks, and the first distance measure for a certain vector is the vector and the input vector. It is the first index that expresses the distance, and is defined using the inner product of the vector and the input vector and the sum of squares of the components of the vector, and the second distance measure for the average vector of a set of vectors is , A second index representing the distance between the average vector of the vector set and the input vector, the first distance measure for each vector constituting the vector set, and the vector constituting the vector set And a cross term defined using the inner product of the pair of A first distance measure is calculated for each representative output vector registered in each codebook. For each codebook, predetermined by selecting a representative output vector that minimizes the first distance measure from the smallest of the first distance measures or from each of a plurality of groups of representative output vectors. A number of representative output vectors (hereinafter referred to as candidate representative output vectors) are respectively determined. A second distance measure for the average vector of a set of candidate representative output vectors selected one by one from each codebook is calculated for each of a plurality of sets of different candidate representative output vectors. A set of candidate representative output vectors that minimizes the second distance measure is determined, and an index indicating a set of representative output vectors corresponding to the set of candidate representative output vectors is output. In the power table, the value of the sum of squares of the components of each representative output vector registered in each codebook is registered in advance, and the square of the component of the representative output vector necessary for calculating the first distance measure is stored in advance. The sum value is obtained with reference to the power table. In the cross table, values of cross terms defined using inner products of representative output vector pairs each selected from two different codebooks are registered in advance for a plurality of different representative output vector pairs. The value of the cross term for the candidate representative output vector pair necessary for calculating the second distance measure is obtained with reference to the cross table.

  The value of the formula that is determined independently of the input vector in the definition formula of the distance scale (first distance scale, second distance scale) is calculated in advance, and when calculating the distance scale, By referring to the value, the value of the expression can be obtained without being calculated many times. Thereby, the amount of calculation can be further reduced. Moreover, the calculation can be performed at high speed.

[First embodiment]
A multi-vector quantization apparatus 100 according to the first embodiment of the present invention will be described with reference to FIGS. FIG. 1 is a diagram illustrating a functional configuration of multi-vector quantization apparatus 100. FIG. 2 is a flowchart showing a processing example of the multi-vector quantization apparatus 100.

First, symbols are defined as follows.
X, Y: code book u: input vector x_j: j-th representative output vector in code book X y_m: representative output vector of vector number m in code book Y D: representative output vector in code books X, Y Number of dimensions (number of components)
Nx: number of representative output vectors stored in codebook X Ny: number of representative output vectors stored in codebook X x (i, j): i-th component of representative output vector x_j of codebook X y (I, m): i-th component of representative output vector y_m of codebook Y u (i): i-th component of input vector u

  In this example, the code book is configured by a code book storage unit which is an arbitrary storage unit such as a magnetic recording device, an optical disk, a magneto-optical recording medium, and a semiconductor memory. That is, each code book corresponds to each code book storage unit. Therefore, the code book is also called a code book storage unit. In this example, the code book X corresponds to the code book X storage unit 31, and the code book Y corresponds to the code book Y storage unit 32. Note that what is stored in the codebook storage unit is a representative output vector, and this set of representative output vectors may be considered as a codebook.

The input sample sequence is input from the input terminal 1 to the multi-vector quantization apparatus 100 for each predetermined number L of input samples. The input sample is an arbitrary sample, for example, a time domain sample or a frequency domain coefficient.
The L input samples constitute one L-dimensional input vector u. In this case, the component of the input vector u is L input samples. From the viewpoint of the input vector u, it can be considered that the input vector u is input from the input terminal 1.

For example, when the input sample is a frequency domain coefficient, u (i) corresponds to a larger frequency domain sample as the element number i is larger.
The codebook X storage unit 31 stores Nx D-dimensional representative output vectors x_j (j = 0,..., Nx−1). In this example, L = D, and the input vector u and the representative output vector have the same number of dimensions. Nx is an arbitrary predetermined natural number.

  Similarly, the code book Y storage unit 32 stores Ny D-dimensional representative output vectors y_m (m = 0,..., Ny−1). Ny is an arbitrary predetermined natural number.

<Step S1>
The distance calculation unit 21 of the first distance scale calculation unit 2 calculates a first distance measure d_prex (j) for each of Nx representative output vectors x_j stored in the codebook X storage unit 31 (step S11). The first distance measure for a certain vector is a first index representing the distance between the vector and the input vector u. For example, the first distance scale is obtained by deleting a term consisting only of an input vector from the Euclidean distance formula and multiplying it by an integer. For example, the first distance measure d_prex (j) for the representative output vector x_j is defined as the following equation (4). Thus, the first distance measure for the representative output vector x_j is defined using, for example, the inner product of the representative output vector x_j and the input vector, and the sum of squares of the components of the representative output vector. The calculated Nx first distance measures d_prex (j) are sent to the small codebook index creation unit 41 of the candidate representative output vector determination unit 4.

Similarly, the distance calculation unit 22 of the first distance scale calculation unit 2 calculates a first distance measure d_prey (m) for each of Ny representative output vectors y_m stored in the codebook Y storage unit 32 (step). S12). For example, the first distance measure d_prey (m) for the representative output vector y_m is defined as the following equation (5). The calculated Ny first distance measures d_prey (m) are sent to the small codebook index creation unit 42 of the candidate representative output vector determination unit 4.

<Step S2>
The small codebook index creation unit 41 of the candidate representative output vector determination unit 4 uses the first distance measure d_prex (j) calculated by the distance calculation unit 21 from the codebook X storage unit 31 to determine a predetermined number Npx. One representative output vector is selected (step S21). The selected representative output vector is referred to as a candidate representative output vector.

Information about the candidate representative output vector is sent to the second distance scale calculator 5 and the minimum distance determiner 7 as a small codebook index list Xs = (xs — 0, xs — 1,..., Xs_Npx−1). Here, xs_u (u = 0,..., Npx−1) is an index representing a candidate representative output vector. A list of first distance measures Dxs = (Dxs — 0, Dxs — 1,..., Dxs_Npx−1) for each candidate representative output vector is also sent to the second distance measure calculator 5. Here, Dxs_u (u = 0,..., Npx−1) is a first distance measure for the candidate representative output vector represented by the index xs_u.
A specific method for selecting candidate representative vectors will be described. Here, although two methods are illustrated, candidate representative vectors may be selected by a method other than these methods.

* First method *
The small codebook index creation unit 41 rearranges the Nx representative output vectors x_j in ascending order of the first distance measure d_prex (j), and the Npx representatives in ascending order of the first distance measure d_prex (j). The output vector is selected as a candidate representative output vector. Specifically, the process shown in FIG. 3 is performed. MAXVAL is a sufficiently large number such as le + 20 (= 10 ^ 20).

* Second method *
A second method for selecting candidate representative vectors will be described with reference to FIG. The small codebook index creation unit 41 generates Npx groups by collecting Nx representative output vectors x_j by Nx / Npx. Then, by selecting the representative output vector x_j having the smallest first distance measure d_prex (j) for each group, Npx representative output vectors are selected as candidate representative output vectors. Specifically, the processing illustrated in FIG. 5 is performed.

When a candidate representative output vector is selected by this second method, Nx and Npx are set in advance so that Nsub = Nx / Npx is an integer, in other words, Nx is divisible by Npx.
In this example, all the groups are composed of Npx representative output vectors, but the number of representative output vectors included in each group may be different for each group.

  The small codebook index creation unit 42 of the candidate representative output vector determination unit 4 uses the first distance measure d_prey (m) calculated by the distance calculation unit 22 from the codebook Y storage unit 32 to determine a predetermined number Npy. One representative output vector is selected (step S22). Since the method of selecting the representative output vector is the same as the method of selecting the small codebook index creating unit 41 described above, the duplicate description is omitted.

  Information about the candidate representative output vector that is the selected representative output vector is sent to the second distance scale calculator 5. Specifically, the small codebook index list Ys = (ys — 0, ys — 1,..., Ys_Npy−1) is sent to the second distance scale calculator 5 and the minimum distance determiner 7. Here, ys_v (v = 0,..., Npy−1) is an index representing a candidate representative output vector. Also, a list of first distance measures Dys = (Dys — 0, Dys — 1,..., Dys_Npy−1) for each candidate representative output vector is sent to the second distance measure calculator 5. Here, Dys_v (v = 0,..., Npy−1) is a first distance measure for the candidate representative output vector represented by the index ys_v.

