FR2773659A1 - METHOD FOR ENCODING A VECTOR OF A NETWORK REPRESENTING A QUANTIFIED SIGNAL AND CORRESPONDING DECODING METHOD - Google Patents

Abstract

The invention concerns such a method for coding a vector and also a corresponding decoding method and a method for producing a dictionary of partial vectors which is used, according to their characteristic, in such methods.

Description

The present invention relates to a method of encoding a vector of a

  representative network of a quantized signal. Such a vector is for example obtained by a network vector quantization operation. It can also be issued by a

  transmission system of vectors or blocks of data.

  A network vector quantization method is known and is generally used in audio, video and multimedia signal compression systems in the broad sense. Network vector quantization is the multidimensional extension of uniform scalar quantization. The latter consists in quantifying separately a signal, for example representative of each pixel of an image, in 2N levels where Nest the number of bits allocated to the quantizer As for the vector quantization on network, it is associated with a regular network and allows to determining a quantization vector, or quantized vector, belonging to the network in question whose components are representative of the values taken by the signals to be coded. More precisely, the quantization operation thus consists in determining, from an original vector each of which components is representative of the value taken by a signal to be encoded and therefore belongs to an uncountable set, such as the set of real numbers R, a quantized vector x, each of whose components belongs to a countable set such that set of relative numbers Z. Such a method is for example described by CONWAY JH and SLOANE NJ.A. in an article entitled "Fast quantizing and decoding algorithms for lattice quantizers and codes" published in IEEE Transaction on Information Theorv of March 1982 For example, if the vectororiginel is the vector (1.3, 2.6, -3 2), the vector quantized on a network D3 is the vector x = {I, 2, -3} A network is a set of vectors of a dimension space / forming an additive group, in the mathematical sense of the term. a book written by CONWAY JH and SLOANE N. JA entitled "Sphere Packings, Lattices and groups", published in 1993 by Springer Verlag (New York, NY) The networks for which the present invention finds optimal application satisfy the following condition : if a vector v, with n components, belongs to the considered network, then all the vectors u obtained by permutations carried out on the components of the vector v also belong to the network. For example, if the vector, I, 2, 1, 0} belongs to the network then the vector {2, 1, 0, 1} too. For example, the various conventional types of networks satisfying this present condition are those known in the literature as network names Z ,,, A ,,, D ,, the network.

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  cubic face-centered (D "), and the E8 network, or the Gosset network, which is described by T, GOSSET in an article entitled" On the regular and semi-regular figures in space of n

  dimensions "appeared in Messenger Math., vol 29, 1900.

  Once the quantized vector x has been obtained, it remains to assign to it, generally by an indexing operation, also called numbering or labeling of vectors, a code. This operation of indexing a vector consists, from there, in searching for its index in a dictionary. For the decoding, the inverse operation is carried out which is done from an index and which makes it possible to find in the same dictionary the considered vector. Since in general the signals thus processed have special statistical properties and, in order to reduce the search costs in the dictionary which is generally large, particular indexing methods are used. A method known as two-component product coding method, polar coding, or spherical vector quantization consists of transmitting a two-component code, one is relative to the norm of the quantized vector while the other is relative to its phase, called angle dimension ti = 2. We therefore associate with every quantized vector x a product code of the form (pa, x). If this method makes it possible to obtain a gain in terms of the calculation time of the code search procedure and in terms of flow necessary for the transmission of this code, the fact remains that it is necessary to have a dictionary including all the vectors that can be used by the application We know t also a method that uses the concept of vector leader said. It is described by LAMBLIN and ADOUL in an article entitled "Algorithm of spherical vector quantization from the Gosset network of order 8" published in

  the Annals of Telecommunications, vol 43, to 3-4 of 1988.

  According to this method, starting from each vector of the network, we consider the set of vectors that are obtained by permutations of the components of said vector. Among these vectors, we define a representative which is then named leader vector and which is noted / It can be shown that this set of vectors is an equivalence class, in the mathematical sense of the term. Generally, the vector leader / chosen to represent the other vectors is the one whose t! components are ordered from

  decreasing manner such that / (O) _> (/)> ... / (- I).

  In the following description, we will designate a set whose vectors that the

  constitute have identical components but in a different order by the equivalence class term

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  FIG. 1 shows a diagram illustrating a quantization and coding method. The quantization operation itself is performed, from a signal to code.s, by a quantization unit 10 which delivers the quantized vector x This is the object, on the one hand, of a search of the vector leader / representative of the set of vectors that have the same components as said vector quantized x by the unit 20 and, secondly, a calculation of the rank t of this vector quantized x in this set by the unit 30 From the leader vector /, a unit 40 determines the index i of the leader / found vector by the unit 20 and the unit 50 determines, from this index i

  and rank I of the leader vector /, the code c of the quantized vector x.

  There is shown in FIG. 2 a diagram illustrating a decoding method.

  The unit 60 determines from the code c received, on the one hand, the index i from which it deduces the leader vector /. and, on the other hand, the row r. From these two elements / and t, a unit determines the quantized vector x Then a unit 80 reconstructs the signal. who

was coded in 10.

  For the encoding, in particular for the determination of the index i of the leader vector / corresponding to the quantized vector x, a vector dictionary leader / Similarly, for decoding, in particular for recovering from the index i, is used. deduced from the received code c, the leader / concerned vector, a dictionary of

leader / vectors.

  These dictionaries are normally, in the state of the prior art, stored permanently in respective memories of the encoder and the decoder used. However, even if they are of reduced size compared to an exhaustive dictionary of vectors, the dictionaries of leading vectors require the implementation of a relatively important storage capacity The object of the present invention is to propose a method which solves this problem and thus avoids the use of a large memory capacity

  for memorizing the leading vectors.

