FR2764751A1 - QAM coding/decoding apparatus - Google Patents

Abstract

The apparatus includes a first labeller for associating, with the information to be coded, K initial first degree polynomials, and a coder, performing a polynomial calculation. In order to form K coded sequences of P coded polynomials (where P \- K and the first sequence is equal to one of the K initial polynomials, whilst the other sequences are equal to the product of the preceding polynomial and a predetermined polynomial), a sequence of P resultant polynomials are formed equal to the sums of the coded polynomials of the same rank as the K coded sequences. A second one to one labeller labels the points of a QAM signal constellation with the Q<2> (where Q is a power of a prime number) resultant polynomials for two adjacent points of the constellation. The polynomials labelling them have one identical coefficient and the other coefficient differing only by modulo Q. A QAM modulator for is also included.

Description

o10 The present invention relates to a device and a method

decoding of coded information.

It applies in particular to the reception of information transmitted by modulation of amplitudes in quadrature, on a channel of

any transmission using this modulation.

Quadrature signal amplitude modulation is well known in the communications field. According to this modulation technique, an item of information to be transmitted is associated with a signal of constant frequency but the amplitude and phase of which are representative of said item of information. However, on reception, these signals can sometimes be difficult to identify when during transmission the signal has been

distorted, or noisy.

The invention intends to remedy these drawbacks by proposing a method and a device for decoding coded information exhibiting a

increased noise resistance.

To this end, according to a first aspect, the present invention is aimed at a device for decoding so-called "initial" coded information, characterized in that it comprises: a demodulator adapted to demodulate P signals modulated at the points of a constellation with quadrature amplitude modulation, in a so-called sequence

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"demodulated" of P so-called "demodulated" points and representative of a Kuple of "initial" information, - a processing means suitable for: choosing K-uples of demodulated points capable of allowing the calculation of the K-tuples of initial information to which they correspond,

determine, for each of the K-uples of selected demodulated points, K-

uples, called "neighbors", of points in said constellation which are close to the K-tuple of demodulated points chosen, calculate, for each K-tuple of neighboring points, the initial information K-tuple to which it corresponds and assign this K- uple of initial information of an affinity depending on the distance between said K-uple of neighboring points and the chosen K-uple of demodulated points to which it is attached, add up, for each calculated initial information K-up, or for each initial information of the calculated initial information K-tuples, the affinities assigned to it, and estimate, respectively, the initial information K-tuples actually coded, or each initial information item of the information K-tuples initials, actually coded

as being the one with the highest sum of affinities.

According to a second aspect, the present invention is aimed at a device for decoding coded information, characterized in that it comprises: a demodulator adapted to demodulate P successive signals in quadrature amplitude modulation, the two components of which are representative of the coefficients of K first degree polynomials called “initial polynomials”, in a so-called “demodulated” sequence of P first degree polynomials, called “demodulated”, the coefficients of the same degree of said demodulated polynomials being successively representative of one of the components of the corresponding demodulated signal, and

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- a processing means suitable for: choosing K-uples of demodulated polynomials capable of allowing the calculation of the K-uples of initial polynomials to which they correspond, determining, for each of the K-uples of demodulated polynomials chosen, K-uples of so-called "neighboring" polynomials representative of K-tuple of points of the constellation close to the K-tuple of pairs of components represented by the K-tuple of demodulated polynomials chosen, calculate, for each K-tuple of neighboring polynomials, the K-tuple of initial polynomials to which it corresponds and assign this K-tuple of initial polynomials of an affinity depending on the distance between said K-tuple of points represented by the K-tuple of neighboring polynomials and the K-tuple of pairs of components represented by the K-tuple of demodulated polynomials chosen to which it is attached, add, for each K-tuple of initial polynomials calculated or for each initial polynomial of the K-tuple of initial polynomials calculated, of the affinities assigned to it, and estimate, respectively, 2 o the K-tuple of initial polynomials actually encoded or each initial polynomial of the K-tuple of initial polynomials, effectively encoded

as being the one with the highest sum of affinities.

Thanks to these arrangements, each of the points or polynomials of the demodulated sequence is associated with neighboring points or polynomials which have a high probability of corresponding to the initial information, according to known laws on noise affecting signals modulated by modulation of amplitudes in quadrature: for a Gaussian channel, the risk of confusion is linked to the distance between neighboring points of the constellation and the proximity between two of the pairs of demodulated quadrature components

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corresponds to a high probability of confusion between the modulated signals of which

they are from.

Thus, the invention makes it possible to decode information coded by: a coding means which performs a polynomial calculation: to form K so-called “coded” sequences with a number P greater than or equal to K of so-called “coded” polynomials, the first encoded polynomial of each of these K sequences being equal to one of the K initial polynomials and each of the other encoded polynomials of said sequence being equal to the o10 product of the polynomial preceding it in the sequence by a predetermined polynomial, and to form a sequence said "resultant" of P so-called "resultant" polynomials respectively equal to the modulo Q sums of the coded polynomials of the same rank of the K coded sequences, a second one-to-one labeling means adapted to label the Q2 pairs of numbers representative of the coordinates of the Q2 points d 'a constellation of signals in quadrature amplitude modulation at Q2 points, by the resulting Q2 polynomials, in such a way that, if two points of the constellation have an identical coordinate and the other e coordinate as close as possible, then the polynomials labeling them will have an identical coefficient and the other coefficient differing only by 1 modulo Q, and - a modulator adapted to convert each of the P resulting polynomials into a modulated signal of amplitudes in quadrature whose pair of amplitudes is

labeled by said polynomial.

The device according to the invention is, by comparison with the devices using the so-called "maximum likelihood" method which consists in carrying out a correlation between all the code words and what has been received, of simpler construction and more efficient operation. fast while

with comparable performance.

3 0 According to particular characteristics, the processing means is adapted to affect each K-tuple of initial polynomials with an affinity

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decreasing as a function of the distance between the K-tuple of points represented by the K-tuple of neighboring polynomials and the K-tuple of pairs of components

represented by the K-tuple of demodulated polynomials chosen to which it is attached.

Thanks to these arrangements, the summed affinities are each representative of the probability that the K-tuple of neighboring polynomials considered is the K-tuple of initial polynomials which is at the origin of the K-tuple of demodulated polynomials. According to a third aspect, the present invention relates to a method of decoding so-called "initial" coded information, characterized in that it comprises: a demodulation operation, during which P signals modulated at the points d are demodulated. 'a constellation with quadrature amplitude modulation, in a so-called "demodulated" sequence of P points called "demodulated" and representative of a K-tuple of "initial" information, - a processing phase comprising one: an operation of choice, during which one chooses K-uples of demodulated points likely to allow the calculation of the K-uples of initial information to which they correspond, a determination operation during which one determines, for each of the K-uples of selected demodulated points, K-uples, called “neighbors”, of points in said constellation which are close to the K-uples of demodulated points chosen,

a calculation operation during which we calculate, for each K-

uple of neighboring points, the initial information K-uple to which it corresponds and we assign this initial information K-uple with an affinity depending on the distance between said K-uple of neighboring points and the K-uple of points demodulated chosen to which it is attached, a summation operation during which we sum, for each K-tuple of initial information calculated, or for each initial item of information, K-tuples of initial information calculated,

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the affinities which are assigned to it, and an estimation operation during which one estimates, respectively, the K-tuple of initial information effectively coded, or each initial information of the K-tuple of initial information, effectively coded

as being the one with the highest sum of affinities.

