Method for calculating a correspondence table allowing the efficient implementation of a flexible modulator in a turbo receiver

Abstract

Method for calculating a correspondence table allowing the efficient implementation of a soft modulator in a turbo receiver The invention relates to the determination of a correspondence table between a variance of input samples of a soft demodulator, an a priori variance, AP, average of LLR bits AP provided by a decoder (203), and a coefficient used to calculate an output signal of a modulator (205) and its variance, in a turbo receiver.It comprises: a step (501) of determining sets of LLR bits AP and corresponding to several , a step (502) of classifying, for each , the LLR bits AP into corresponding boxes, a step (503) of generating a table having as inputs and , and as output an a posteriori variance, APP, average , using the correspondences between and , and the correspondences between LLR bits AP and , a step (504) of calculating: The invention also relates to the corresponding computer programs and media. Figure for the abstract: Figure 5.

Description

Title of the invention: Method for calculating a correspondence table allowing the efficient implementation of a flexible modulator in a turbo receiver Technical field

[0001] The invention lies in the field of telecommunications, and more particularly in the field of receivers for radio communication systems.

[0002] More specifically, the invention aims to define a method for calculating a correspondence table that can be used to efficiently implement a flexible modulation function in a turbo receiver. Prior art

[0003] The transfer of information from a source to a destination involves its propagation through a transmission channel which may be, for example, a radio channel, a wired channel (for example, a coaxial cable), an acoustic channel, etc. Some propagation means generate so-called "inter-symbol interference" (or ISI) on the received signal. In other words, the received signal sampled at a given time, after compensation for propagation and processing delays and having correct synchronization, does not only contain the symbol sent (possibly amplified and with a phase disturbance) plus noise, but a mixture (linear combination) of symbols sent.

[0004] It is common to use equalizers to reduce the harmful effect of inter-symbol interference. Many equalization methods have been studied in the past years. They try to approach the theoretical optimal performances (given by the bound of the matched filter) while trying to be achievable in practice. In other words, these algorithms must have a computational complexity, a memory occupation and a processing latency compatible both with the applications that use the receivers in question and the constraints of the hardware platforms on which they are implemented. The general problem of equalization is therefore to find the algorithm offering the right compromise between performance and implementation complexity in relation to the targeted applications.

[0005] There are different classes of equalizers: linear equalizers, Decision Feedback Equalizers (DFE), Interference Cancellation Equalizers, etc. Each type of equalizer has its strengths and weaknesses.

[0006] [Fig.l] very roughly represents the key elements of a transmission chain for digital radio communications equipment. The bits to be transmitted are first coded by a channel coder 101, which aims to allow the receiver to detect and correct possible transmission errors. The coded bits are then processed by an interleaver 102, which reorders them so as to improve their robustness against transmission errors and disturbances in the propagation channel. Note that the interleaver is not mandatory. The interleaved bits are then shaped by a modulator 103, which transforms them into complex symbols in order to transmit them efficiently on the propagation channel. The receivers sequentially implement the successive inverse processes of demodulation, deinterleaving and decoding.

[0007] Higher-performance receivers are known as turbo-receivers, in which the reception algorithm blocks are declined in iterative form, as shown in [Fig.2]. There is therefore a reiterated exchange of probabilistic information between the processing blocks which makes it possible to improve the performance of the receiver. These iterations require the presence of a soft modulator 205 to process the signals transmitted by the decoder, in addition to the soft demodulator 204 which generates the information transmitted to the decoder from the samples it receives, which is why we speak of a soft demodulation / modulation block 202. We speak of turbo equalization when successive iterations 211 are carried out between the decoder 203 and the equalizer 201, passing through the soft demodulation / modulation block 202. The iterations 211 are called turbo iterations.We speak of simple DFE equalization (or possibly self-iterated equalization) when successive iterations 210 are carried out between the equalizer 201 and the flexible demodulation / modulation block 202. The iterations 210 are called self-iterations. A turbo receiver carries out at least one turbo equalization, and can carry out none, one or more self-iterations. Note that a detector, for example a MIMO detector (acronym for Multiple Input Multiple Output), can be used instead of the equalizer.

[0008] The soft demodulator / modulator 202 therefore comprises two blocks: a soft demodulation block 204, configured to supply the decoder 204 from equalized symbols supplied to the equalizer 201, and a soft modulation block 205 (in English soft mapper), configured to reform sequences of samples transmitted to the equalizer from information including that supplied by the decoder.

[0009] When the transmission includes interleaving of the bits, the turbo receiver also includes a deinterleaver 206, and an interleaver 207 for reorganizing the data transmitted by the decoder. The remainder of the description ignores the interleaver and deinterleaver, since these treatments do not influence the content of the transported data, but only their organization.

[0010] The flexible modulation blocks of the turbo receivers of the prior art seek to estimate the symbols of a modulated digital signal (or return signal) and their reliability starting from an observation (received signal), a measurement of the noise disturbing this received signal, and a priori information (AP) relating to the signals sent. These estimates can be used for: - derive an estimate of the propagation channel (or some of its parameters) between the transmitter and the receiver; - derive an estimate of the signal or receiver parameters such as, for example, the clock offset, or the time of signal reception; - derive link quality metrics, such as for example the mutual information between the transmitted and received symbols, the reliability of the estimate of the sent signal, the signal-to-noise ratio or signal-to-noise plus interference.