  To this end, a method of encoding a vector, said quantized vector, is characterized in that said representative index of said leader vector is determined from a dictionary giving for each leader vector having the same norm as said quantized vector its index , said vectors of said dictionary being determined by calculation and stored temporarily in a memory at the time of forming said code

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  According to another characteristic of the invention, said coding method consists in scanning the space corresponding to the hypercadran of the hypersphere of radius equal to the desired norm and storing, in a predetermined order, the vectors of this hypersphere.

  space which are absolute leading vectors.

  According to another characteristic of the invention, said coding method consists in scanning the space corresponding to the hypersphere of radius equal to the desired standard and storing, in a predetermined order, the vectors of this space which are

leading vectors.

  According to another characteristic of the invention, said method of coding a vector consists in considering, at each step of a polling process constituted by successive steps, a vector and to record it in the dictionary only if it presents the desired standard, and in that said scanning process consists of a first step, to consider the vector / la, 0 ... / whose all components are zero except for the first component, whose standard || / | is

  less than or equal to the desired standard p and which is such that the norm of the vector I '(a, 1,.

  0 .....) whose first component is equal to the value of the first component increased by one unit is greater than the desired standard p. in a second step, considering the vector t = {r -, .... (X- / whose all components are equal to the first component of the previously considered vector decremented by one unit, to be decremented, in successive steps, of one unit each time, the last component of the vector considered until reaching the value zero, while keeping the other components at their respective values, then for all the components of the vectors thus obtained, to decrement by one unit the component just left of the component that has just been canceled in the previous step, then equal all the components to the right of said component decremented to the value of said component, to repeat the successive steps of decrementing the last component According to a Another characteristic of the invention is that the vector scanning process is interrupted when the vector in question is the null vector. vector scanning is interrupted when the vector considered is the vector of which, the first component being negative,

  the standard is higher than the desired standard.

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  According to another characteristic of the invention, said vectors of said dictionary are determined and stored by first considering the vector of which only the first component is not zero, the value of said first component being determined on the one hand , that the norm of said vector is lower than the desired standard and, secondly. that the norm of the vector of which only the first component is not zero and is equal to said value increased by one unit is greater than said desired standard, then by launching a function S for a position variable equal to zero, for a given vector equal to said vector thus considered and for the desired standard, said function S, for the position variable equal to any value d and a given vector, being provided for a) determining a vector, said analyzed vector, which, if the position variable is zero, is equal to said given vector and, if not, is equal to said given vector with the d "" i component equal to the (d-1), component of said given vector, b) storing said analyzed vector if its norm is equal to the desired standard. or, if the norm of said vector is lower than the desired standard, launching the same function S for a value of the position variable incremented by one unit and for a vector

gives equal to said analyzed vector.

  c) determine a new vector analysis by decrementing by one unit the value of the component dnn and

d) start again at step b).

  According to another characteristic of the invention, in step d) of said method, it consists in recommencing step b) as long as the component is not less than a value for which the norm of said vector The analyzer is greater than the desired standard, otherwise it is not necessary to exit from the function S. According to another characteristic of the invention, in step d), it consists in starting again at step b) as long as the "" component is not zero, if not leave the function S. The present invention also relates to a method of decoding a normally constituted code, an index representative of a vector, said vector leader, whose components are the components of the vector quantified to recover but not necessarily in the same order, and a characteristic of said quantized vector to be recovered which discriminates it from the other vectors belonging to the set of vectors which have the same components as said leader vector, said method being able to determine, from said index, the corresponding leader vector. then, to

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  from said characteristic and said leader vector, said quantized vector to be recovered According to the invention, said decoding method is characterized in that said leader vector corresponding to the index contained in said code is determined from a dictionary giving for each leader vector having the same norm as said vector quantized its index, said vectors of said dictionary being determined by calculation and stored temporarily in a memory at the time of searching for said

leader vector.

  According to another characteristic of the invention, said decoding method consists in scanning the space corresponding to the hypercadran positive of the hypersphere of radius equal to the desired norm and storing, in a predetermined order, the vectors of this

  space which are absolute leading vectors.

  According to one variant, said decoding method consists of scanning the space corresponding to the hypersphere of radius equal to the desired norm and to memorize, in a

  predetermined order, the vectors of this space which are leading vectors.

  According to another characteristic of the invention, said decoding method consists in considering, at each step of a polling process consisting of successive steps, a vector and to record it in the dictionary only if it presents the standard desired, and in that said scanning process comprises: at a first step, considering the vector / - {a, 0, ....., O whose all components are zero except for the first component, whose standard || / 11 is

  less than or equal to the desired standard p and which is such that the norm of the vector I '(a 1.

  0, .., O) whose first component is equal to the value of the first component increased by one unit is greater than the desired standard p. at a second step, to consider the vector / = a-I ..... a-I} whose all components are equal to the first component of the vector previously

  considered decremented by one unit.

  to decrement, in successive steps, one unit each time, the last component of the vector considered up to obtain the value zero, while keeping the other components at their respective values, then for all the components of the vectors thus obtained, decrementing by one unit the right-hand component of the component that has just been canceled in the previous step, and then equaling all the components to the right of said component decremented to the value of said component,

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  to repeat the successive steps of decrementing the last component According to another characteristic of the invention, the process of polling the

  vectors is interrupted when the vector considered is the null vector.

  According to one variant, the vector scanning process is interrupted when the vector in question is the vector of which, the first component being negative,

  the standard is higher than the desired standard.