According to a fourth aspect, the present invention relates to a method of decoding coded information, characterized in that it comprises: a demodulation operation during which P successive signals are demodulated in quadrature amplitude modulation, of which the two components are representative of the coefficients of K first degree polynomials called "initial polynomials", in a so-called "demodulated" sequence of P first degree polynomials, called "demodulated", the coefficients of the same degree of said demodulated polynomials being successively representative of l 'one of the components of the corresponding demodulated signal, and - a processing phase comprising: a selection operation during which K-uples of demodulated polynomials are chosen capable of allowing the calculation of the K-tuple of initial polynomials to which they correspond, a determination operation during which one determines, for each of the K-uples of demodulated polynomials chosen, K-uples of polynomials s called "neighbors" representative of K-tuple of points of the constellation close to the K-tuple of pairs of components represented by the K-tuple of demodulated polynomials chosen,

a calculation operation, during which we calculate, for each K-

uple of neighboring polynomials, the K-uple of initial polynomials to which it corresponds and we assign this K-uple of initial polynomials of an affinity

depending on the distance between the K-tuple of points represented by said K-

uple of neighboring polynomials and the K-uple of pairs of components

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represented by the K-tuple of demodulated polynomials chosen to which it is attached, a summation operation, during which the sum is made, for each K-tuple of initial polynomials calculated or for each initial polynomial of the K-tuple of initial polynomials calculated, the affinities which are assigned to it, and an estimation operation, during which one estimates, respectively, the K-tuple of initial polynomials actually coded or each initial polynomial of the K-tuple of initial polynomials actually coded

as being the one with the highest sum of affinities.

The invention also relates to a computer, a facsimile machine, an information processing system, an information capture system (such as a camcorder, a digital camera, a scanner, a copier, etc.) and a system for reproducing information (such as a printer, a copier, etc.), characterized in that they comprise a decoding device as briefly described above and a device comprising a microprocessor suitable for implementing implements the process such as

succinctly set out above.

This method and these devices having the same advantages as the devices succinctly described above, they are not

recalled here.

Other advantages, purposes and features will emerge from the

description which follows, made with reference to the accompanying drawings in which:

- Figure 1 shows, on a 64-QAM constellation, the start of a signal representative of information from a 6-tuple, - Figure 2 shows, on a 64-QAM constellation, the start of four sequences whose second symbol is one of the four closest neighbors of a received signal,

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- figure 3 represents a simplified functional diagram of a coding device in the form of signals representative of 6-information uples, - figure 4 represents a simplified electronic diagram of a coding device in the form of signals representative of 6 - multiple information, - Figure 5 shows an operating flowchart of the encoding device illustrated in Figure 4, by direct coding of polynomials, - Figure 6 shows an operating flowchart of the encoding device illustrated in Figure 4, by coding indirect polynomials, - figure 7 represents a simplified functional diagram of a device for decoding signals representative of 6-uples of information, - figure 8 represents a simplified electronic diagram of a device for decoding signals representative of 6 - multiple information, - Figure 9 shows an operating flowchart of the decoding device illustrated in Figure 8, for the reception of information likely to be represented by a single 6-tuple, - figure 10 represents an operating flowchart of the decoding device illustrated in figure 8, for the reception of information likely to be represented by three 6-tuple, and - figures 11 to 13 illustrate a variant of the operating flowcharts presented with reference to FIGS. 9 and 10, according to which the neighboring polynomials and the affinities associated with the initial polynomials which they

represent are determined in a particularly simple manner.

In a 64-QAM constellation, i.e. representative of signals emitted in quadrature amplitude modulation, at Q = 8 different values for the in-phase and in-phase quadrature signals, it can be useful for encoding information, to provide this constellation of operations

addition and / or multiplication, the results being calculated modulo Q = 8.

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Preferably, Q is a power of a prime number, and, more preferably, a power of 2, which makes it possible to use

many well-known mathematical tools.

Each 6-tuple is identified with a so-called "initial" polynomial of degree 1 in B, of type a = ao + a, B, o ao and a, are integers with values between O and Q-1 = 7, limits included , and o B is a symbol used in calculations according to the rule 1 + B + B2 = 0. Each of the 64 polynomials is mapped to one of the 64-QAM signals by labeling shown in

figures 1 and 2.

According to this labeling (hereinafter called second labeling): - the degree factor O in B is represented by the in-phase component, such that: the factor O corresponds to the component -5 _5 the factor 1 corresponds to the component -3 factor 2 corresponds to component -1 factor 3 corresponds to component +1 factor 4 corresponds to component +3 factor 5 corresponds to component +5 factor 6 corresponds to component + 7 factor 7 corresponds to the component -7 - and the factor of degree 1 in B is represented by the component in phase quadrature, in such a way that: the factor O corresponds to the component -5 the factor I corresponds to the component -3 the factor 2 corresponds to component -1 factor 3 corresponds to component +1 factor 4 corresponds to component +3 factor 5 corresponds to component +5 3 o factor 6 corresponds to component +7

the factor 7 corresponds to the component -7.

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In the case K = 1, K being the number of 6-uples of binary data which represent the information to be encoded, this second particular labeling is one of those which make it possible to make the least variable possible

the energies of the sequences of 12 signals whose constitution is exposed below

below. By making the choice of the second labeling above, among the possible sequences of signals, one chooses - on the one hand, to label the Q2 pairs of numbers representative of the components of the Q2 points of a constellation of signals in modulation of quadrature amplitudes at Q2 points, by Q2 polynomials, in such a way that, if two points of the constellation have an identical coordinate and the other coordinate as close as possible, then the polynomials labeling them will have an identical coefficient and the other coefficient differing only by 1 modulo Q, and - on the other hand, to represent the information to be transmitted, a set of sequences, all of which the mean square deviation of the ratio of the energy to the mean energy of all the sequences of said set, is lower than it is on average for the other sets of sequences containing

each the same number of suites as said set.

The set of elements a is a finite ring of polynomials, which ring has 64 elements and which is called Z8 (B). It has an addition operation and a multiplication operation defined below, the integers being reduced modulo Q = 8 and the polynomials in B being reduced modulo

B2 + B + 1.

By choosing one of the elements, g, of Z8 (B) whose first non-zero power which is equal to 1 is the twelfth power (we then say that the period of g is 12), for example g = 1 + 7B, each information a of Z8 (B) is then encoded by the sequence (a, ag, ag2, ..., ag1l), the multiplication used here being done in Z8 (B). Each element of this sequence is associated, by the second labeling, with an element of the 64-QAM constellation (also called 64-QAM, in French, initials of the words "modulation of amplitude in l 2764751 quadrature" with 64 states), as illustrated in figure 1. The emission of the signal associated with the sequence (a, ag, ag2, ..., ag1l), provides an encoding method

of the 6-tuple considered.

By knowing any of the elements of the sequence (u, ug, ug2,

., ug11), also noted (u0, ul, u2, ..., ull), we can find the element..DTD: u which is at the origin.