<Step S3>
In the cross table storage unit 6, the value of the cross term defined by using the inner product of a pair of representative output vectors selected from two different codebook storage units one by one for a plurality of pairs of different representative vectors. Each is pre-calculated and stored. A set of cross term values for a pair of representative output vectors stored in the cross table storage unit is called a cross table. The cross table corresponds to the cross table storage unit.

In this example, all pairs of each representative output vector x_j stored in the codebook X storage unit 31 and each representative output vector y_m stored in the codebook Y storage unit 32 are defined by the following equation (6). The value of the cross term is calculated and stored in advance.

  The second distance scale calculation unit 5 calculates an average vector of a set of candidate representative output vectors selected one by one from each code book storage unit (in this example, the code book X storage unit 31 and the code book Y storage unit 32). For each of a plurality of different sets of candidate representative output vectors. The calculated second distance measure is sent to the minimum distance determination unit 7.

Here, the second distance measure for the average vector of a set of vectors is a second index representing the distance between the average vector of the set of vectors and the input vector, and for each vector constituting the set of vectors. , And a cross term defined using an inner product of at least one vector pair constituting the vector set. For example, the second distance scale is obtained by deleting a term consisting only of an input vector from the Euclidean distance formula and multiplying it by an integer. In this example, the second distance measure d (j, m) for the vector set composed of the representative output vector x_j and the representative output vector y_m is defined by the following equation (6 ′).

その際、第二距離尺度計算部５のクロス項参照部５ａが、クロス項ｃｒｏｓｓ（ｘｓ＿ｕ，ｙｓ＿ｖ）の値を、クロステーブル記憶部６に記憶された対応する代表出力ベクトルのペア（ｘｓ＿ｕ，ｙｓ＿ｖ）のクロス項の値を参照して求める。この例では、加算のみで第二距離尺度ｄ（ｕ，ｖ）を計算することができ、計算効率が良い。 Therefore, the second distance scale calculator 5 calculates the second distance based on the following equation (7) for all pairs of each xs_u in the small codebook index list Xs and each ys_v in the small codebook index list Ys. Each of the scales d (u, v) is calculated.

At that time, the cross term reference unit 5a of the second distance scale calculation unit 5 uses the value of the cross term cross (xs_u, ys_v) as a pair of representative output vectors (xs_u, ys_v) stored in the cross table storage unit 6. ) By referring to the value of the cross term. In this example, the second distance scale d (u, v) can be calculated only by addition, and the calculation efficiency is good.

<Step S4>
The minimum distance determining unit 7 selects a candidate representative output vector set (xs_u, ys_v) that minimizes the second distance scale d (u, v) calculated by the distance calculating unit, and sets the candidate representative output vector set. An index representing a set of representative output vectors corresponding to is output. Specifically, the processing illustrated in FIG. 6 is performed.
As described above, if the value of the cross term is calculated and stored in the cross table storage unit 6 in advance, the value of the cross term can be obtained only by referring to the cross table storage unit 6. For this reason, it is not necessary to recalculate the value of the cross term, and the amount of calculation can be reduced. In addition, computation can be performed at high speed.

[Second Example]
With reference to FIG. 7, the multi-vector quantization apparatus 101 according to the second embodiment will be described. FIG. 7 is a diagram illustrating a functional configuration of the multi-vector quantization apparatus 101. As illustrated in FIG.
The multi-vector quantizing apparatus 101 according to the second embodiment calculates the first distance measure when the first distance measure calculating unit 2 calculates the first distance measure regardless of the input vector u in the definition formula of the first distance measure. This is different from the multi-vector quantizing apparatus 100 according to the first embodiment in that the sum of squares (also referred to as a power term) that can be obtained is obtained by referring to the power table storage units 81 and 82. Below, it demonstrates centering on the distance calculation parts 211 and 221 and the power table memory | storage parts 81 and 82 which are different parts from a 1st Example. The other points are the same as those of the multi-vector quantizing device according to the first embodiment, and therefore redundant description is omitted.

In the power table storage unit 81, the sum of squares of the components of each representative output vector x_j stored in the codebook X storage unit 31 is calculated and stored in advance. Specifically, the square sum powx (j) (j = 0, 1,..., Nx−1) defined by the following equation (8) is calculated and stored. A set of square sums of representative output vector components stored in the power table storage unit is referred to as a power table. The power table corresponds to the power table storage unit.

Similarly, in the power table storage unit 82, the sum of squares of the components of each representative output vector y_m stored in the codebook Y storage unit 32 is calculated and stored in advance. Specifically, the square sum powy (m) (m = 0, 1,..., Ny−1) defined by the following equation (9) is calculated and stored.

The distance calculation unit 211 of the first distance scale calculation unit 2 calculates the first distance measure d_prex (j) for each representative output vector x_j stored in the codebook X storage unit 31 based on the following equation (10). To do. At that time, the square sum reference unit 211a of the distance calculation unit 211 refers to the code book X storage unit 31 to obtain the value of the square sum powx (j). The distance calculation unit 211 calculates Σ _{i = 0} ^D−1 (−4u (i) · x (i, j)) obtained by calculation, and powx (j) obtained by referring to the square sum reference unit 211a. Is added to calculate the first distance measure d_prex (j).

Similarly, the distance calculation unit 221 of the first distance scale calculation unit 2 sets the first distance scale d_play (m) for each representative output vector y_m stored in the codebook Y storage unit 32 to the following equation (11). Calculate based on. At this time, the sum of squares reference unit 221a of the distance calculation unit 221 refers to the codebook Y storage unit 32 and obtains the value of the sum of squares power (m). The distance calculation unit 221 calculates Σ _{i = 0} ^D−1 (−4u (i) · y (i, m)) obtained by calculation and the square sum powy (m obtained by referring to the square sum reference unit 221a). ) Is added to calculate the first distance measure d_prey (m).

  In this way, the value of the portion that can be calculated only from the representative output vector is calculated in advance and stored in the power table storage units 81 and 82 regardless of the input vector u in the definition formula of the first distance scale. Thus, the value of the portion can be obtained only by referring to the power table storage units 81 and 82. For this reason, it is not necessary to calculate the sum of squares again, and the amount of calculation can be further reduced.

  The power table storage units 81 and 82 may not be separated. That is, the square sum powx (j) and the square sum powy (m) are stored in the same power table storage unit (not shown), and each of the square sum reference units 211a and 221a stores the same power table storage unit. The square sums powx (j) and powy (m) may be obtained by referring to them.

[Third embodiment]
The multi-vector quantization apparatus 102 according to the third embodiment performs multi-vector quantization on an input vector u having a different dimensionality L for each input. That is, in this example, the number of dimensions L of the input vector u does not necessarily match the number of dimensions D of the representative output vectors x_j and y_m. However, it is assumed that the dimension number L of the input vector u is less than or equal to the dimension number D of the representative output vectors x_j and y_m.

  Hereinafter, the multi-vector quantization apparatus 102 according to the third embodiment will be described with reference to FIG. The same parts as those of the multi-vector quantization apparatus 100 according to the first embodiment are denoted by the same reference numerals, and redundant description is omitted.

ここで、Ｌ次元以上のベクトルからＬ個の成分を抽出して得られるＬ次元ベクトルを第一縮小ベクトルとすれば、上記式（１２）の計算は、各代表出力ベクトルｘ＿ｊに対応する第一縮小ベクトルについての第一距離尺度ｄ＿ｐｒｅｘ（ｊ）と考えることができる。 The distance calculation unit 212 of the first distance scale calculation unit 2 uses the first distance measure d_prex (j) for each representative output vector x_j stored in the codebook X storage unit 31 as the number of dimensions (length) of the input vector u. ). Specifically, the first distance scale d_prex (j) is obtained based on the following formula (12).

Here, if an L-dimensional vector obtained by extracting L components from L-dimensional or higher vectors is a first reduced vector, the calculation of the above equation (12) is the first corresponding to each representative output vector x_j. It can be thought of as the first distance measure d_prex (j) for the reduced vector.