  According to another characteristic of the invention, said vectors of said dictionary are determined and stored by first considering the vector of which only the first component is not zero, the value of said first component being determined on the one hand that the norm of said vector is lower than the desired standard and, secondly, that the norm of the vector of which only the first component is not zero and is equal to said value increased by one unit is greater than said standard desired, then by launching a function S for a position variable equal to zero, for a given vector equal to said vector thus considered and for the desired standard, said function S, for the position variable equal to any value d and a vector given, being provided for a) determining a vector, said analyzed vector, which, if the position variable is zero, is equal to said given vector and, if not, is equal to the given vector audit with the component equal to the (d-I) m component of said given vector, b) storing said analyzed vector if its norm is equal to the desired standard, or, if the norm of said vector vector is less than the desired standard, launching the same function S for a value of the position variable incremented by one unit and for a given vector equal to said analyzed vector, c) determining a new vector analyzed by decrementing by one unit the value of the component d '' m and

d) start again at step b).

  According to another characteristic of the invention, in step d), it consists in recommencing step b) as long as the diem component is not less than a value for which the norm of said analyzed vector is greater than the desired standard, if not out of the function S. According to a variant, in step d), it consists in starting again at step b) as long as the ole of component is not zero, if not leaving the function S .

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  The present invention further relates to a method for producing a partial dictionary of vectors which all have as their norm a desired standard, for example, the norm of a given vector and whose components are ordered in a decreasing manner.

  from left to right, said vectors then being called leading vectors.

  According to one characteristic of the invention, said method for developing a dictionary consists in considering, at each step of a scanning process constituted by successive steps, a vector and not registering it in the dictionary unless it presents the desired standard, and in that said scanning process consists of a first step, to consider the vector I la, 0 ...., O whose all components are zero except for the first component, whose the norm MI / is less than or equal to the desired norm p and which is such that the norm of the vector I '(c., 0, .0., () whose first component is equal to the value of the first component a augmented by one unit is greater than the desired standard p in a second step, consider the vector / = fa- I ..., a- / c, all components of which are equal to the first component of the vector previously considered decremented by one unit, to decrement, by successive stages ssives, from one unit each time, the last component of the vector considered up to obtain the value zero, while maintaining the other components at their respective values, then for all the components of the vectors thus obtained, to decrement by one unit the component just left of the component that has just been canceled in the previous step, then equal all the components to the right of said component decremented to the value of said component, to repeat the successive steps of decrementation of the last

component.

  According to another characteristic of the invention, the process of scanning

  vectors is interrupted when the vector considered is the null vector.

  According to one variant, the vector scanning process is interrupted when the vector in question is the vector of which, the first component being negative,

  the standard is higher than the desired standard.

  According to another characteristic of the invention, said vectors of said dictionary are determined and stored by first considering the vector of which only the first component is not zero, the value of said first component being determined on the one hand , that the standard of said vector is lower than the desired standard and,

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  on the other hand, that the norm of the vector of which only the first component is not zero and is equal to said value increased by one unit is greater than said desired standard, then by launching a function S for an equal position variable at zero, for a given vector equal to said vector thus considered and for the desired standard, said function S, for the position variable equal to any value d and a given vector, being provided for a) deteliminate a vector, said vector analyzed , which, if the position variable is zero, is equal to said given vector and, if not, is equal to said vector

  given with the d.n. component equal to the (d-1) '' 'component of said given vector.

  b) storing said analyzed vector if its norm is equal to the desired standard, or, if the norm of said vector is lower than the desired standard, launching the same function S for a value of the position variable incremented by one unit and for a vector gives equal to said analyzed vector, c) determining a new vector analyzed by decrementing by one unit the value of the component and d) starting from step b) According to another characteristic of the invention in step d), it consists in starting again in step b) as long as the d "'component is not lower than a value for which the norm of said analyzed vector is higher than the desired norm, otherwise going out of the function S. According to a variant, in step d), it consists in starting again at step b) as long as the di "m 'component is not zero, otherwise leaving the function S The characteristics of the invention mentioned above, as well as others,

  appear more clearly on reading the following description of two examples of

  implementation treats in connection with the accompanying drawings among which FIG. 1 is a diagram illustrating a quantization and coding method for which a method of the invention can be implemented; FIG. 2 is a diagram illustrating a decoding method for which a method of the invention can be implemented; 3a and 3b are lists of vectors with their respective ranks which belong to the same equivalence class represented respectively by a leader vector / = {a, h, c, d / and a leader vector / {2, 1 , 0, -1], FIG. 4 illustrates the scanning process of the space as it is operated according to a method according to the invention,

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  FIG. 5 illustrates a method for determining partial dictionary of leader vectors according to the invention. FIG. 6 is a flowchart of the step of storing a method according to the invention, FIG. 7 is a flowchart of a function which is implemented in a partial dictionary method of absolute leader vectors according to the invention, and FIG. 8 is a flowchart of a function which is implemented in a method of partial dictionary determination of signed leading vectors according to

The invention.

  According to the invention, the dictionaries necessary for the coding operation or the decoding operation are not permanently stored, but only a part of them, at the moment of their use, is calculated and then stored. This part of the dictionary is the one that lists all the leading vectors that have the same norm as the quantized vector.

  In the following description, we will call vector leader / a vector which is the

  representative of a set of vectors that all have the same components, in a different order What gives it its property of representative of this set is that its components are ordered, for example but not necessarily in the

decreasing sense.