However, on any channel, noise causes a

uncertainty about the effective value of u.

In this case, to estimate the value of u, it may be useful 1o to observe a certain number N of neighbors closest to the approximate value v; from ui. For example, for i = 1 and N = 4, figure 2 illustrates the neighbors A1, B1, C1 and Dl of v1 = 0.3 + 4.7 B: A, is "labeled" 0 + 5B B1 is "labeled "1 + 5B Cl is" labeled "0 + 4B De is" labeled "1 + 4B By multiplying these third labels by gló, we obtain the points of the constellation which can correspond to the values AI, B1, Cl and Dl: Ao, Bo, Co and Do, that is: Ao labeled 1 + 7 B Bo labeled 6 + 2 B 2 5 C0 labeled 4 + 4 B Do labeled 2 + 7 B. We observe in figure 2 that, although the points AI, B1, C1 and Dl are close in the constellation 64- QAM, the points Ao, Bo, C0 and Do

3 o may not be.

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The simplest version of the decoding process consists in first selecting a subset V (v) of elements of the 64-QAM constellation which are close to vi. Then, for each value of i (between 0 and 11), the label ti, that is to say the polynomial of degree 1 in B which is associated with each of the i elements of the subset V (v.) , is multiplied by g12- to obtain a tag of an element of the 64-QAM constellation which is likely to be at the origin of the sequence (uo, ul, ..., u11). The estimate of u will then be the element of Z8 (B) whose label is most often considered

as likely to be that of u, for all the elements of the sub-

1o sets V (v. ,, i ranging from 0 to 11.

We observe that several possibilities exist to specify the

subsets V (v) of so-called "neighboring" polynomials of a demodulated polynomial.

The first consists in choosing the N elements of the constellation which are closest to vi. A second possibility consists in defining V (vi) as the subset of the elements of the constellation whose distance from v / is less than a predetermined distance. A third possibility consists in combining the first two possibilities: one selects at most N elements of the 64-QAM constellation whose distance to v / is less than a predetermined value. According to one variant, the neighborhood information can be refined by defining an affinity which takes into account the effective distance of vi with each of the elements of the subset V (v) -. Thus, using the Euclidean distance d applied to the 64-QAM constellation, the affinity of v; with u, noted

aff (v /, u), will then be given by the maximum value of the two numbers D2-

d2 (v1, u) and O, D2 being a predetermined positive constant number. Before the reception of the signals v ;, for each element u of the 64-QAM constellation, the function w (u) is initialized to 0. On reception of each vi, each function w (u) is incremented by the value of the affinity of v; with u (increment performed during operation 906, figure 9). The decoding estimate (operation 909, figure 9) will then be the element u whose final function w (u) will be the highest,

after receipt of vI1.

Of course, the result is better when D increases because we then approach the so-called maximum likelihood decoding method.

Encoding for a number K of 6-uples equal to 2 or 3.

Consider that sets of 12, for K = 2 (respectively 18, for K = 3), binary data are to be represented by

sequences of length 12 of elements of Z8 (B).

Let us first consider the case K = 3. The 18 binary data are identified by a triplet a = (a (1), a (2), a (3)), of elements a (i) of Z8 (B) , called 1o "initial" polynomials. The so-called "resultant" sequence of 12 so-called "resultant" polynomials v = (v0, vl, ... v11) is then obtained by the matrix product v = aG, in which G is a 3 x 12 matrix of elements of Z8 (B): 1 g g2 g3 ... g11 G = 1 g2 g4 g6 ... g10 (1) 1 g3 g6 g9 g9 We observe that the matrix G is associated with its second

column (g, g2, g3).

According to a variant, the triplet (a ('), a (2), a (3)) is put in relation not with the matrix product, but with the sequence u of Z8 (B) determined by induction as follows : uo = a (1) ul = a (2) U2: = a (3) Ui + 3 = (6 + 6B) ui + 2 + 6ui + l + 5 u, (2) This resulting sequence corresponds to a product matrix of the 3 0 triplet of initial polynomials (a (1), a (2), a (3)) by an invertible 3 x 3 matrix, which is not explained here to provide so-called "prior" polynomials, then by a multiplication of the result of this matrix product, formed of the "prior" polynomials, by the matrix G. Thus, the use of an invertible matrix of dimensions K x K, matrix equal to the inverse of the matrix formed by K first columns of the matrix G, makes it possible to make the coding systematic, i.e. the K first resulting polynomials are each representative of one and only one

initial polynomial.

FIG. 6 refers to this so-called "indirect" coding, by

comparison with the so-called "direct" coding illustrated in FIG. 5.

The case K = 2 is simpler. 12 binary data are to be encoded there, associated with the sequence of initial polynomials a = (a (), a (2 "), in which a (}) and a (2) are elements of Z8 (B). encoding G comprises the first two lines of the matrix given above in (1): G = 1 g g2 g3 ... g11 (3) 1 g2 g4 g6 ... g910 and makes it possible to provide by the same product matrix as explained above, the

so-called "resulting" polynomials.

o As a variant, the encoding method of (a ('), a (2)) is, by induction, defined by: uo = a () u = a (2) Ui + 2 = (1 + 4B) ui + ., + (3 + 6B) ui (4) The remarks made above concerning the first recurrence associated with K = 3 being valid for this second recurrence,

associated with K = 2.

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Decoding for K = 3 v = (vo, vl, ..., vll) is the received and demodulated sequence, resulting from the P modulated signals corresponding, by means of the second labeling to the sequence of resulting polynomials, or transmitted code, u = (u0, ul, ..., u1) = a G, v being a so-called "demodulated" sequence of P points or polynomials called "demodulated" and representative of the information K-tuple

"initials".

i, j and k are indices defined by 0 = <i <j <k = <11 and G (iJk) is the 3 x 3 matrix containing the columns of the matrix G of indices i, j and k: 9 / gi gk G (i, jk) = g2i g2ij g2k (5) 93i 3j 3k g3i gay g3k We can show that if the determinant of G (ijk) is an invertible element of Z8 (B), then the inverse of G ( iJk) exists and from (ui, uj, Uk) = (a (), a, a (3)) G (i'j'k), it is possible to find a = (a ('), a2), a (3)) by using 2 oa = (ui, uj, Uk) (G (i'Jk)) l (6) It is known that G (i'j'k) is invertible if and only if the residues modulos 3 of i, j and k are all different. For example G (2610) is invertible because said modulos 3 residues are 2, 0 and 1, while G (4'5'7) is

not invertible because said residues are 1, 2 and 1.

In total there are 64 invertible G (iq'k) matrices, associated with

triples (i, j, k) with i in {0,3,6,9}, j in {1,4,7,10} and k in {2, 5,8,11}.

By now defining three subsets of neighbors V (v,), V (vj) and V (vk) in ZB (B) respectively neighbors of the three signals (vi, vyj, Vk) relating to a (1), a ( 2) eta (3), for each (ui, Uj, Uk) possible with invertible G (ik), with ui in V (vj), uj in V (v) and Uk in V (vk), we compute the estimate â of information a, such that ô = (ui uj, u, U) (G (ijk)) l (7) and we assign it an affinity which depends on the distance between the K-tuple of points represented by the K-tuple of neighboring polynomials (ui, uj, u0 and the K-tuple of component pairs represented by the chosen K-tuple of demodulated polynomials (vi,

vj, Vk) to which it is attached.