上記式（１３）の計算は、各代表出力ベクトルｙ＿ｍの第一縮小ベクトルの第一距離尺度ｄ＿ｐｒｅｙ（ｍ）と考えることができる。 Similarly, the distance calculation unit 222 of the first distance scale calculation unit 2 uses the first distance scale d_play (m) for each representative output vector y_m stored in the codebook Y storage unit 32 as the number of dimensions of the input vector u. Obtained in the range of (length). Specifically, the first distance scale d_play (m) is obtained based on the following formula (13).

The calculation of the above equation (13) can be considered as the first distance measure d_play (m) of the first reduced vector of each representative output vector y_m.

  The small codebook index creation unit 41 selects Npx candidate representative output vectors that reduce the first distance measure d_prex (j) calculated by the distance calculation unit 212. Similarly, the small codebook index creation unit 42 selects Npy candidate representative output vectors that reduce the first distance measure d_play (m) calculated by the distance calculation unit 222. The method of selecting the candidate representative output vector and the processing of the other small codebook index creation units 41 and 42 are the same as in the first embodiment.

The cross table storage unit 61 stores the number of Kc dimensions for all combinations of the representative output vectors x_j stored in the codebook X storage unit 31 and the representative output vectors y_m stored in the codebook Y storage unit 32. In the range of (length), the value of the cross term cross (j, m) defined by the following formula (14) is calculated and stored in advance. Here, Kc is an arbitrary natural number. For example, if Kc is the number of dimensions that is most frequently used among the number of dimensions L of the input vector u, the amount of calculation can be reduced.

  If a Kc-dimensional vector obtained by extracting Kc components from L-dimensional or higher vectors is used as the second reduced vector, the cross-table storage unit 61 includes two different codebook storage units (in this example, codebooks). A cross term value of a pair of second reduced vectors corresponding to a pair of representative output vectors selected from the X storage unit 31 and the code book Y storage unit 32) one by one. It can be said that each pair is calculated and stored in advance. Here, the second reduced vector pair corresponding to the representative output vector pair is a vector composed of the second reduced vectors respectively corresponding to the representative output vectors.

  The second distance scale calculator 51 is a second distance measure for the average vector of the first reduced vector set corresponding to the set of candidate representative vectors (xs_u, ys_v) selected one by one from each codebook storage unit. d (u, v) is calculated for all pairs of each xs_u in the small code index list Xs and each ys_v in the small codebook index list Ys. The first reduced vector set corresponding to the representative output vector set is a vector composed of the first reduced vectors respectively corresponding to the representative output vectors.

In the following, the processing differs depending on the magnitude relationship between Kc and L, so that the case is divided.
(A) When Kc = L When Kc = L, the second distance scale calculation unit 51 calculates the second distance scale d (u, v) based on the following equation (15). At this time, the cross term reference unit 5 a obtains the value of the cross term cross (xs_u, ys_v) with reference to the cross table storage unit 61. Since Kc = L, correction of the value of the cross term is unnecessary.

(B) When Kc> L When Kc> L, the second distance scale calculator 51 calculates the second distance scale d (u, v) based on the following equation (16). Since Kc> L, the dimension component added to the excess of the cross terms stored in the cross table storage unit 61 is subtracted.

The value of the second distance scale d (u, v) defined by the above equation (16) is obtained by the cross term reference unit 5a, the cross term difference calculation unit 5b, and the first addition unit 5c of the second distance scale calculation unit 5. Calculated. The cross term reference unit 5 a obtains the value of the cross term cross (xs_u, ys_v) with reference to the cross table storage unit 61. The cross term difference calculation unit 5b includes a cross term for a pair of Kc-dimensional second reduced vectors corresponding to a pair of candidate representative output vectors and a pair of an L-dimensional first reduced vector corresponding to a pair of candidate representative output vectors. The value of the difference with respect to the cross term (in this case, −2 · Σ _{i = L} ^kc−1 x (i, xs_u) · y (i, ys_v)) is calculated. The first adder 5c calculates the second distance measure d (u, v) by adding the values of the terms of the above equation (16).

(C) When Kc <L When Kc <L, the second distance scale calculator 51 calculates the second distance scale d (u, v) based on the following equation (17). Since Kc <L, dimension components not included in the cross terms stored in the cross table storage unit 61 are added.

The value of the second distance scale d (u, v) defined by the above equation (17) is obtained by the cross term reference unit 5a, the cross term difference calculation unit 5b, and the first addition unit 5c of the second distance scale calculation unit 5. Calculated. The cross term reference unit 5a refers to the cross table storage unit 61 to obtain the value of the cross term cross (xs_u, ys_v). The cross term difference calculation unit 5b includes a cross term for a pair of Kc-dimensional second reduced vectors corresponding to a pair of candidate representative output vectors and a pair of an L-dimensional first reduced vector corresponding to a pair of candidate representative output vectors. The value of a difference with respect to the cross term (in this case, + 2 · Σ _{i = L} ^Kc−1 x (i, xs_u) · y (i, ys_v)) is calculated. The first adder 5c calculates the second distance measure d (u, v) by adding the values of the terms of the above equation (17).

  The second distance scale calculator 51 adds the values of the first term to the third term on the right side of the equation (17), and the first adder 5c calculates the difference calculated by the cross term difference calculator 5b. The second distance scale d (u, v) may be calculated by adding or subtracting the value to or from the added value. When subtraction is performed, the cross term difference calculation unit 5b calculates the absolute value of the difference.

Note that the second addition unit 5d of the second distance scale calculation unit 51 uses the value of the cross term cross (xs_u, ys_v) obtained by the cross term reference unit 5a and the value of the difference calculated by the cross term difference calculation unit 5b. , The cross term value for the first reduced vector pair corresponding to the candidate representative vector pair (xs_u, ys_v) may be obtained. In this case, the first adder 5c adds the value of the cross term obtained by the second adder 5d, the first distance measure Dxs_u, and the second distance measure Dxs_v, whereby the second distance measure d ( u, v).
Thus, even when the number of dimensions of the input vector u is variable, multi-vector quantization processing is possible.

[Fourth embodiment]
The multi-vector quantization apparatus 103 according to the fourth embodiment calculates the first distance scale calculation unit 2 regardless of the input vector u in the definition formula of the first distance scale when calculating the first distance scale. This is different from the multi-vector quantizing apparatus 102 according to the third embodiment in that the sum of squares, which is a part capable of performing the above, is obtained with reference to the power table storage units 83 and 84.

  Hereinafter, the multi-vector quantization apparatus 103 according to the fourth embodiment will be described with reference to FIG. FIG. 9 is a diagram illustrating a functional configuration of the multi-vector quantization apparatus 103 according to the fourth embodiment. The same parts as those of the multi-vector quantization apparatus 102 according to the third embodiment are denoted by the same reference numerals, and redundant description is omitted.

In the power table storage unit 83, a square sum powx (j) determined by the following equation (18) is calculated and stored for each j (j = 0,..., Nx−1). That is, the sum of squares of the components of the Kc-dimensional second reduced vector corresponding to each representative output vector x_j stored in the codebook X storage unit 31 is calculated and stored in advance.

Similarly, the power table storage unit 84 stores a square sum powy (m) determined by the following equation (19) for each m (m = 0,..., Ny−1). That is, the sum of squares of the components of the Kc-dimensional second reduced vector corresponding to each representative output vector y_m stored in the codebook X storage unit 32 is calculated and stored in advance.

  The distance calculation unit 212 calculates a first distance measure d_prex (j) for the first reduced vector corresponding to each representative output vector x_j stored in the codebook X storage unit 31. Since the process is different depending on the magnitude relationship between Kc and L, cases are classified.

(A) Kc = L
When Kc = L, the distance calculation unit 212 calculates the value of the first distance measure d_prex (j) based on the following equation (20). At that time, the square sum reference unit 212a refers to the power table storage unit 83 to obtain the value of the square sum powx (j). Since Kc = L, correction of the sum of squares is unnecessary.