  For example, if we consider a vector [1,2, -1,0 /, it belongs to a set of vectors that have all the components 2,1,0 and -1 but in a different order from each other Thus, the vector {-1,2,0,10 also belongs to this set. This set is represented by the vector which also has the same components, but ordered, for example in decreasing direction. So this is the vector, says

leading vector, {2,1,0, -1J].

  We can show that the set of vectors that have the same components and are represented by the same leader vector / forms an equivalence class, in the mathematical sense of the term. In addition, all vectors that belong to the same equivalence class can be ordered so that it is possible to associate a rank, denoted r, which corresponds to their order number in the equivalence class to which they belong. They belong by way of example, we give in FIG. 3a, the list of vectors belonging to an equivalence class whose leader vector is [a, h, c, d? as well as their respective ranks

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  FIG. 3b, the list of vectors belonging to an equivalence class whose leader vector is 2, 1.0, -1] and their respective ranks. We

  note that the signed leader vector is the vector {2,1,0, -1].

  In the remainder of the description, the equivalence class, the set of

  vectors that have the same components as a given vector x and are represented by

the same leader vector signed /.

  Another type of leader vector can be used for coding operations and

  decoding. These are the absolute leading vectors.

  An absolute leader vector is a vector which is deduced from a leader vector I by taking the absolute values of the components of the latter and then ordering them in the manner of the leading vectors. The components of an absolute leader vector all belong to the vector. set of integers N. The leading vectors from which the absolute leading vectors are deduced are called signed leading vectors, since their components belong to the set of relative numbers Z It can be shown that the set consisting of the union of all the classes equivalence generated by the signed leading vectors I from which one can deduce a single absolute leader vector / also forms an equivalence class, also said to be outperforming equivalence, of which said absolute leader vector can be the representative Moreover, all the classes of equivalence which belong to the same superclass of equivalence are ordered and it is thus possible to associate them with a rank corresponding to spond to their order number in the superclass of equivalence to which they belong. The use of absolute leader vectors, instead of signed leading vectors, for coding and decoding operations has a certain advantage because their dictionary is necessarily restricted to a vector dictionary.

signed leaders. Note that in this case, the units 40 and 60 of Figs. 1 and 2

determine a

  Absolute leader vector instead of a signed leader vector.

  For the creation of an absolute leader vector dictionary of the same standard equal to a desired standard, the method of the invention consists in scanning the hypercadran positive of the hypersphere of radius equal to the desired standard. Through this process of searching, we look for the leading vectors that have a desired standard and this, in a given order

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  To do this, in a first step (see Fig. 4), we start by considering the vector I {a, 0, ..., O] whose all components are zero except for the first component, whose standard 1 | / || is less than or equal to the desired norm p and which is such that the norm of the vector '(a, 1, 0, ..., 0) whose first component is equal to the value of the first component acr increased by one unit is greater than the desired standard p Then, we consider, in a second step, the vector / = [aI, .... cr- /, whose all components are equal to the first component of the previously considered decremented vector of a unit. Then, in successive successive steps, one unit each time to decrement the last component of the vector considered until it becomes zero, while keeping the other components at their respective values. [ca-I / .... t- /, 0, / The penultimate component is then decremented by one unit

  and the component on her right is equal to her. We now have the vector / Ia - /, .....

  a-2, a-2} As before, the last component of the vector considered is then again decremented by one unit each time until it becomes zero, while keeping the other components at their respective values L penultimate component is again decremented by one unit The same process is implemented until this penultimate component also becomes zero Then we have the vector / = I a-1, ... [ . a-I. 0, O0 Then, it is the component which is immediately to the left of the two null components which is decremented and the components on its right are equal to it We then have the vector /: ia-1, ... , ct-2, a-2, a-2 /. The process begins again Generally, when all the components to the right of a component of order i are null, this component is decremented by one unit and all those which are on its right are equal to it. Then, we decrement one unit each

  the last component until it becomes zero.

  At each stage of the scanning process as described above, if the standard

  is equal to the desired standard, the vector considered is recorded.

  For the creation of a dictionary of signed leading vectors, the method of the invention consists in scanning the complete hypersphere of radius equal to the desired standard. This method proceeds in the manner described above concerning the absolute leader vector dictionary. with the difference that we stop the successive decrementations of each component when it is negative, the norm of the vector considered is greater than the desired standard

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  We will describe, in connection with FIG. 5, a Particular Implementation of the Method for Determining a Partial Dictionary of Lead Vectors According to the Invention A first step 100 is an initialization in which, on the one hand, a calculation variable d representative of the analyzed component as well as a variable of order I are equal to zero and, on the other hand, a vector /(aO, ..., O) whose first component a is initialized to the value of an initialization variable such that the standard of this vector] 11l / be less than or equal to the desired norm p of the quantized vector x and the norm of the vector I '(a 1, 0, ...., O) whose first component is equal to the value of the initialization variable increased by one is greater than the norm p of the quantized vector x. So we have: 11 / 11-. A second step 200 consists in implementing a function, Sd, /. o) which is a function of the value taken by the calculation variable dl, of the leading vector considering / and

  of the PC standard. This function is recursive in the sense that it is called

  This function is now described, in a first mode of implementation,

in relation with Fig 6.

  Preliminarily, we call component 1 (d) of a vector I s component sea

  counted from the left, the one completely left having the order number 0.