The decoded estimate is then the triplet a which is has the sum of the affinities, when equation (7) provides said triplet, for all the

i, j, k, ui, uj and uk values.

The decoding method can be refined as explained above for the case K = 1. For example for K = 3, at the start, the weight w (a) is initialized to O for each a of Z8 (B). Define the affinity of a with (vy, Vj, v) as the maximum of O and of D2 - d2 (vi, u) - d2 (vj, u) - d2 (vk, ud), D2 being a

positive number.

For each value of (ij, k) corresponding to an invertible matrix, the value of w (a) is incremented by the affinity for each a and the decoding estimate is the triplet a which has the highest value of w ( at).

Decoding for K = 2.

For K = 2, G is a 2 x 12 matrix containing 48 sub-

Invertible matrices G (i, j) corresponding to all the pairs (ij) such that 9- 'has an inverse by the operation of multiplication, condition equivalent to different modulos 3 residues. The decoding process is then similar to

the one exposed above for K = 3.

Variants According to a variant, we count each element a (i) of each triplet, among the 64 possible elements, and not each triplet (a ('), a (2),

17 2764751 a (3)) which reduces the memory to three (for K = 3) times 64 elements, to

compare

at 643 = 262,144 triplets.

According to another variant, the signal / noise ratio is estimated and the number of considered neighbors is reduced when the signal / noise ratio is high, in order to reduce the complexity or the slowness of the method. According to another variant, we take an affinity equal to the distance for a given subset, then to the distance from the most

near out of subset for all elements outside of subset.

Description of a particular embodiment

The particular embodiment described and shown relates to the coding of binary information capable of being represented by a number K of 6-uples, and the transmission of amplitude-modulated signals.

in quadrature, using 64 pairs of different amplitudes.

In Figure 1 is shown, on a 64-QAM constellation, the

start of a signal representative of information from a single 6-tuple (K = 1).

We observe that a 6-tuple having been associated with a so-called "initial" polynomial a = 2 + 7B, the first four so-called "resultant" polynomials of the so-called "resultant" sequence u which correspond to this initial polynomial are: Uo = 2 + 7B, ul = uo (1 + 7B) = 2 + 7B + 14B + 49B2 = 2-49-49B + 21B = -47-28B = 1 + 4B, u2 = 5 + 7 B = u1 (1+ 7B), and

U3 = 4 + B = u2 (1 + 7B).

In the same way for 12> i> 3,

ui = ui1 (1 + 7B) = u_ g.

equation in which g = 1 + 7B is a particular polynomial whose period is 12, the factors of degree 0 and I in B being calculated modulo Q = 8, and B2

being replaced by -7-7B.

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The transmitted signal which corresponds to the 6-tuple of binary information then comprises the succession of 12 signals whose in-phase and in-phase quadrature amplitudes correspond to the "resulting" polynomials.

u ,, with the connection, or second labeling, of the constellation 64-

QAM with these polynomials which is illustrated in figure 1: - the factor of degree O in B is represented by the in-phase component, such that: the factor O corresponds to the component -5 the factor I corresponds to the component -3 factor 2 corresponds to component -1 factor 3 corresponds to component +1 factor 4 corresponds to component +3 factor 5 corresponds to component +5 factor 6 corresponds to component +7 factor 7 corresponds to the component -7 - and the factor of degree 1 in B is represented by the component in phase quadrature, in such a way that: the factor O corresponds to the component -5 the factor 1 corresponds to the component -3 the factor 2 corresponds at component -1 factor 3 corresponds to component +1 factor 4 corresponds to component +3 factor 5 corresponds to component +5 factor 6 corresponds to component +7

the factor 7 corresponds to the component -7.

When K is greater than or equal to two, i.e. when a plurality of 6-uples must be represented by the sequence of twelve resulting polynomials, the i-th polynomial resulting from this sequence comes from the sum of the products matrixes of the first 6-tuple with g ', of the second 6-tuple with g2i .., and of the j-th 6-tuple with gi. Each polynomial resulting from the resulting sequence thus formed is related to a pair of amplitude according to

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the second labeling discussed above before providing a signal of

quadrature amplitude modulation.

In FIG. 3 is represented, in the form of a simplified functional diagram, a device for encoding information in the form of signals representative of 6-uples of information. A data producer 301 supplies sequences of a number K of 6-uples of binary data, these can, for example, come from a storage means, a transmission means or a

means of data processing.

A first labeling means 302 associates, in a one-to-one fashion, with each of the K 6-uples supplied by the data producer 301, a degree 1 polynomial at B called the initial polynomial. For example, for K = 3, 18 binary data represented by three 6-uples are represented by three

initial polynomials a (1), a (2), a (3) of elements of Z8 (B).

An encoding means 303 performs a matching of the initial polynomial provided by the first labeling means

302 with a sequence of 12 resulting polynomials.

In the case K = 3, the three 6-uples, are identified by the triplet of initial polynomials a = (a (1, a (2, a (3)) and this triplet is encoded in a resulting sequence, of 12 polynomials results v = (vo, vy, ... vy), obtained by performing the matrix product yv = aG, in which G is the 3 x 12 matrix of elements of Z8 (B): 1 g g2 g3 ... g11l G = 1 g2 g4 g6 g10 (1) 1 g3 g6 g9 ... g9 A second labeling means 308 then performs a second labeling, i.e. a matching of the sequence of resulting polynomials provided by the means for encoding polynomials 303, with the sequence of 12 pairs of signal modulation amplitudes in

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phase and in phase quadrature, according to the exposed correspondence rule

above next to Figure 1.

The data producer provides 12 x K less often than 6-

greater than the encoding means provides pairs of amplitudes. Also, a clock 305, which controls the operation of the encoding means 303 and of the second labeling means 308, is associated with a counter 304 which divides by 12 x K the number of pulses of the clock 305 and which provides the synchronization signals from the data producer 301 and the first

means of labeling 302.

A modulator 306 of known type performs the quadrature amplitude modulation corresponding to the pairs of amplitude values which are transmitted to it by the second labeling means 308. An antenna

307 broadcasts the signals exiting modulator 306.

Figure 4 shows a simplified electronic diagram of a

device for encoding information in the form of signals representative of 6-

more information. This coding device is illustrated in the form of a block diagram and represented under general reference 401. It comprises, interconnected by an address and data bus 402: - a central processing unit 406; - a random access memory 404; - a read only memory 405; an input port 403 used to receive the information that the encoding device must transmit; an output port 408 allowing the device to transmit the sequence of pairs of amplitudes put in correspondence with the sequence of resulting polynomials; and, independently of the bus 402: the modulator 306 modulating in quadrature amplitude modulation an electrical signal by assigning to two signals in phase quadrature the pairs of amplitudes coming to it from the output port 408;

- the transmitting antenna 307 which emits radio waves.