距離計算部２１２の二乗和参照部２１２ａは、パワーテーブル記憶部８３を参照して二乗和ｐｏｗｘ（ｊ）の値を求める。二乗和差分計算部２１２ｂは、代表出力ベクトルについての第一縮小ベクトルの成分の二乗和と、その代表出力ベクトルについての第二縮小ベクトルの成分の二乗和の差分（この例では、−Σ_ｉ＝Ｌ ^Ｋｃ−１（ｘ（ｉ，ｊ））^２）を計算する。加算部２１２ｃは、上記式（２１）の各項の値を加算することにより第一距離尺度ｄ＿ｐｒｅｘ（ｊ）を計算する。 (B) Kc> L
In the case of Kc> L, the distance calculation unit 212 calculates the value of the first distance measure d_prex (j) based on the following equation (21). Since Kc> L, the extra dimension component is subtracted.

The sum of squares reference unit 212a of the distance calculation unit 212 refers to the power table storage unit 83 to obtain the value of the sum of squares powx (j). The sum-of-squares difference calculation unit 212b calculates the difference between the sum of squares of the components of the first reduced vector for the representative output vector and the sum of squares of the components of the second reduced vector for the representative output vector (in this example, −Σ _{i = L} ^Kc-1 (x (i, j)) ² ) is calculated. The adder 212c calculates the first distance measure d_prex (j) by adding the values of the terms of the above equation (21).

(C) Kc <L
When Kc <L, the distance calculation unit 212 calculates the value of the first distance measure d_prex (j) based on the following equation (22). Since Kc <L, dimension components not included in the sum of squares stored in the power table storage unit 83 are added.

The sum of squares reference unit 212a of the distance calculation unit 212 refers to the power table storage unit 83 to obtain the value of the sum of squares powx (j). The sum-of-squares difference calculation unit 212b calculates a difference between the sum of squares of the components of the first reduced vector for the representative output vector and the sum of squares of the components of the second reduced vector for the representative output vector (in this example, + Σ _{i = Kc} ^L-1 (x (i, j)) ² ) is calculated. The adder 212c calculates the first distance measure d_prex (j) by adding the values of the terms of the above equation (22).

  The distance calculation unit 212 adds the values of the first and second terms on the right side of the formula (21), and the addition unit 5c adds the difference value calculated by the square sum difference calculation unit 212b. The first distance scale d_perx (j) may be calculated by adding or subtracting to the value of. In the case of subtraction, the square sum difference calculation unit 212b calculates the absolute value of the difference.

  The second addition unit 212d of the distance calculation unit 212 adds the value of the square sum powx (j) obtained by the square sum difference calculation unit 212b and the difference value calculated by the square sum difference calculation unit 212b. Thus, the value of the sum of squares for the first reduced vector pair corresponding to the candidate representative vector pair (x_j, y_m) may be obtained. In this case, the adding unit 212c adds the value of the sum of squares obtained by the second adding unit 212d and the values of the first term and the second term on the right side of the above equation (21), thereby obtaining the first second distance. A scale d_perx (j) is obtained.

（Ｂ）Ｋｃ＞Ｌの場合には、下記式（２４）に基づいて第一距離尺度ｄ＿ｐｒｅｙ（ｍ）を計算し、

（Ｃ）Ｋｃ＜Ｌの場合には、下記式（２５）に基づいて第一距離尺度ｄ＿ｐｒｅｙ（ｍ）を計算する以外は、距離計算部２１２の処理は距離計算部２２２の処理と同様であるため重複説明を省略する。

Similar to the distance calculation unit 212, the distance calculation unit 222 calculates a first distance measure d_play (m) for the first reduced vector corresponding to each representative output vector y_m stored in the codebook Y storage unit 32. . Similar to the distance calculation unit 212, processing differs depending on the magnitude relationship between Kc and L.
(A) When Kc = L, the first distance scale d_play (m) is calculated based on the following equation (23):

(B) When Kc> L, the first distance scale d_play (m) is calculated based on the following equation (24):

(C) In the case of Kc <L, the processing of the distance calculation unit 212 is the same as the processing of the distance calculation unit 222 except that the first distance scale d_play (m) is calculated based on the following formula (25). Therefore, duplicate explanation is omitted.

[Fifth Example]
In the third embodiment, the first reduced vector is a vector obtained by extracting L components (specifically, i = 0,..., L−1 components) having a small element number from L-dimensional or higher vector components. The second reduced vector is a vector obtained by extracting Kc components (specifically, components of i = 0,..., Kc−1) having a small element number from L-dimensional or higher vector components. In the fifth embodiment, the first reduced vector extracts L components (specifically, i = D−L,..., D−1) having a large element number from among the L-dimensional or higher vector components. The second reduced vector is a vector obtained by extracting Kc components (specifically, i = D−Kc,..., D−1) having a large element number from L-dimensional and higher vector components. It is. In this respect, the fifth embodiment is different from the third embodiment, and the other points are the same as the third embodiment. Differences from the third embodiment are as follows.

第一距離尺度計算部２の距離計算部２２２は、上記式（１３）に代えて、下記式（２７）に基づいて第一距離尺度を求める。

クロステーブル記憶部６１には、上記式（１４）に代えて、下記式（２８）により定義される各クロス項ｃｒｏｓｓ（ｊ，ｍ）の値が予め計算されて、記憶されている。

The distance calculation unit 212 of the first distance scale calculation unit 2 obtains the first distance scale based on the following equation (26) instead of the above equation (12).

The distance calculation unit 222 of the first distance scale calculation unit 2 obtains the first distance scale based on the following equation (27) instead of the above equation (13).

In the cross table storage unit 61, instead of the above formula (14), the value of each cross term cross (j, m) defined by the following formula (28) is calculated and stored in advance.

第二距離尺度計算部５２は、Ｋｃ＜Ｌの場合は、上記式（１７）に代えて、下記式（３０）により定義される第二距離尺度ｄ（ｕ，ｖ）の値を求める。

When Kc> L, the second distance scale calculation unit 51 obtains the value of the second distance scale d (u, v) defined by the following expression (29) instead of the above expression (16).

When Kc <L, the second distance scale calculation unit 52 obtains the value of the second distance scale d (u, v) defined by the following expression (30) instead of the above expression (17).

[Sixth embodiment]
In the fourth embodiment, the first reduced vector is a vector obtained by extracting L components (specifically, i = 0,..., L−1 components) having a small element number from among the L-dimensional or higher vector components. The second reduced vector is a vector obtained by extracting Kc components (specifically, components of i = 0,..., Kc−1) having a small element number from L-dimensional or higher vector components. In the sixth embodiment, the first reduced vector extracts L components (specifically, i = D−L,..., D−1) having a large element number from among the L-dimensional or higher vector components. The second reduced vector is a vector obtained by extracting Kc components (specifically, i = D−Kc,..., D−1) having a large element number from L-dimensional and higher vector components. It is. In this respect, the sixth embodiment is different from the fourth embodiment, and is otherwise the same as the fourth embodiment. Differences from the fourth embodiment are as follows.

パワーテーブル記憶部８４には、上記式（１９）に代えて、下記式（３２）により定義される各二乗和ｐｏｗｙ（ｍ）がそれぞれ予め計算されて記憶されている。

In the power table storage unit 83, each square sum powx (j) defined by the following equation (31) is calculated and stored in advance instead of the above equation (18).

In the power table storage unit 84, instead of the above equation (19), each square sum power (m) defined by the following equation (32) is calculated and stored in advance.

距離計算部２１２は、Ｋｃ＞Ｌの場合には、上記式（２１）に代えて、下記式（３４）により定義される第一距離尺度ｄ＿ｐｒｅｘ（ｊ）を計算する。

距離計算部２１２は、Ｋｃ＜Ｌの場合には、上記式（２２）に代えて、下記式（３５）により定義される第一距離尺度ｄ＿ｐｒｅｘ（ｊ）を計算する。

When Kc = L, the distance calculation unit 212 calculates the first distance scale d_prex (j) defined by the following equation (33) instead of the above equation (20).

When Kc> L, the distance calculation unit 212 calculates the first distance measure d_prex (j) defined by the following equation (34) instead of the above equation (21).

When Kc <L, the distance calculation unit 212 calculates the first distance measure d_prex (j) defined by the following equation (35) instead of the above equation (22).