  Thus, for a vector equal to 1 (xy, z, w), we have I (0) x 1 (1) y 1 (2) z 1 (3) w In a first step 10, we verify that the value of the calculation variable d is smaller than the dimension of the network n, otherwise one leaves the function S (d, /, p) while not carrying out any computation. In step 20, it is verified that the value of the calculation variable d is equal to zero. If so, it means, as will be understood later that it is the first law that the function S is called. In this case, we keep the coordinates of the vector I as they were defined during the initialization or during the previous steps Otherwise, in step 21, the diCmc component of the vector I is equal to the value of the ( d- / J) "" "'component of the vector /: 1 (d) 1 (d1-1)

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  We verify in step 30 that the dic "c component of the vector I is not negative or zero, in this case we would go out of the function S (d, 1, p). In step 31, we compare the value of the norm 11ljl of the vector I computed hitherto with the value of the norm variable p If these two values are equal, then the vector / is a leader vector which can be stored in the memory at step 41, since precisely there is If they are different, we verify, in step 32, if the norm || / || of the vector / is lower than the norm value p If this is the case, we throw, at the step 42, the function S (d 1,., p) for a calculation variable equal to the current value of d increased by one unit, for the vector I so far calculated and always for the value of the equal standard variable at p.

  that it is by this call of the function S that we can say that it is recursive.

  If this is not the case, it is carried directly to the next step. In step 50, the component dcn "c component of vector 1 (I (d) t (d) - is decremented by one unit. The process of memorizing step 4 is explained in relation to Fig. 7. This process of memorization proper takes place at step 412 where the vector / considered is memorized in a manner associated with the value taken by the command variable I It will be recalled that at the initialization step 100, the value of the order variable I is initialized to zero At step 411 of the process 41, this variable I is incremented by one unit. Thus, at each new implementation of the storage, this variable is incremented by unity and consequently gives the serial number of the unit.

memorization considered.

  Note that the association of the vector / memorized and the variable I is for example carried out, either explicitly in the sense that they are both stored in any box of a memory, or implicitly in the direction where the vector / is stored in a single box of a memory whose address is obtained by

  addition of a reference address with the value 1.

  As an example, we will now consider the creation of the partial vector dictionary of dimension 2 vectors whose standard is 5. We define the standard here as

  being the sum of the absolute values of the components.

  In step 100, the calculation variable d is initialized and the variable of order I is set to 0 and the vector / is initialized to the vector {5,0}. Indeed, we have II {5,0} 11 <5 <cj {6,0} 11

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  In step 200, the function S (0, [5.0 /, 5) is started. We have d,, t and d ::: O. We are thus led to the step 30 where the component of the vector I is positive (1 (d) '0) so that we are led to step 31. There, since the norm of the vector I is equal to the value of the desired norm p, | 1 | / l = p. We are thus led to the step 41 where the vector / 5, 0 /, is memorized since it has the desired standard I / 1 = p In step 41], the variable of order I becomes equal to I and the vector / [5, 0, is stored associated with the value I = IA step 50. is decremented by one the component of the vector I so that the analyzed vector is now / = / 4.0 / It is then brought back to the stage 31 which itself leads (one has 11 = 4, p) to step 32. The norm of the vector / being positive,

  the function N, </ /, / 4.0 /, 5) S (1, [4.0 /, 5) is implemented.

  In step 21 of the function S (/, (4, (0.5j., The value / (1) of the first component of the vector / is equal to that of the zero-order component 1 / (0) (1 (1) = 1 ()), so that the new vector I analyzed is now the vector (4,4 /.) The vector component / is positive, but its norm is greater than the value of the desired standard Step 50 is therefore carried out directly The analysis vector is then the vector [4,3] and then, because of a succession of steps, the vectors 4,2 / and [4,1 / are also analyzed.

  vector has its norm | I / Il which is equal to p = 5. It is thus stored in step 41.

  In step 41 1, the variable I is incremented by one unit and becomes equal to 2. In step 412, the vector 4, 1] is stored in association with the value I = 2. In step 50, the first component 1 (1) of the vector I is now decremented to become equal to 0. The vector I thus becomes the vector (4,0), at step 30, we leave the function S (1, [4 , 0 /, 5), which was started by step 42, to arrive at step 50 of the function S (0, / 4,0 / ,, 5) The zero order component 1 (0) the vector / is then decremented by one unit and the vector I analyzed becomes I = (3, 0 / The steps 31 and 32 then lead to the step 42 where the function S (1, (3.0)), ), at step 21 of the function S (d / ,, 13,0,, 5), the first component 1 (1 /) of the vector / is equal to the zero-order component of the vector 1 (1 (1) 1 (0)) so that

  the new vector / analyzed is now the vector {3,3].

  This vector has its norm which is greater than the desired norm p We are therefore led directly to the step 50 where the analyzed vector becomes the vector (3,2, This vector has its norm which is equal to 5, so that is led to step 3 1 which itself

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  proceeds to step 41 where the vector / {3,2] is then stored with the value of the variable I = 3. At step 50, the vector 1 analyzed becomes the vector {3,1,. The function S ('2, (3,.), 5) is now started in step 42 but returns immediately to the

  measure o the calculation variable d is equal to 2, the dimension of the network.

  This return is at step 50 where the vector analyzed / becomes the vector [3, 0,. We

  then comes out of the function S (I, {3,0 t, 5).

  It will be understood that the process continues until the last vector analyzed is the vector / 0,0 /. Thus, step 200 of FIG. 4. The following vectors have therefore been stored in the memory associated with the value of variable I which gives the order of these vectors: order I = I / 5.0 / order I = 2, t1 / order I = 3 / 3.2 / This constitutes a partial dictionary of absolute leader vectors which can be used in a coding process or in a decoding method. It will be noted, on the one hand, that the memorized vectors are leading vectors, ie that is, their components are ordered so that the highest value components are in the weakest positions and that, on the other hand,

they themselves are ordained.