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Random access memory 404 notably comprises registers in which variables and intermediate data necessary for the operation of the coding device are stored: i which represents the index of a column of the Van Der Monde matrix; -j which represents the index of a row of the Van Der Monde matrix; - totranseq which contains the sequence of resulting polynomials and pairs of amplitudes representing them according to the correspondence rule set out in FIG. 1; and - a (), a (2), ..., a (K which represent the initial polynomials which correspond to the 6-uples of information to be encoded via the

first labeling.

The read only memory 405 is suitable for keeping the operating program of the central processing unit 406 as well as the polynomial g which defines the Van Der Monde matrix implemented and the TABCOR correspondence table relating the resulting polynomials and the pairs of amplitudes of the 64-QAM constellation. The central processing unit 406 is suitable for implementing the flowcharts described in FIGS. 5 and 6. FIG. 5 represents an operating flowchart of the coding device illustrated in FIG. 4, for the direct coding of the polynomials

called "initial".

Following the start 500, a test 501 determines whether there is information to be transmitted or not. When the result of the 501 test is negative, the

test 501 is repeated.

When the result of the test 501 is positive, the operation 502 carries out a first labeling of each 6-tuple of information to be transmitted by association of this 6-tuple with an initial polynomial a (i) of Z8 (B). Operation 3 o 503 then consists in initializing the value of variable i to 0. Operation 504

then consists in increasing the value of the variable i by 1.

22 2764751

Operation 505 then consists in multiplying the row matrix made up of the initial polynomials a (1), a (2), ..., a (K) by the i-th column of the Van Der Monde matrix G described above. above, the product of the polynomial au) by the polynomial g9 'being modulo Q = 8 and modulo the second-degree polynomial described above and providing a so-called "coded" polynomial of a so-called "coded" sequence of P = 12 polynomials , the sum of the coded polynomials of rank i giving a so-called "resulting" polynomial of rank i in a so-called "resultant" sequence of polynomials, each coefficient being calculated modulo Q = 8,

and storing the resulting polynomial in the totranseq register.

It is observed that, in doing so, the coding means performs a polynomial calculation: to form K so-called "coded" sequences with a number P greater than or equal to K of so-called "coded" polynomials, the first coded polynomial of each of these K sequences being equal to one of the K initial polynomials and each of the other encoded polynomials of said sequence being equal to the product of the polynomial preceding it in the sequence by a predetermined polynomial, the coefficients of the encoded polynomials being calculated modulo Q and the encoded polynomial being calculated modulo an irreducible polynomial of degree two, and to form a so-called "resultant" sequence of P so-called "resultant" polynomials respectively equal to the modulo Q sums of the coded polynomials of the same rank of the K coded sequences, The test 506 then determines whether the variable i reached the value 12, or not. When the result of test 506 is negative, operation 504 is repeated. When the result of the test 506 is positive, the operation 507 consists in transmitting to the modulator the sequence of pairs of associated amplitudes, according to the correspondence rule exposed with reference to FIG. 1 and called 3o second labeling, to the resulting polynomials, in order to as the modulator

23 2764751

performs quadrature amplitude modulation of an electrical signal with

said pairs of amplitudes.

FIG. 6 represents an operating flowchart of the coding device illustrated in FIG. 4, by indirect coding of polynomials, in the case where K = 3. Test 601 of the flowchart of FIG. 6 corresponds to test 501 of the flowchart of FIG. 5. The operations 600, 602, 604, 605, and 608 of the flowchart of FIG. 6 correspond respectively to the

operations 500, 502, 503, 504 and 507 of the flowchart of Figure 5.

Operation 603 consists in determining the first three resulting polynomials u0, u1 and u2, as being respectively equal to the

polynomials a (>), a (2> and a (3).

Operation 606 consists in determining the following resulting polynomials according to the formula Ui + 3 = (6 + 6B) ui + 2 + 6ui + 1 + 5 ui (2) It is observed here that the encoding means performs here the polynomial calculation in implementing a recurrence equivalent to: - during operation 602, first labeling: associate with the information to be coded K so-called "preliminary" polynomials then, multiply a matrix formed of these K preliminary polynomials by an invertible matrix of dimensions K x K to produce the K initial polynomials, and - during operation 606, perform the matrix polynomial calculation exposed in

look at operation 505.

Test 607 determines whether the variable i has reached the value 9 or not. It is thus observed that the coding can include any labeling

direct (figure 5) or indirect (figure 6) of the information to be transmitted.

24 2764751

We will now describe the decoding devices and methods associated with the encoding devices and methods exposed opposite

Figures 1 and 3 to 6.

In FIG. 2 is shown the second value of a quadrature amplitude modulated signal received by a decoding device, in the case where K is equal to 1, that is to say when only a 6-uple has been coded. This second signal value corresponds to the so-called "demodulated" polynomial 0.4 + 4.6 B. Four so-called "neighboring" polynomials of the demodulated polynomial

l0 are defined, A1 = 0 + 5B, B1 = 1 + 5B, C1 = 0 + 4B andD1 = 1 + 4B.

By multiplying these four polynomials by gl ', we find four values of the initial polynomials which, in the present case, are the most

likely to form an estimate of the value sought.

Figure 7 shows a simplified block diagram of a

device for decoding signals representative of 6-uples of information.

A receiving antenna 701 receives the radio signals and transmits them to a demodulator 702. The demodulator 702 supplies so-called "demodulated" polynomials representative of the pairs of amplitudes of the signals.

radio signals received by the antenna 701. A means of definition 703 of sub-

2o sets associates with each demodulated polynomial a set V / (u) of

so-called neighboring polynomials.

A matrix product determination means 704 performs, for all the square sub-matrices of the Van Der Monde matrix which are invertible, square sub-matrices made up of K columns referenced i, j, 25 ..., a matrix product of each row matrix made up of K neighboring polynomials of the demodulated polynomials respectively referenced i, j, ..., by

the inverse of the Van Der Monde submatrix considered.

A storage means 705 stores each of the K initial polynomials resulting from these matrix products by assigning it an affinity which is a function of the distance between the pairs of components.

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represented by the K-tuple of demodulated polynomials and by the K-tuple of

neighboring polynomials which were used to determine said initial polynomials.

An estimation means 706 estimates the polynomials representative of the information encoded as being equal to a matrix comprising the initial K polynomials of which the sum of the affinities is the highest, once all of said invertible square sub-matrices have been used. The initial polynomials estimated by the estimation means 706 are transmitted to a data recipient, so that these polynomials are processed,

transmitted or stored, for example.

Figure 8 shows a simplified electronic diagram of a

device for decoding signals representative of 6-uples of information.

This decoding device is illustrated in the form of a block diagram and represented under general reference 801. It comprises, interconnected by an address and data bus 802: - a central processing unit 806; - a RAM 804; - a read only memory 805; - an input port 803 used to receive the information that the decoding device must process; - an output port 807 allowing the device to transmit the

sequence of polynomials estimated at data recipient 707.

and, independently of the bus 802: - the demodulator 702 receiving the signals coming from it from the receiving antenna 701 and transmitting pairs of amplitudes to the port

input 803.