距離計算部２２２は、Ｋｃ＞Ｌの場合には、上記式（２４）に代えて、下記式（３７）により定義される第一距離尺度ｄ＿ｐｒｅｙ（ｍ）を計算する。

距離計算部２２２は、Ｋｃ＜Ｌの場合には、上記式（２５）に代えて、下記式（３８）により定義される第一距離尺度ｄ＿ｐｒｅｙ（ｍ）を計算する。

When Kc = L, the distance calculation unit 222 calculates the first distance scale d_play (m) defined by the following equation (36) instead of the above equation (23).

When Kc> L, the distance calculation unit 222 calculates the first distance measure d_play (m) defined by the following equation (37) instead of the above equation (24).

When Kc <L, the distance calculation unit 222 calculates the first distance scale d_play (m) defined by the following equation (38) instead of the above equation (25).

[Seventh embodiment]
In the above embodiment, the cross table storage unit is provided, and the second distance scale calculation unit calculates the second distance scale by obtaining the value of the cross term with reference to the cross table storage unit. However, even if the cross table storage unit is not provided, if the power table storage unit is provided, the effect of the present invention of reducing the amount of calculation can be obtained. The multi-vector quantization apparatus 104 according to the seventh embodiment is different from the other embodiments in this point. Since the other points are the same as those of the other embodiments, the same reference numerals are given and redundant description is omitted.

The multi-vector quantizing device 104 according to the seventh embodiment will be described with reference to FIG. FIG. 11 is a diagram illustrating a functional configuration of the multi-vector quantization apparatus 104.
Multi-vector quantization apparatus 104 does not have a cross table storage unit. Therefore, the second distance scale calculation unit 52 calculates the second distance scale by calculating and calculating the value of the cross term by itself.

  However, in the power table storage units 81 and 82, the value of the sum of squares of the components of the representative output vectors stored in the code book storage units (code book X storage unit 31 and code book storage unit 32) is calculated in advance. Has been remembered. Then, the distance calculation units 211 and 221 of the first distance scale calculation unit 2 obtain the sum of squares of the components of the candidate representative vectors by referring to the power table storage units 81 and 82 as in the second embodiment. Calculate the first distance measure. The distance calculation units 211 and 221 do not need to calculate the sum of squares of the components of the representative output vector again.

For this reason, the multi-vector quantization apparatus 104 of the seventh embodiment can also reduce the amount of calculation, and has a rational effect that the calculation can be performed at high speed.
The multi-vector quantization apparatus 104 of the seventh embodiment is an embodiment in which the cross table storage unit 6 is deleted from the multi-vector quantization apparatus 101 of the second embodiment. The cross table storage unit may be deleted in the same manner for the embodiments having other power table storage units.
As another example, FIG. 12 illustrates a functional configuration of a multi-vector quantization apparatus 104 in which the cross table storage unit 61 is deleted from the multi-vector quantization apparatus 103 of the fourth embodiment.

[Modifications, etc.]
In any of the above embodiments, multi-vector quantization is performed using two code books. However, multi-vector quantization may be performed based on three or more code books instead of two code books.

とする。また、ｄ＿ｐｒｅｚ（ｔ）を代表出力ベクトルｚ＿ｔについての第一距離尺度とすると、代表出力ベクトルｘ＿ｊ、代表出力ベクトルｙ＿ｍ及び代表出力ベクトルｚ＿ｔから構成されるベクトルの組の平均ベクトルについての第二距離尺度ｄ（ｊ，ｍ，ｔ）は例えば下記式（３９）のように定義される。

In the first embodiment, a case where multi-vector quantization is performed based on three codebooks will be described as an example. As the i-th element of the t-th vector z_t in the codebook Z storage unit (not shown), z (i, t) is the cross term cross (j, m) for the representative output vector pair (x_j, y_m). ), The cross term cross ₁ (m, t) for the representative output vector pair (y_m, z_t) and the cross term cross2 (t, j) for the representative output vector pair (z_t, x_j), respectively.

And If d_prez (t) is the first distance measure for the representative output vector z_t, the second distance measure for the average vector of the set of vectors composed of the representative output vector x_j, the representative output vector y_m, and the representative output vector z_t. For example, d (j, m, t) is defined as in the following formula (39).

この場合、各クロス項ｃｒｏｓｓ（ｊ，ｍ）（ｊ＝０，…，Ｎｘ−１、ｍ＝０，…，Ｎｙ−１），ｃｒｏｓｓ_１（ｍ，ｔ）（ｍ＝０，…，Ｎｙ−１、ｔ＝０，…，Ｎｚ−１），ｃｒｏｓｓ_２（ｔ，ｊ）（ｔ＝０，…，Ｎｚ−１、ｊ＝０，…，Ｎｘ−１）の値がそれぞれ予め計算されて、クロステーブル記憶部６に記憶されている。 Here, the first distance measure d_prex (j) for the representative output vector x_j, the first distance measure d_prey (m) for the representative output vector y_m, and the first distance measure d_prez (t) for the representative output vector z_t are, for example, It is defined as follows.

In this case, each cross term cross (j, m) (j = 0,..., Nx−1, m = 0,..., Ny−1), cross ₁ (m, t) (m = 0,..., Ny−) 1, t = 0,..., Nz−1), cross ₂ (t, j) (t = 0,..., Nz−1, j = 0,..., Nx−1) are respectively calculated in advance, It is stored in the cross table storage unit 6.

That is, cross terms cross (j, m), cross ₁ (m, t), cross ₂ (t defined by using the inner product of a pair of representative output vectors selected one each from two different codebook storage units. , J) are pre-calculated and stored for each of a plurality of different representative output vector pairs.

The cross term reference unit 5a of the second distance scale calculation unit 5 refers to the cross table storage unit 6 and uses the cross terms cross (j, m), cross ₁ (m, t), cross ₂ (t, j). Find the value. Then, using the obtained cross term value, a second distance measure d (() about an average vector of a set (xs_u, ys_v, zs_r) of candidate representative output vectors selected one by one from each codebook storage unit. xs_u, ys_v, zs_r) is calculated. zs_r is a candidate representative output vector selected from the codebook Z storage unit.
Thus, the number of code books (number of code book storage units) in the first embodiment can be set to 3 or more. The same applies to the other embodiments.

The first distance scale and the second distance scale may be calculated by attaching a predetermined weight w (i) to each element number i. By calculating with weights w (i) (w (i) is a real number greater than or equal to 0), weight w (i) that is relatively larger than other weights w (i _b ) in input vector u. can be more intensively encoded component u _{(i a)} of the element number _{i a} carrying thereon an _a). For example, it is assumed that the input sample is a frequency domain coefficient, and the higher the element number i, the higher the frequency domain coefficient is associated with, and the higher frequency domain coefficient is to be encoded with priority. In this case, the larger the element number i, the larger the weight w (i).

距離計算部２２は、上記式（５）に代えて、下記式（４１）により定義される第一距離尺度を計算する。

クロステーブル記憶部６には、上記式（６）に代えて、下記式（４２）により定義されるクロス項の値が予め計算されて記憶されている。

Hereinafter, specific examples will be described with reference to the first embodiment and the second embodiment. It is possible to calculate the first distance measure and the second distance measure by weighting similarly in other embodiments.
The distance calculation unit 21 calculates a first distance measure d_prex (j) defined by the following equation (40) instead of the above equation (4).

The distance calculation unit 22 calculates a first distance scale defined by the following equation (41) instead of the above equation (5).

In the cross table storage unit 6, instead of the above equation (6), the value of the cross term defined by the following equation (42) is calculated and stored.

  Since the second distance measure is defined by the addition of the first distance measure d_prex (j), the first distance measure d_prey (m), and the cross term cross (j, m) as illustrated in the above equation (6 ′). As described above, each of the first distance scale d_prex (j), the first distance scale d_prey (m), and the cross term cross (j, m) is obtained with the weight w (i), thereby obtaining the above formula (6 The second distance scale d (i, m) exemplified in ') is also a distance scale with a weight w (i).