  It will be noted that the network space that has been scanned by the method just described is that for which all the components of the vectors therein have positive values. As a result, the partial dictionary thus calculated is a

  Absolute leader vector dictionary.

  Now, with reference to FIG. 6, a second embodiment of a function which is used in a method according to the invention which differs from the previous one in that the space which is scanned is that for which the components of the vectors can take negative values. As a result, it allows training

  a partial dictionary of signed leading vectors.

  The essential difference, visible in the diagram of FIG. 6, with respect to the process described in connection with FIG. 5 is found in step 30 where it is now verified that when di '' component of the vector / is negative, the norm of the vector

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  / is not greater than the desired standard. If this is the case, then we leave the function S

  considered, otherwise we are led to step 31.

  As will be seen later, this new condition of step 30 causes the method to scan all the leading vectors which are included in the space limited by the hypersphere of radius equal to the desired standard. By way of example, we have considered the creation of the partial partial dictionary of vectors of dimension 2 whose norm is 5. We define the norm here as being the sum of the absolute values of the components of the vector considered in step 100, we so initializes the calculation variable d to the value 0 and the vector I is initialized to the vector {5,0} In fact, we have 11 {5,0} <5 <{6,0} In step 200, the function (O, 5.0 /., W5) is started. We have J _n and d 0. Moreover, the cm of component of the vector / is positive (its norm || / || is lower than the desired norm p) so that we are led to step 31 Here, since the norm of the vector I is equal to the value of the desired standard p (11/1 = -p), we are led to the step 41 where the vector I [5,0 / is stored at step 41 1, the order variable I becomes equal to I and the vector / 15.0 / is stored associated with the value I-1 In step 50, the component di "c component of the vector I is decremented by one unit so that the analyzed vector is now / = {4,0). We are then brought back to the step 31 which itself leads, since the standard 11111 of the vector is equal to 4 and is therefore different from p. step 32 and thence, since the norm of the vector / is less than the value of the desired standard p in step 42 o the function S (d- + 1 /, (4,0,5) J - S (1, 4.0 / ,, 5) is implemented In step 21 of the function S (1f (4.0), 5), the value 1 (1) of the first component of the vector I is equal to that of the zero order component 1 (0) (f1 (1) = 1 (0)), so that the new vector / analvse is now the vector {4,4 / La d1 "component of the vector / is always positive so that one is led to step 31, then, the standard of this vector being different from the desired standard, in step 32 and finally, the norm being greater than the desired standard, at step 50 which is therefore implemented The vector analyzed is the vector {4,31 then. because of the same sequence of steps, the vectors {4, 2, * and [4, 1 / are then analyzed. The latter vector has its MI standard which is equal to ap = 5. It is therefore stored in step 41. In step 411, the variable I is incremented by one unit and becomes equal to 2. In step 412, the vector (4.1) is memorized in association with the value 1 2

1 8 2773659

  In step 50, the first component 1 (1) of the vector / is decremented for

  become equal to 0. The vector I thus becomes the vector (4, 0.

  Following the results of the various steps 30, 31, 32 and 33, the function S (2 ,, '/ 4, 0 / ,, 5) is implemented. Nevertheless, in this, step 10 is such that the output is immediate. Step 50 of the function S (1, {4.0, 5) is then implemented and the vector analyzed becomes the vector ( 4, -1l / The divac component of the leader vector I analyzed is therefore negative Its norm is not, however, greater than the desired norm p At the stage, it is therefore brought to step 31 o, since the norm of the vector / is equal to the desired standard, it leads to the step 41 o this vector is stored with the value of the variable 1 = 3 The following vector is the vector 4, -2 / whose d "" component is negative and whose norm equal to 6 is greater than the desired norm p 5. It follows that we leave the function S (I, 4.0 / 5,) where we end up at the stage 50 of the function S (O, [4., 0, 5) which is thus implemented The vector analyzed then becomes the vector 3.0 (Sa of 'nc component is positive but its norm] 1 / 1l is less than p, although (read function (/, 3.0], 5) is In step 21 of this function S (1, [3, 0! 5), the new analysis vector becomes the vector [3,3,. Its component dc is positive but its norm is higher than the desired norm so that one is directly led to step 50. Laà, the vector analyzed becomes the vector (3,2) whose norm is equal to the value of the desired standard p = 5, so that it is recorded in step 41, with the value of the variable I which is equal to 4 Then, will be successively analyzed the vectors / 3.1., / 3.0] and [3, -1 for which the norm is lower than the desired norm p = 5, so that the function S with d = 2 is started (the output is immediate) Then comes the vector (3, - 2] whose norm is equal to the desired norm p = 5. This vector is then recorded in step 41 with the value of the variable I = 4. The vector [3, -3, is then analyzed, but its i: component being negative and its norm being higher than the norm desired, one leaves the function S to come to analyze the vectors whose component of order zero is 2 Thus, will be analyzed the vectors f2, i2, [2,1}, {2,0., (2-1., {2, -2J el (2, -3, The latter is the only one registered in this list and, with the value I = 5,

  The process continues as just described The vectors / I, 4}, 'f, -5 /.

  -1.-4 / t and / -2, -37 are then recorded with respectively the values of the variable of order I equal to 6, 7, 8 and 9

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  Then, step 200 is left. The following vectors have been stored in the memory, and in this order O, 5, 0f Io, 4 1. / 44 /

3 [3.2;

4/3, -2 /

: 'A -3,

6/1, -4 /

7 o. -5

8 -4

9 [-2, -3

  As before, it will be noted, on the one hand, that the memorized vectors are sign leading vectors, that is to say that their components are ordered and that, on the other hand, they themselves are ordered. They thus form a partial dictionary of signed leading vectors which can be used, either in a coding process, or in

a decoding method.