Random access memory 804 notably comprises registers in which variables and intermediate data necessary for the operation of the coding device are stored: i, j and k which represent the indices of the columns of the Van Der Monde matrix; - v which represents the estimated polynomials;

26 2764751

- u0, ul, ... ull, which contain the demodulated polynomials resulting from the demodulation of the sequence of resulting polynomials; and - V (v) which defines, for each of the demodulated polynomials,

neighboring polynomials.

The 805 read only memory is suitable for keeping the program

allowing the operation of the central unit 806, the inverse of the sub-

Invertible matrices which include K = 3 columns of the Van Der Monde matrix, as well as the table TAB (i, j, k) of the triples (i, jk) of the set {0,3,6,9} x

{1,4,7,10} x {2,5,8,11}.

1 0 Figure 9 shows an operating flowchart of the decoding device illustrated in Figure 8, for the reception of information likely to be represented by a single 6-uple and therefore also a single

initial polynomial.

After start 901, in which the sums of affinities associated with each polynomial are reset to 0, test 902 determines whether a quadrature amplitude modulated signal is received. When the result

of test 902 is negative, test 902 is repeated.

When the result of test 902 is positive, operation 903 consists in demodulating the signal received into a so-called “demodulated” sequence v of 12 so-called “demodulated” polynomials associated with 12 successive pairs of amplitudes that said signal presents, according to the rule correspondence

shown next to Figure 1.

Operation 904 consists in defining neighboring polynomials of each demodulated polynomial, for example by considering as neighboring polynomials only the four closest polynomials in the 64-QAM constellation. Operation 904 also consists in associating an affinity with each of the neighbors as a decreasing function of the distance between the demodulated polynomial and said neighbor. We observe the polynomials which are not considered

as neighbors thus have zero affinity.

Operation 905 consists, for each polynomial ti neighboring the i-

ith demodulated polynomial, to determine a polynomial u0 = tg (12-i).

Operation 906 consists in memorizing the polynomial uo by attributing to it an increment of the value of the affinity of ti with vi. Operation 907 consists of increasing the value of i by I. Test 908 determines whether the variable i

has reached the value 12, or not.

* When the result of test 908 is negative, operation 904 is repeated. When the result of test 908 is positive, operation 909 performs the estimation of u, the polynomial representative of the 6-tuple of information transmitted by the encoding device, by taking the value of the polynomial uo which has the

highest sum of affinities.

o10 FIG. 10 represents an operating flowchart of the decoding device illustrated in FIG. 8, for the reception of information

likely to be represented by three 6-uples.

The operations 1001, 1002 and 1003 correspond

respectively to operations 901, 902 and 903 of the flowchart of FIG. 9.

1 5 Operation 1004 consists in taking, in the table TAB (i, j, k), the next triplet of values (i, j, k) which corresponds to the column numbers of the Van Der Monde matrix G which form an invertible 3x3 sub-matrix. Operation 1005 consists in forming triplets of polynomials said to be neighbors of the triplet of demodulated polynomials (u ;, uj, Uk) and in assigning to each of these triplets of neighboring polynomials an affinity which is a decreasing function of the sum of the squares of the Euclidean distances of each of the points represented by a neighboring polynomial (by the second labeling) with the pair

of components of the corresponding demodulated polynomial.

Operation 1006 consists in calculating a triplet of polynomials

â = (ui, Uj, Uk) i) (G (jk) -

o (Ui, Uj, Uk) is the row matrix made up of the three polynomials ui, uj and Uk; and (G (i'J'k) -i is the inverse matrix of the matrix made up of the columns

3 o numbered i, jet k of the Van Der Monde matrix (1).

28 2764751

Operation 1007 consists of storing the â triplet of

initial polynomials by assigning it the affinity defined during operation 1005.

The test 1008 determines whether all the triples of the table TAB (i, j, k) have been implemented. When the result of test 1008 is negative, operation 1004 is repeated. When the result of test 1009 is positive, operation 1009 consists in estimating the triplet of initial polynomials representative of the three 6-uples of data transmitted by the encoding device as being the triplet of which

the sum of the affinities is the highest.

According to a variant, the K-uples of neighboring polynomials of a K-

uple of demodulated polynomials are determined as being the NK K-uples of polynomials whose polynomial of each rank in said K-uple represents one of the N points of the constellation closest to the pair of components represented by the demodulated polynomial of same rank in the K-uple of

demodulated polynomials.

In particular, FIGS. 11 to 13 illustrate a variant of the operating flowcharts presented with reference to FIGS. 9 and 10, according to which the neighboring polynomials and the affinities associated with polynomials

initials which they represent are determined in a particularly simple manner.

According to this variant, conversion tables kept in read only memory are used to attribute to each pair of components represented by a demodulated polynomial a list of neighbors and, to each so-called neighbor polynomial thus determined, an affinity with said demodulated polynomial, decreasing affinity with the distance between pairs of components

represented by the demodulated and neighboring polynomials.

This variant has the advantage of being implemented by

very simple and very fast electronic circuits.

In FIG. 11 is shown a distribution into three zones of a square pattern which, by axial symmetry, the axes of which are the edges of said

pattern, covers the entire 64-QAM constellation.

Here, N is equal to 4. For each demodulated polynomial, we determine the 4 neighboring polynomials as the 4 polynomials of the constellation

29 2764751

closest to the pair of components represented by the demodulated polynomial, using a correspondence table which puts a correspondence: - the pairs of components of the zone 1101 with the four points of the constellation 1110 affected by the affinity max {D2 2/4, 0} 1111 affected with max affinity {D2 - 4/4, 0} 1112 affected with max affinity {D2 - 8/4, 0}, and 1113 affected with max affinity {D2 - 4/4, 0} (figure 12) - the pairs of components of the zone 1102 with the four points of the constellation 1110 affected by the affinity D2 1111 affected by the affinity max {D2 - 4/4, 0}, i5 1113 affected with max affinity {D2 10/4, 0}, and 1117 affected with max affinity {D2 - 16/4, 0} (figure 13) the pairs of components of zone 1103 with the four points of constellation 1110 affected by affinity D2 1111 affected by max affinity {D2 - 10/4, 0}, 1113 affected by max affinity {D2 - 4/4, 0}, and

1115 assigned the max affinity {D2 - 16/4, 0}.

As mentioned above, D2 can be chosen arbitrarily.

According to variants: the neighbors of a K-tuple of demodulated polynomials are determined as being those which represent a K-tuple of points of the constellation whose distance to the K-tuple of pairs of components represented by said K-tuple of demodulated polynomials, in the constellation, is less than a threshold value, - the neighbors of a K-tuple of demodulated polynomials are determined as being those which represent a K-tuple of points of the constellation of which 3 0

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each of the components is equal to or immediately greater than or less than the corresponding component of the K-tuple of pairs of components represented by the K-tuple of demodulated polynomials, - the neighbors of a K-tuple of demodulated polynomials are determined to be a number predetermined N of K-tuple of polynomials which represent the N K-tuple of points of the constellation closest to the K-tuple of component pairs represented by said K-tuple of demodulated polynomials, or - N being a predetermined number, the neighbors of a K-tuple of demodulated polynomials are determined as being the NK K-tuple of polynomials whose lo polynomial of each rank in said K-tuple represents one of the N points of the constellation closest to the pair of components represented by the demodulated polynomial of the same rank in the K-tuple of demodulated polynomials,

- each K-tuple of initial polynomials is affected by the same affinity.