パワーテーブル記憶部８２には、上記式（９）に代えて、下記式（４４）により定義される二乗和ｐｏｗｙ（ｍ）が計算されて記憶されている。

距離計算部２１１は、上記式（１０）に代えて、下記式（４５）により定義される第一距離尺度ｄ＿ｐｒｅｘ（ｊ）を計算する。

距離計算部２２１は、上記式（１１）に代えて、下記式（４６）により定義される第一距離尺度ｄ＿ｐｒｅｙ（ｍ）を計算する。

In the second embodiment, the power table storage unit 81 calculates and stores a square sum powx (j) defined by the following equation (43) instead of the above equation (8).

The power table storage unit 82 calculates and stores a square sum powy (m) defined by the following equation (44) instead of the above equation (9).

The distance calculation unit 211 calculates a first distance measure d_prex (j) defined by the following equation (45) instead of the above equation (10).

The distance calculation unit 221 calculates a first distance measure d_play (m) defined by the following equation (46) instead of the above equation (11).

  When the configuration of the multi-vector quantization apparatus of each of the above-described embodiments is realized by a computer, the processing contents of functions that each apparatus should have are described by a program. The processing functions are realized on the computer by executing the program on the computer.

The program describing the processing contents can be recorded on a computer-readable recording medium. The computer-readable recording medium may be any medium such as a magnetic recording device, an optical disk, a magneto-optical recording medium, or a semiconductor memory. Specifically, for example, the magnetic recording device may be a hard disk device or a flexible Discs, magnetic tapes, etc. as optical discs, DVD (Digital Versatile Disc), DVD-RAM (Random Access Memory), CD-ROM (Compact Disc Read Only Memory), CD
-R (Recordable) / RW (ReWritable), etc., MO (Magneto-Optical disc), etc. as a magneto-optical recording medium, EEP-ROM (Electronically Erasable and Programmable-Read Only Memory), etc. as a semiconductor memory it can.

  The program is distributed by selling, transferring, or lending a portable recording medium such as a DVD or CD-ROM in which the program is recorded. Furthermore, the program may be distributed by storing the program in a storage device of the server computer and transferring the program from the server computer to another computer via a network.

  As an execution form different from the above-described embodiment, the computer may read the program directly from the portable recording medium and execute processing according to the program. Each time is transferred, the processing according to the received program may be executed sequentially. Also, the program is not transferred from the server computer to the computer, and the above-described processing is executed by a so-called ASP (Application Service Provider) type service that realizes the processing function only by the execution instruction and result acquisition. It is good. Note that the program in this embodiment includes information that is used for processing by an electronic computer and that conforms to the program (data that is not a direct command to the computer but has a property that defines the processing of the computer).

In this embodiment, the present apparatus is configured by executing a predetermined program on a computer. However, at least a part of these processing contents may be realized by hardware.
In addition, the various processes described above are not only executed in time series according to the description, but may be executed in parallel or individually according to the processing capability of the apparatus that executes the processes or as necessary. Needless to say, other modifications are possible without departing from the spirit of the present invention.

The figure which illustrates the function structure of the multiple vector quantization apparatus 100 by a 1st Example. The flowchart which illustrates the flow of processing of the multiple vector quantization apparatus 100 by a 1st Example. The flowchart which illustrates the flow of the 1st process of the small codebook index creation part 41. FIG. The conceptual diagram which illustrated the 2nd method of selection of a candidate selection vector. The flowchart which illustrates the flow of the 2nd process of the small codebook index preparation part 41. FIG. 6 is a flowchart illustrating a process flow of a minimum distance determination unit 7; The figure which illustrates the function structure of the multiple vector quantization apparatus 101 by a 2nd Example. The figure which illustrates the function structure of the multiple vector quantization apparatus 102 by a 3rd Example. The figure which illustrates the function structure of the multiple vector quantization apparatus 103 by 4th Example. The figure which illustrates the function structure of the multiple vector quantization apparatus by background art. The figure which illustrates the function structure of the multiple vector quantization apparatus 104 by 7th Example. The figure which illustrates the function structure of the multiple vector quantization apparatus 105 by 7th Example.

Claims (16)