  The modes of implementation of the present invention make it possible to find the index of a signed or absolute leader vector without having recourse to a permanent dictionary of leading vectors. On the other hand, partial dictionaries of leading vectors are used which require less memory capacity. Thus, the fact of scanning only the network space limited to the vectors of the same standard makes it possible to dispense with the use of high capacity memories. For example, in the case of a Da network, the size of the dictionary used is divided by 9 compared to that of a comprehensive dictionary.

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Claims (17)

  1) A method of encoding a vector, said quantized vector, obtained by vector quantization on a network of a signal, said method consisting in determining a vector, said leader vector, which comprises the same components as said quantized but ordered vector, determining a characteristic of said quantized vector which discriminates it from other vectors belonging to the set of vectors which have the same components as said leader vector, and forming a code from, on the one hand, a representative index of said vector vector leader, and, secondly, said characteristic of said quantized vector, characterized in that said representative index of said leader vector is determined from a dictionary giving for each leader vector having the same standard as said quantized vector its index, said vectors of said dictionary being determined by calculation and stored temporarily in   a memory at the time of forming said code.   2) A method of coding a vector according to claim 1, characterized in that said leader vector comprises the same components as said quantized vector but arranged in descending order in the ascending order of the components, by example from left to right.   3) A method of encoding a vector according to claim 1 or 2, characterized in that it consists in scanning the space corresponding to the hypercadran positive hypersphere radius equal to the desired standard and to memorize, in an order   predetermined, the vectors of this space which are absolute leading vectors.   4) A method of coding a vector according to claim 1 or 2, characterized in that it consists of scanning the space corresponding to the hyperspheres of radius equal to the desired standard and to memorize, in a predetermined order, the vectors of this space which are leading vectors.   5) Method of encoding a vector according to one of claims 3 or 4,   characterized in that it consists in considering, at each step of a scanning process consisting of successive steps, a vector and to record it in the dictionary only if it presents the desired standard, and in that said scanning process consists: at a first step, to consider the vector 1 = {a, 0 ....., 0] whose all components are zero except for the first component, whose norm | 1 | i is less than or equal to the desired norm p and which is such that the norm of the vector /'(a.- 1, 21 2773659   0, ..., O) whose first component is equal to the value of the first component increased by one unit is greater than the desired standard p. in a second step, consider the vector l = {a-1, .... a-1} whose all components are equal to the first component of the previously considered vector decremented by one unit, to decrement, in successive steps , from one unit each time, the last component of the vector considered up to obtain the value zero, while keeping the other components at their respective values, then for all the components of the vectors thus obtained, to decrement by one unit the component just left of the component that has just been canceled in the previous step, then equal all the components to the right of said component decremented to the value of said component, to repeat the successive steps of decrementing the last component. 6) encoding method according to claim 5, characterized in that the vector scanning process is interrupted when the vector is the null vector. 7) encoding method according to claim 5, characterized in that the vector scanning process is interrupted when the vector is the vector whose first component is negative, the standard is greater than the desired standard.  8) encoding method according to claim 2, characterized in that said vectors of said dictionary are determined and stored by first considering the vector of which only the first component is not zero, the value of said first component being determined so on the one hand, that the norm of said vector is lower than the desired norm and, on the other hand, that the norm of the vector of which only the first component is not zero and is equal to said value increased by one unit is greater than said desired standard, then throwing a function S for a position variable equal to zero, for a given vector equal to said vector thus considered and for the desired standard, said function S, for the position variable equal to a value any d and a given vector, being provided for 222773659   a) determining a vector, said analyzed vector, which, if the position variable is zero, is equal to said given vector and which, in the opposite case, is equal to said given vector with the di "m component equal to the (d -1) 'component of said given vector, b) storing said analyzed vector if its norm is equal to the desired norm, or, if the norm of said vector is lower than the desired norm, launch the same function S for a value of the variable position incremented by one unit and for a given vector equal to said analyzed vector, c) determining a new vector analyzed by decrementing by one unit the value of the component di'c and d) start again at step b).   9) coding method according to claim 8, characterized in that in step d), it consists in starting again at step b) as the di 'component is not less than a value for which the standard of said analyzed vector is greater than the desired standard, otherwise to leave the function S. 10) Coding method according to claim 8, characterized in that in step d), it consists in starting again at step b) both that the di "component is not zero, if not leave the function S. fi l) Method of decoding a code to recover a quantized vector representative of a signal that has been quantified on a network, said code normally consisting of an index representative of a vector, said leader vector, whose components are the components of the quantized vector to be recovered but not necessarily in the same order, and a characteristic of said quantized vector to be recovered which discriminates against other app vectors comprising the set of vectors that have the same components as said leader vector, said method consisting in determining, from said index, the corresponding leader vector, then, from said characteristic and said leader vector, said quantified vector to be recovered , characterized in that said leader vector corresponding to the index contained in said code is determined from a dictionary giving for each leader vector having the same standard as said quantized vector its index, said vectors of said dictionary being determined by calculation and stored temporarily in a memory   at the time of searching for said leader vector.   12) decoding method according to claim 11, characterized in that it consists in scanning the space corresponding to the hypercadran positive of the hypersphere of 23 2773659   radius equal to the desired standard and to memorize, in a predetermined order, the vectors   of this space which are absolute leading vectors.   13) decoding method according to claim 11, characterized in that it consists in scanning the space corresponding to the hypersphere of radius equal to the desired standard and to memorize, in a predetermined order, the vectors of this space which are leading vectors.   