The scope of the invention is not limited to the embodiments described and shown but extends, on the contrary to the embodiments of the invention.

improvements and modifications within the reach of those skilled in the art.

31 2764751

Claims (34)

1. Device for decoding so-called "initial" coded information, characterized in that it comprises: a demodulator adapted to demodulate P signals modulated at the points of a constellation with quadrature amplitude modulation, in a so-called sequence. "demodulated" of P points called "demodulated" and representative of a K-tuples of "initial" information, - a processing means suitable for: 10. choosing K-uples of demodulated points capable of allowing the calculation of the K -uple of initial information to which they correspond, determine, for each of the K-uples of selected demodulated points, K- uples, called "neighbors", of points in said constellation which are close to the K-tuple of demodulated points chosen, 15. calculate, for each K-tuple of neighboring points, the initial information K-tuple to which it corresponds and to assign this K-tuple of initial information with an affinity depending on the distance between said K-tuple of neighboring points and the chosen K-tuple of demodulated points to which it is attached, sum, for each K-tuple of initial information calculated, or for each initial information of the calculated initial information K-uples, of the affinities assigned to it, and estimate, respectively, the initial information K-tuple actually coded, or each initial information of the K-tuple initial information, actually coded as being the one with the highest sum of affinities. 3 0 2. Device for decoding coded information, characterized in that it comprises: 32 2764751 - a demodulator adapted to demodulate P successive signals in quadrature amplitude modulation, the two components of which are representative of the coefficients of K first degree polynomials called “initial polynomials”, into a so-called “demodulated” sequence of P first degree polynomials , called "demodulated", the coefficients of the same degree of said demodulated polynomials being successively representative of one of the components of the corresponding demodulated signal, and a processing means suitable for: choosing K-uples of demodulated polynomials capable of allowing the o0 calculation of the K-tuples of initial polynomials to which they correspond, determining, for each of the K-uples of demodulated polynomials chosen, K-uples of so-called "neighboring" polynomials representative of K-uples of points of the constellation close to the K-tuple of pairs of components represented by the K-tuple of demodulated polynomials chosen, calculate, for each K-tuple of neighboring polynomials, the K-tuple of initial polynomials that l it corresponds and assign this K-tuple of initial polynomials with an affinity depending on the distance between said K-tuple of points represented by the K-tuple of neighboring polynomials and the K-tuple of pairs of components represented by the K- uple of demodulated polynomials chosen to which it is attached, sum, for each K-tuples of initial polynomials calculated or for each initial polynomial of the K-uples of initial polynomials calculated, of the affinities assigned to it, and estimate, respectively, the K- tuple of initial polynomials effectively coded or each initial polynomial of the K-tuple of initial polynomials, effectively coded 3 o as being the one with the highest sum of affinities. 33 2764751 3. Decoding device according to claim 2, characterized in that, the two components being representative of the coefficients of a single polynomial of the first degree called “initial polynomial”, K thus being equal to 1, the processing means is suitable for choosing all the demodulated polynomials. 4. Decoding device according to any one of the claims 1 to 3, characterized in that the distance between two Kuples of pairs of components of the constellation is a function of the sum of the K squares of Euclidean distances between the pairs of components of the same 1st row in said K-uples. 5. Decoding device according to any one of the claims 2 to 4, characterized in that the neighbors of a K-uple of demodulated polynomials are determined as being those which represent a K-tuple of points of the constellation whose distance to the K-tuple of pairs of components represented by said K-tuple of demodulated polynomials, in the constellation, is less than a threshold value. 6. Decoding device according to any one of 2o claims 2 to 4, characterized in that the neighbors of a K-uple of demodulated polynomials are determined to be those which represent a K-tuple of points of the constellation each of whose components is equal to or immediately greater than or less than the corresponding component of the K-tuple of pairs of components represented by the Kuple of polynomials demodulated. 7. Decoding device according to any one of claims 2 to 4, characterized in that the neighbors of a K-uple of demodulated polynomials are determined to be a predetermined number N of K-uples of polynomials which represent the N K-uples of points of the 34 2764751 constellation closest to the K-tuple of pairs of components represented by said K-uple of demodulated polynomials. 8. Decoding device according to any one of the claims 2 to 4, characterized in that, N being a predetermined number, the neighbors of a K-tuple of demodulated polynomials are determined to be the NK K-uples of polynomials whose polynomial of each rank in said K- uple represents one of the N points of the constellation closest to the pair of components represented by the demodulated polynomial of the same rank l0 in the K-tuple of demodulated polynomials. 9. Decoding device according to any one of claims 2 to 8, characterized in that it uses a matrix G of dimensions K x P. 10. Decoding device according to claim 9, characterized in that said matrix is a Van der Monde matrix of type 1 gg g3 .. gP -1 2 o G = 1 g2 g4 g6 gP-2 1 gk g2k g3k g .. Pk g being a polynomial of degree 1 whose period is equal to P. 11. Decoding device according to claim 10, characterized in that, the two components of the P signals being representative of the coefficients of two polynomials of the first degree called "initial polynomials", K thus being equal to 2, and the number Q of different values of the components of the initial polynomials being a power of 2, - the processing means is adapted to: 3 5 choose, in the sequence of the P initial polynomials, the pairs of ranks i andj whose modulo 3 residues are different. 12. Decoding device according to claim 10, characterized in that, the two components of the P signals being representative of the coefficients of three polynomials of the first degree called “initial polynomials”, K thus being equal to 3, and the number Q of values. different from the components of the initial polynomials being a power of 2, - the processing means is adapted to: 10. choose, in the sequence of the P initial polynomials, the triplets of rank i, j, k whose modulo 3 residues of i, jet k are all different. 13. Decoding device according to any one of claims 2 to 12, characterized in that the processing means is suitable to assign each K-tuple of initial polynomials of the same affinity. 14. Decoding device according to any one of the claims 2 to 12, characterized in that the processing means is suitable to assign each K-tuple of initial polynomials with a decreasing affinity as a function of the distance between the K-tuple of points represented by the K-tuple of neighboring polynomials and the K-tuple of pairs of components represented by the K- uple of demodulated polynomials chosen to which it is attached. 15. Decoding device according to any one of the claims 2 to 14, characterized in that the processing means is suitable to: sum, for each initial polynomial of the K-tuple of calculated initial polynomials, of the affinities assigned to it, and estimate each initial polynomial of the K-tuple of initial polynomials 3 o actually coded as being the one which has the sum d 'affinities higher. 36 2764751 16. Decoding device according to any one of claims 2 to 14, characterized in that the processing means is suitable to: 5. make the sum, for each K-tuple of initial polynomials calculated, of the affinities which are assigned to it, and estimate the K-tuple of initial polynomials actually coded as being the one with the highest amount of affinities. 17. Computer characterized in that it comprises a information decoding according to any one of claims 1 to 16. 18. Facsimile machine characterized in that it comprises a device decoding device according to any one of claims 1 to 16. 19. Information capture system, characterized in that it comprises an information decoding device according to any one of the following. claims 1 to 16. 20. Information reproduction system, characterized in that it comprises an information decoding device according to any one. of claims 1 to 16. 21. Information processing system, characterized in that it comprises an information encoding device according to any one. of claims 1 to 16. 