In the plurality of codebooks, a predetermined number of representative output vectors are respectively registered,
The first distance measure for a vector is the first index that represents the distance between the vector and the input vector, and is defined using the inner product of the vector and the input vector, and the sum of squares of the components of the vector. And
The second distance measure for the average vector of a set of vectors is a second indicator that represents the distance between the average vector of the set of vectors and the input vector,
A first distance measure calculating step for calculating a first distance measure for each representative output vector registered in each of the codebooks;
For each of the codebooks, by selecting a representative output vector that minimizes the first distance measure in advance from the smallest first distance measure or each of a plurality of groups of representative output vectors. A candidate vector determining step for respectively determining a predetermined number of representative output vectors (hereinafter referred to as candidate representative output vectors);
A second distance measure calculating step for calculating a second distance measure for an average vector of a set of candidate representative output vectors, each one selected from each of the codebooks, for each of a plurality of different candidate representative output vector sets;
Determine a candidate representative output vector set that minimizes the second distance scale calculated in the second distance scale calculation step, and output an index indicating a representative output vector set corresponding to the candidate representative output vector set A minimum distance determining step to perform,
In a multi-vector quantization method having
In the power table, the value of the sum of squares of the components of each representative output vector registered in each codebook is registered in advance,
The first distance scale calculation step includes a sum of squares reference step for obtaining a value of a sum of squares of components of the representative output vector necessary for calculating the first distance scale by referring to the power table.
And a multi-vector quantization method. In the plurality of codebooks, a predetermined number of representative output vectors are respectively registered,
The first distance measure for a vector is the first indicator of the distance between that vector and the input vector,
The second distance measure for the average vector of a set of vectors is a second index that represents the distance between the average vector of the set of vectors and the input vector, and each of the vectors that make up the set of vectors. Defined using a first distance measure and a cross term defined using the dot product of the pair of vectors that make up the set of vectors,
A first distance measure calculating step for calculating a first distance measure for each representative output vector registered in each of the codebooks;
For each of the codebooks, by selecting a representative output vector that minimizes the first distance measure in advance from the smallest first distance measure or each of a plurality of groups of representative output vectors. A candidate vector determining step for respectively determining a predetermined number of representative output vectors (hereinafter referred to as candidate representative output vectors);
A second distance measure calculating step for calculating a second distance measure for an average vector of a set of candidate representative output vectors, each one selected from each of the codebooks, for each of a plurality of different candidate representative output vector sets;
Determine a candidate representative output vector set that minimizes the second distance scale calculated in the second distance scale calculation step, and output an index indicating a representative output vector set corresponding to the candidate representative output vector set A minimum distance determining step to perform,
In a multi-vector quantization method having
In the cross table, values of cross terms defined using inner products of representative output vector pairs each selected from two different codebooks are registered in advance for a plurality of different representative output vector pairs. And
The second distance scale calculation step includes a cross term reference step for obtaining a cross term value for a pair of candidate representative output vectors necessary for calculating the second distance measure with reference to the cross table. ,
And a multi-vector quantization method. In the plurality of codebooks, a predetermined number of representative output vectors are respectively registered,
The first distance measure for a vector is the first index that represents the distance between the vector and the input vector, and is defined using the inner product of the vector and the input vector, and the sum of squares of the components of the vector. And
The second distance measure for the average vector of a set of vectors is a second index that represents the distance between the average vector of the set of vectors and the input vector, and each of the vectors that make up the set of vectors. Defined using a first distance measure and a cross term defined using the dot product of the pair of vectors that make up the set of vectors,
A first distance measure calculating step for calculating a first distance measure for each representative output vector registered in each of the codebooks;
For each of the codebooks, by selecting a representative output vector that minimizes the first distance measure in advance from the smallest first distance measure or each of a plurality of groups of representative output vectors. A candidate vector determining step for respectively determining a predetermined number of representative output vectors (hereinafter referred to as candidate representative output vectors);
A second distance measure calculating step for calculating a second distance measure for an average vector of a set of candidate representative output vectors, each one selected from each of the codebooks, for each of a plurality of different candidate representative output vector sets;
Determine a candidate representative output vector set that minimizes the second distance scale calculated in the second distance scale calculation step, and output an index indicating a representative output vector set corresponding to the candidate representative output vector set A minimum distance determining step to perform,
In a multi-vector quantization method having
In the power table, the value of the sum of squares of the components of each representative output vector registered in each codebook is registered in advance,
The first distance scale calculation step includes a square sum reference step of obtaining a value of a sum of squares of components of the representative output vector necessary for calculating the first distance scale by referring to the power table,
In the cross table, values of cross terms defined using inner products of representative output vector pairs each selected from two different codebooks are registered in advance for a plurality of different representative output vector pairs. And
The second distance scale calculation step includes a cross term reference step for obtaining a cross term value for a pair of candidate representative output vectors necessary for calculating the second distance measure with reference to the cross table. ,
And a multi-vector quantization method. The multi-vector quantization method according to claim 1 or 3,
The number of dimensions L of the input vector is equal to or less than the number of dimensions of each representative output vector registered in each codebook, and Kc is a natural number equal to or less than the number of dimensions of each representative output vector registered in each codebook.
An L-dimensional vector obtained by extracting L components from an L-dimensional or higher vector is defined as a first reduced vector, and a Kc-dimensional vector obtained by extracting Kc components from an L-dimensional or higher vector is defined as a second reduced vector. As
The first distance measure calculating step is a step of calculating a first distance measure for a first reduced vector corresponding to each representative output vector registered in each codebook,
The second distance scale calculation step includes a plurality of different second distance scales for the average vector of the first reduced vector set corresponding to the set of candidate representative output vectors selected one by one from each of the codebooks. Obtaining an average vector of a set of first reduced vectors corresponding to a set of candidate representative output vectors,
In the power table, the value of the sum of squares of the components of the second reduced vector corresponding to each representative output vector registered in each codebook is registered in advance.
The first distance scale calculation step includes:
A sum of squares reference step for obtaining a value of the sum of squares of the components of the second reduced vector corresponding to the representative output vector with reference to the power table;
When the values of L and Kc are different, the difference between the sum of squares of the components of the first reduced vector corresponding to the representative output vector and the sum of squares of the components of the second reduced vector corresponding to the representative output vector is calculated. A sum-of-squares difference calculating step,
A sum-of-squares addition step for obtaining a value of the sum of squares of the first reduced vector corresponding to the representative output vector by adding or subtracting the value of the calculated sum of squares difference; and
including,
And a multi-vector quantization method. The multi-vector quantization method according to claim 2 or 3,
The number of dimensions L of the input vector is equal to or less than the number of dimensions of each representative output vector registered in each codebook, and Kc is a natural number equal to or less than the number of dimensions of each representative output vector registered in each codebook.
An L-dimensional vector obtained by extracting L components from an L-dimensional or higher vector is defined as a first reduced vector, and a Kc-dimensional vector obtained by extracting Kc components from an L-dimensional or higher vector is defined as a second reduced vector. As
The first distance measure calculating step is a step of calculating a first distance measure for a first reduced vector corresponding to each representative output vector registered in each codebook,
The second distance scale calculation step includes a plurality of different second distance scales for the average vector of the first reduced vector set corresponding to the set of candidate representative output vectors selected one by one from each of the codebooks. Obtaining an average vector of a set of first reduced vectors corresponding to a set of candidate representative output vectors,
The cross table includes a plurality of different pairs of second reduced vectors in which the values of the cross terms for the second reduced vector pair corresponding to the pair of representative output vectors respectively selected from two different codebooks. Are registered in advance,
The cross term reference step is a step of obtaining a cross term value for a second reduced vector pair corresponding to the candidate representative output vector pair with reference to the cross table,
The second distance scale calculation step includes:
When the values of L and Kc are different, the cross term of the first reduced vector pair corresponding to the candidate representative output vector pair and the second reduced vector pair cross term corresponding to the candidate representative output vector pair A cross term difference calculating step for calculating a difference value of
An addition step for obtaining a second distance measure for an average vector of a set of first reduced vectors corresponding to the set of candidate representative output vectors by adding or subtracting the calculated difference value;
including,
And a multi-vector quantization method. The multi-vector quantization method according to claim 1 or 3,
A first codebook X and a second codebook Y are provided as the plurality of codebooks. The first codebook X includes a D-dimensional representative output vector x_j (j = 0,..., Nx−1 (Nx is an arbitrary number). Natural number)), D-dimensional representative output vectors y_m (m = 0,..., Ny−1 (Ny is an arbitrary natural number)) are registered in the second codebook Y,
The i-th component of the representative output vector x_j registered in the first codebook X is x (i, j), the first distance measure for the representative output vector x_j is d_prex (j),
The i-th component of the representative output vector y_m registered in the second codebook Y is y (i, m), and the first distance measure for the representative output vector y_m is d_play (m).
Let u (i) be the i-th component of the input vector u.
The square sum powx (j) of the components of the representative output vector x_j is

As
The first distance measure d_prex (j) for the representative output vector x_j is

Defined as
The square sum powy (m) of the components of the representative output vector y_m is

As
The first distance measure d_prey (m) for the representative output vector y_m is

Defined as
And a multi-vector quantization method. The multi-vector quantization method according to claim 2 or 3,
A first codebook X and a second codebook Y are provided as the plurality of codebooks. The first codebook X includes a D-dimensional representative output vector x_j (j = 0,..., Nx−1 (Nx is an arbitrary number). Natural number)), D-dimensional representative output vectors y_m (m = 0,..., Ny−1 (Ny is an arbitrary natural number)) are registered in the second codebook Y,
The i-th component of the representative output vector x_j registered in the first codebook X is x (i, j), the first distance measure for the representative output vector x_j is d_prex (j),
The i-th component of the representative output vector y_m registered in the second codebook Y is y (i, m), and the first distance measure for the representative output vector y_m is d_play (m).
The cross term cross (j, m) defined using the inner product of the pair of representative output vectors (x_j, y_m) is

Defined as
The second distance measure d (j, m) for the average vector of the set of vectors composed of the representative output vector x_j and the representative output vector y_m is:

A multi-vector quantization method characterized in that Each of the plurality of codebooks stores a predetermined number of representative output vectors,
The first distance measure for a vector is the first index that represents the distance between the vector and the input vector, and is defined using the inner product of the vector and the input vector, and the sum of squares of the components of the vector. And
The second distance measure for the average vector of a set of vectors is a second indicator that represents the distance between the average vector of the set of vectors and the input vector,
First distance scale calculating means for calculating a first distance scale for each representative output vector stored in each of the codebooks;
For each of the codebooks, by selecting a representative output vector that minimizes the first distance measure in advance from the smallest first distance measure or each of a plurality of groups of representative output vectors. Candidate vector determining means for respectively determining a predetermined number of representative output vectors (hereinafter referred to as candidate representative output vectors);
A second distance measure calculating means for calculating a second distance measure for the average vector of a set of candidate representative output vectors, one each selected from each of the codebooks, for each of a plurality of different candidate representative output vector sets;
A set of candidate representative output vectors that minimizes the second distance scale calculated by the second distance scale calculating means is determined, and an index indicating the set of representative output vectors corresponding to the candidate representative output vector set is output. Means for determining a minimum distance,
In a multi-vector quantizer having
In the power table storage means, the value of the sum of squares of each representative output vector component stored in each codebook is stored in advance.
The first distance scale calculating means includes a sum of squares reference means for obtaining a value of a sum of squares of the components of the representative output vector necessary for calculating the first distance scale with reference to the power table storage means. ,
A multi-vector quantizer characterized by that. Each of the plurality of codebooks stores a predetermined number of representative output vectors,
The first distance measure for a vector is the first indicator of the distance between that vector and the input vector,
The second distance measure for the average vector of a set of vectors is a second index that represents the distance between the average vector of the set of vectors and the input vector, and each of the vectors that make up the set of vectors. Defined using a first distance measure and a cross term defined using the dot product of the pair of vectors that make up the set of vectors,
First distance scale calculating means for calculating a first distance scale for each representative output vector stored in each of the codebooks;
For each of the codebooks, by selecting a representative output vector that minimizes the first distance measure in advance from the smallest first distance measure or each of a plurality of groups of representative output vectors. Candidate vector determining means for respectively determining a predetermined number of representative output vectors (hereinafter referred to as candidate representative output vectors);
A second distance measure calculating means for calculating a second distance measure for the average vector of a set of candidate representative output vectors, one each selected from each of the codebooks, for each of a plurality of different candidate representative output vector sets;
A set of candidate representative output vectors that minimizes the second distance scale calculated by the second distance scale calculating means is determined, and an index indicating the set of representative output vectors corresponding to the candidate representative output vector set is output. Means for determining a minimum distance,
In a multi-vector quantizer having
In the cross table storage means, values of cross terms defined using inner products of pairs of representative output vectors each selected from two different codebooks are stored in advance for a plurality of pairs of different representative output vectors. Remembered,
The second distance scale calculating means obtains a cross term value for a candidate representative output vector pair necessary for calculating the second distance scale by referring to the cross table storage means. including,
A multi-vector quantizer characterized by that. Each of the plurality of codebooks stores a predetermined number of representative output vectors,
The first distance measure for a vector is the first index that represents the distance between the vector and the input vector, and is defined using the inner product of the vector and the input vector, and the sum of squares of the components of the vector. And
The second distance measure for the average vector of a set of vectors is a second index that represents the distance between the average vector of the set of vectors and the input vector, and each of the vectors that make up the set of vectors. Defined using a first distance measure and a cross term defined using the dot product of the pair of vectors that make up the set of vectors,
First distance scale calculating means for calculating a first distance scale for each representative output vector stored in each of the codebooks;
For each of the codebooks, by selecting a representative output vector that minimizes the first distance measure in advance from the smallest first distance measure or each of a plurality of groups of representative output vectors. Candidate vector determining means for respectively determining a predetermined number of representative output vectors (hereinafter referred to as candidate representative output vectors);
A second distance measure calculating means for calculating a second distance measure for the average vector of a set of candidate representative output vectors, one each selected from each of the codebooks, for each of a plurality of different candidate representative output vector sets;
A set of candidate representative output vectors that minimizes the second distance scale calculated by the second distance scale calculating means is determined, and an index indicating the set of representative output vectors corresponding to the candidate representative output vector set is output. Means for determining a minimum distance,
In a multi-vector quantizer having
In the power table storage means, the value of the sum of squares of each representative output vector component stored in each codebook is stored in advance.
The first distance scale calculating means includes square sum reference means for obtaining a value of a sum of squares of representative output vector components necessary for calculating the first distance scale with reference to the power table storage means. ,
In the cross table storage means, values of cross terms defined using inner products of pairs of representative output vectors each selected from two different codebooks are stored in advance for a plurality of pairs of different representative output vectors. Remembered,
The second distance scale calculating means obtains a cross term value for a candidate representative output vector pair necessary for calculating the second distance scale by referring to the cross table storage means. including,
A multi-vector quantizer characterized by that. The multi-vector quantizer according to claim 8 or 10,
The number of dimensions L of the input vector is equal to or less than the number of dimensions of each representative output vector stored in each codebook, and Kc is a natural number equal to or less than the number of dimensions of each representative output vector stored in each codebook.
An L-dimensional vector obtained by extracting L components from an L-dimensional or higher vector is defined as a first reduced vector, and a Kc-dimensional vector obtained by extracting Kc components from an L-dimensional or higher vector is defined as a second reduced vector. As
The first distance scale calculating means is a means for calculating a first distance measure for a first reduced vector corresponding to each representative output vector stored in each codebook,
The second distance scale calculation means calculates a plurality of different second distance scales for the average vector of the first reduced vector set corresponding to the set of candidate representative output vectors selected one by one from each of the codebooks. Means for obtaining an average vector of a set of first reduced vectors corresponding to a set of candidate representative output vectors;
In the power table storage means, the value of the sum of squares of the components of the second reduced vector corresponding to each representative output vector stored in each codebook is stored in advance,
The first distance scale calculation means includes:
A sum of squares reference means for obtaining a value of the sum of squares of the components of the second reduced vector corresponding to the representative output vector with reference to the power table storage means;
When the values of L and Kc are different, the difference between the sum of squares of the components of the first reduced vector corresponding to the representative output vector and the sum of squares of the components of the second reduced vector corresponding to the representative output vector is calculated. Means for calculating the sum of squared differences,
A sum-of-squares addition means for obtaining a value of the sum of squares of the first reduced vector corresponding to the representative output vector by adding or subtracting the calculated difference value of the sum of squares;
including,
A multi-vector quantizer characterized by that. The multi-vector quantization apparatus according to claim 9 or 10,
The number of dimensions L of the input vector is equal to or less than the number of dimensions of each representative output vector stored in each codebook, and Kc is a natural number equal to or less than the number of dimensions of each representative output vector stored in each codebook.
An L-dimensional vector obtained by extracting L components from an L-dimensional or higher vector is defined as a first reduced vector, and a Kc-dimensional vector obtained by extracting Kc components from an L-dimensional or higher vector is defined as a second reduced vector. As
The first distance scale calculating means is a means for calculating a first distance measure for a first reduced vector corresponding to each representative output vector stored in each codebook,
The second distance scale calculation means calculates a plurality of different second distance scales for the average vector of the first reduced vector set corresponding to the set of candidate representative output vectors selected one by one from each of the codebooks. Means for obtaining an average vector of a set of first reduced vectors corresponding to a set of candidate representative output vectors;
The cross table storage means includes a plurality of different second reduced vectors having values of cross terms for second reduced vector pairs corresponding to representative output vector pairs selected one by one from two different codebooks. Each of the pairs is stored in advance,
The cross term reference means is means for obtaining a cross term value for a second reduced vector pair corresponding to the candidate representative output vector pair by referring to the cross table storage means,
The second distance scale calculation means includes:
When the values of L and Kc are different, the cross term of the first reduced vector pair corresponding to the candidate representative output vector pair and the second reduced vector pair cross term corresponding to the candidate representative output vector pair A cross term difference calculating means for calculating a difference value of
Adding means for obtaining a second distance measure for an average vector of a set of first reduced vectors corresponding to the set of candidate representative output vectors by adding or subtracting the calculated difference value;
including,
A multi-vector quantizer characterized by that. The multi-vector quantizer according to claim 8 or 10,
A first codebook X and a second codebook Y are provided as the plurality of codebooks. The first codebook X includes a D-dimensional representative output vector x_j (j = 0,..., Nx−1 (Nx is an arbitrary number). Natural number)), D-dimensional representative output vectors y_m (m = 0,..., Ny-1 (Ny is an arbitrary natural number)) are stored in the second codebook Y,
The i-th component of the representative output vector x_j stored in the first codebook X is x (i, j), the first distance measure for the representative output vector x_j is d_prex (j),
The i-th component of the representative output vector y_m stored in the second codebook Y is y (i, m), and the first distance measure for the representative output vector y_m is d_play (m).
Let u (i) be the i-th component of the input vector u.
The square sum powx (j) of the components of the representative output vector x_j is

As
The first distance measure d_prex (j) for the representative output vector x_j is

Defined as
The square sum powy (m) of the components of the representative output vector y_m is

As
The first distance measure d_prey (m) for the representative output vector y_m is

Defined as
A multi-vector quantizer characterized by that. The multi-vector quantization apparatus according to claim 9 or 10,
A first codebook X and a second codebook Y are provided as the plurality of codebooks. The first codebook X includes a D-dimensional representative output vector x_j (j = 0,..., Nx−1 (Nx is an arbitrary number). Natural number)), D-dimensional representative output vectors y_m (m = 0,..., Ny-1 (Ny is an arbitrary natural number)) are stored in the second codebook Y,
The i-th component of the representative output vector x_j stored in the first codebook X is x (i, j), the first distance measure for the representative output vector x_j is d_prex (j),
The i-th component of the representative output vector y_m stored in the second codebook Y is y (i, m), and the first distance measure for the representative output vector y_m is d_play (m).
The cross term cross (j, m) defined using the inner product of the pair of representative output vectors (x_j, y_m) is

Defined as
The second distance measure d (j, m) for the average vector of the set of vectors composed of the representative output vector x_j and the representative output vector y_m is:

A multi-vector quantizer characterized by being defined as   A multi-vector quantization program for causing a computer to execute each step of the multi-vector quantization method according to claim 1.   The computer-readable recording medium which recorded the multi vector quantization program of Claim 15.

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