14) Decoding method according to one of claims 12 or 13, characterized in   what it consists in considering, at each stage of a scanning process constituted of successive steps, a vector and to record it in the dictionary only if it presents the desired standard, and in that said process of scan consists: in a first step, to consider the vector 1 (a 0, 0 ..., O0 whose all components are zero except for the first component, whose norm I [J1 is less than or equal to desired standard p and which is such that the norm of the vector the (a - I, O, ..., O) whose first component is equal to the value of the first component has increased by one unit is greater than the desired standard p at a second step, consider the vector l = c (aI, ..., aJ] whose all components are equal to the first component of the previously considered vector decremented by one unit, to decrement, in stages successive, one unit each time, the last component of the vector c is considered to obtain the value zero, while maintaining the other components with their respective values, then for all the components of the vectors thus obtained, to decrement by one unit the component just on the left of the component which has just been canceled in the preceding step, then equal all components to the right of said decremented component to the value of said component, to repeat the successive steps of decrementing the last component. Decoding method according to claim 14, characterized in that the vector scanning process is interrupted when the vector in question is the null vector.   16) decoding method according to claim 14, characterized in that the vector scanning process is interrupted when the vector is the vector whose, the first component being negative, the norm is greater than the desired standard. 24 2773659   17) decoding method according to claim 11, characterized in that said vectors of said dictionary are determined and stored by first considering the vector of which only the first component is not zero, the value of said first component being determined so on the one hand, that the norm of said vector is lower than the desired norm and, on the other hand, that the norm of the vector of which only the first component is not zero and is equal to said value increased by one unit is greater than said desired standard, then by launching a function S for a position variable equal to zero, for a given vector equal to said vector thus considered and for the desired standard, said function S, for the position variable equal to a value any d and a given vector, being provided for a) determining a vector, said analyzed vector, which, if the position variable is zero, is equal to said given vector and, which, in the opposite case, is equal to said given vector with the dis component equal to the (d1) i "component of said given vector, b) storing said analyzed vector if its norm is equal to the desired standard, or, if the norm of said vector is less than the desired standard, launching the same function S for a value of the position variable incremented by one unit and for a given vector equal to said analyzed vector, c) determining a new vector analyzed by decrementing by one unit the value of the said component and d) start again at step b).   18) Decoding method according to claim 17, characterized in that in step d), it consists in starting again at step b) as long as the component is not less than a value for which the the norm of said analyzed vector is greater than the desired standard, otherwise it leaves the function S. 19) A decoding method according to claim 17, characterized in that in step d), it consists in starting again in step b) as long as the dis component is not zero, if not leave the function S. r20) 1Procedure for the elaboration of a partial dictionary of vectors usable for the implementation of a method of encoding signals which have been quantified on a network   according to one of claims I to 10 or for the implementation of a method of   vector decoding to recover quantized signals on a network according to   one of claims 11 to 19, said partial vectors having as standard a standard   desired, for example, the standard of a given vector and whose components are 2773659   arranged in a decreasing manner from left to right, said vectors then being called leading vectors, characterized in that it consists in considering, at each step of a scanning process consisting of successive steps, a vector and not register it in the dictionary only if it presents the desired standard, and in that said scanning process consists: at a first step, to consider the vector! = (a, 0, ..., O0 whose all components are zero except for the first component, whose norm IIl is lower than or equal to the desired norm p and which is such that the norm of the vector l (a * 1, 0, ..., O) whose first component is equal to the value of the first component increased by one unit is greater than the desired standard, p to a second stage, to consider the vector 1 = {(a-1 ,.   , aI} whose all components are equal to the first component of the vector previously considered decremented by one unit, to decrement, in successive steps, one unit each time, the last component of the vector considered until the value zero, while keeping the other components at their respective values, then for all the components of the vectors thus obtained, to decrement by one unit the component just left of the component which has just been canceled in the previous step, then equalize all the components to the right of said decremented component to the value of said component, to repeat the successive steps of decrementing the last component.  21) A method of developing a dictionary according to claim 20, characterized in that the vector scanning process is interrupted when the vector .. CLMF: considered is the null vector.   22) A method of producing a dictionary according to claim 20, characterized in that the vector scanning process is interrupted when the vector considered is the vector whose, the first component being negative, the norm is above the desired standard.   23) A method of developing a dictionary according to claim 20, characterized in that said vectors of said dictionary are determined and stored by first considering the vector of which only the first component is not zero, the value of said first component being determined on the one hand, that the standard of said vector is lower than the desired standard and, on the other hand, that the standard of the 26 2773659   vector of which only the first component is not zero and is equal to said value increased by one unit is greater than said desired standard, then launching a function S for a position variable equal to zero, for a given vector equal to said vector thus considered and for the desired standard, said function S, for the position variable equal to any value d and a given vector, being provided for a) determining a vector, said analyzed vector, which, if the position variable is zero, is equal to said given vector and, in the opposite case, is equal to said given vector with the same component equal to the (d- I) 'component of said given vector, b) storing said analyzed vector if its norm is equal to the desired standard, or, if the norm of said vector is lower than the desired standard, launching the same function S for a value of the position variable incremented by one unit and for a given vector equal to t vector analyzed, c) determine a new vector analyzed by decrementing by one unit the value of the diem component and d) start again at step b).   24) A method of developing a dictionary according to claim 23, characterized in that in step d), it consists in starting again at step b) as the di '' component is not less than a value for which the norm of said analyzed vector is greater than the desired norm, otherwise it is outside the function S.) A method for producing a dictionary according to claim 23, characterized in that in step d) it is to start again in step b) as the di '"component is not zero, if not out of the function S.