22. A method of decoding so-called “initial” coded information, characterized in that it comprises: a demodulation operation, during which P signals modulated at the points of a constellation with modulation of amplitudes in 37 2764751 quadrature, in a so-called "demodulated" sequence of P so-called "demodulated" points representative of a K-tuple of "initial" information, a processing phase comprising one: a choice operation, during which one chooses K-uples of demodulated points capable of allowing the calculation of the K-tuples of initial information to which they correspond, a determination operation during which one determines, for each of the K-uples of selected demodulated points, K-uples, called "neighbors", of points in said constellation which are close to the K-tuple of demodulated points chosen, a calculation operation during which we calculate, for each K- uple of neighboring points, the initial information K-uple to which it corresponds and we assign this initial information K-uple with an affinity depending on the distance between said K-uple of neighboring points and the K-uple of points demodulated chosen to which it is attached, a summation operation during which we sum, for each K-tuples of initial information calculated, or for each initial information of the K-uples of initial information calculated, the affinities assigned to it , and an estimation operation during which one estimates, respectively, the K-tuple of initial information effectively coded, or each initial information of the K-tuple of initial information, effectively coded as being the one with the highest sum of affinities. 23. Method for decoding coded information, characterized in that it comprises: a demodulation operation during which P successive signals are demodulated in quadrature amplitude modulation, both of which are 38 2764751 components are representative of the coefficients of K first degree polynomials called “initial polynomials”, in a so-called “demodulated” sequence of P first degree polynomials, called “demodulated”, the coefficients of the same degree of said demodulated polynomials being successively representative of I ' one of the components of the corresponding demodulated signal, and - a processing phase comprising: a selection operation during which K-uples of demodulated polynomials are chosen capable of allowing the calculation of the K-tuple of initial polynomials to which they correspond, 10 a determination operation during which one determines, for each of the K-uples of demodulated polynomials chosen, K-uples of so-called “neighboring” polynomials representative of K-uples of points of the constellation close to the K-uples of pairs of components represented by the K-tuple of demodulated polynomials chosen, 15. a calculation operation, during which we calculate, for each K- uple of neighboring polynomials, the K-uple of initial polynomials to which it corresponds and we assign this K-uple of initial polynomials of an affinity depending on the distance between the K-tuple of points represented by said K- uple of neighboring polynomials and the K-uple of component pairs represented by the chosen K-uple of demodulated polynomials to which it is attached, a summation operation, during which we sum, for each K-uple of initial polynomials calculated or for each initial polynomial of the K-uples of calculated initial polynomials, of the affinities which are assigned to it, and an estimation operation, during which one estimates, respectively, the K-tuple of initial polynomials actually coded or each polynomial initial of the K-tuple of initial polynomials actually encoded 39 2764751 as being the one with the highest sum of affinities. 24. Decoding method according to claim 23, characterized in that, the two components being representative of the coefficients of a single polynomial of the first degree called “initial polynomial”, K thus being equal to 1, during the operation of choice, we choose all demodulated polynomials. 25. A decoding method according to any one of 1o claims 22 to 24, characterized in that the distance between two K-uples of pairs of components of the constellation is a function of the sum of the K squares of Euclidean distances between pairs of components of the same rank in said K-uples. 26. A decoding method according to any one of claims 23 to 25, characterized in that, during the operation of determination, the neighbors of a K-tuple of demodulated polynomials are determined as being those which represent a K-tuple of points of the constellation whose distance to the K-tuple of pairs of components represented by said K-tuple of demodulated polynomials, in the constellation, is less than a threshold value. 27. A decoding method according to any one of the claims 23 to 25, characterized in that, during the operation of determination, the neighbors of a demodulated polynomial K-tuple are determined as being those which represent a K-tuple of points of the constellation each of whose components is equal to or immediately greater than or less than the corresponding component of the K-tuple of pairs of components represented by the K-tuple of demodulated polynomials. 2764751 28. A decoding method according to any one of the claims 23 to 25, characterized in that, during the operation of determination, the neighbors of a K-tuple of demodulated polynomials are determined to be a predetermined number N of K-tuple of polynomials which represent the N K-tuple of points of the constellation closest to the K-tuple of component pairs represented by said K-tuple of demodulated polynomials. 29. A decoding method according to any one of 1o claims 23 to 25, characterized in that, during the operation of determination, N being a predetermined number, the neighbors of a K-tuple of demodulated polynomials are determined as being the NK K-tuple of polynomials whose polynomial of each rank in said K-tuple represents one of the N points of the constellation closest to the pair of components represented by the demodulated polynomial of the same rank in the Kuple of demodulated polynomials. 30. A decoding method according to any one of claims 18 to 21, characterized in that, during the operation of calculation, a matrix G of dimensions K x P. 31 is implemented. Decoding method according to Claim 30, characterized in that the said matrix is a Van der Monde matrix of type 1 g g2 g3 ... gp-1 G = I g2 g4 g6. gP-2 I gk g2k g3k ... gP-k g being a polynomial of degree I whose period is equal to P. 32. Decoding method according to claim 31, characterized in that, the two components of the P signals being representative of the coefficients of two polynomials of the first degree called "initial polynomials", K thus being equal to 2, and the number Q of different values of the components of the initial polynomials being a power of 2, during the choice operation, we chooses, in the sequence of P polynomials demodulated, the pairs of rows i and j whose modulos 3 residues are different. 33. A decoding method according to claim 31, 1o characterized in that, the two components of the P signals being representative of the coefficients of three polynomials of the first degree called “initial polynomials”, K thus being equal to 3, and the number Q of different values of the components of the initial polynomials being a power of 2, during the operation of choice, one chooses, in the sequence of P demodulated polynomials, the triples of ranks i, j, k whose residues modulos 3 of i, j and k are all different. 34. A decoding method according to any one of claims 23 to 33, characterized in that, during the operation of calculation, we assign each K-tuple of initial polynomials of the same affinity. 35. A decoding method according to any one of claims 23 to 33, characterized in that, during the operation of calculation, we assign each K-tuple of initial polynomials with decreasing affinity as a function of the distance between the K-tuple of points represented by the K-tuple of neighboring polynomials and the K-tuple of pairs of components represented by the K-tuple of demodulated polynomials chosen to which it is attached. 36. A decoding method according to any one of the claims 23 to 35, characterized in that: 42 2764751 during the summation operation, we sum for each initial polynomial the K-uples of initial polynomials calculated, the affinities which are assigned to it, and during the estimation operation, we estimate each initial polynomial of the K-tuple of initial polynomials actually coded as the one that presents the highest sum of affinities. 37. A decoding method according to any one of claims 23 to 35, characterized in that: 10. during the summation operation, we add, for each K- uple of initial polynomials calculated, of the affinities which are assigned to it, and during the estimation operation, we estimate the K-uple of initial polynomials actually coded as being that which presents the sum highest affinities. 38. System comprising a microprocessor, characterized in that said microprocessor is adapted to implement the method according to one of any of claims 22 to 37.