[0011] The main use of the return signal is the suppression of intersymbol interference within a signal received on a receiver. The invention therefore applies in particular in the context of a receiver comprising an adaptive decision feedback equalizer (in English Digital Feedback Equalizer, or DFE) allowing equalization of the received symbols.

[0012] Turbo receivers can be used for example for single-carrier communication systems with equalization in the frequency domain (Single Carrier-Frequency Domain Equalization, SC-FDE) or time domain, or for systems with single-carrier modulation with frequency division multiple access (Single Carrier-Frequency Division Multiple Access, SC-FDMA). They can also be used for systems with orthogonal frequency division multiplexing (OFDM), possibly with multiple access (OFDMA), such as the 3GPP cellular standards of 4G and 5G, or the WiMAX (IEEE 802.16) or WiFi (IEEE 802.11) standard, to systems using filtered modulations (Filter Bank Multi-Carrier, FBMC), or to systems using similar techniques.

[0013] Hereinafter, the following definitions are used: - DFE equalizer: any type of equalizer using a return signal estimated by the receiver. This return signal is called "hard" if the estimated signal is composed of symbols belonging to the transmission constellation. The return signal is called "soft" if the estimated symbols it contains do not belong to the transmission constellation but can assume values ​​on the complex plane, - self-iterated DFE equalizer (also called simple DFE here): this is a DFE equalizer where the return signal comes from the soft demapping block, as in [Fig.2], - turbo-iterated DFE equalizer (here also called turbo DFE or turbo DFE): this is a DFE equalizer where, in addition to having a return signal from the soft demodulation block, there is also a return signal from the decoder, as in [Fig.2].

[0014] The invention is presented in the context of a turbo receiver comprising a turbo-iterated DFE equalizer, with or without self-iterations. It is also applicable to the case of a receiver implementing a turbo-iterated linear equalizer with interference cancellation (known as turbo LMMSE-IC) in the frequency domain. In this field it is known that equalizers, turbo or not, based on a soft return signal calculated according to the so-called "Expectation Propagation" (EP) method exhibit good performance. Expectation propagation is a Bayesian approximate inference method that seeks to infer (in other words, estimate) a statistical description of the symbols sent. Expectation propagation models each symbol sent as a Gaussian, and not as a point in the original constellation. A Gaussian is completely defined by its mean and its variance.The symbols of the soft feedback signal correspond to the averages of the Gaussian random variables estimated by expectation propagation. Their reliability coincides with the variance of these Gaussian random variables. Other equalizers, turbo or not, based on soft feedback have good performances, such as equalizers with a posteriori (APP) or extrinsic (EXT) feedback. However, the calculations to obtain the soft feedbacks (performed by the soft modulator 205 of [Fig.2]) are very expensive from a computational point of view.

[0015] Figure 3 schematically represents the structure of a state-of-the-art flexible expectation propagation demodulator / modulator. In this example, the operations 301 for calculating the extrinsic bit log-likelihood ratios (LLRs) L(,( dk ) injected into the decoder are separate from the operations 302 for calculating the flexible feedback EP x^ and v^, although in reality some operations may be common.

[0016] The flexible demodulation / modulation block EP can be called several times within a receiver, in particular following an equalization / detection (in this case it is a self-iteration indexed by the index 5 going from 0 to Xr), or following a decoding test (in this case it is a turbo-iteration indexed by the index r going from 0 to T). For each turbo-iteration ' there are self-iterations. For a turbo iteration given, indexed by the index ', the soft demodulation / modulation block generates times a soft return to the equalizer / detector, without activating the decoder. When the index s reaches the value the soft demodulation / modulation block generates the extrinsic LLR bits and provides them to the decoder. If t = T, the decoder, from the extrinsic LLR bits at input, provides an estimate of the message sent by the transmitter and the reception process stops for this received signal. If t < T, the decoder, from the extrinsic LLR bits at input, provides the soft demodulation / modulation block with probabilistic information on the coded bits sent by the transmitter and increments the turbo index which goes to the value t + 1. The soft demodulator / modulator uses at least this probabilistic information on the coded bits to calculate a new return signal for the equalizer / detector, and resets s = 0, index which will vary up to Lr+i.The operations of the soft modulator 302 are performed on an input data vector Xe comprising K input samples indexed on k = 1, ..., K. The value corresponds to the variance of the additive noise plus residual interference present on the data block Xe. In the following, we will speak more briefly of variance of the residual noise, including all possible disturbances. We consider this variance as constant for all inputs of the data block Xe, which is the case in frequency equalization applications. In other applications, for example time equalization or detection in multi-antenna systems (MIMO), this variance may differ depending on the input of the data block. In this case the following formulas are identical, using an index k for the corresponding variance. The vector is the vector of LLR bits a priori (AP) provided by the decoder.These LLRs are a priori information on the bits dk corresponding to the sent symbol and therefore to the equalized signal (sometimes called observation). Note that the a priori LLRs do not change during the self-iterations performed at turbo-iteration T, and change at each new turbo-iteration since they are generated by the decoder. In the absence of disturbance, x| coincides with the sent symbol which is taken from a constellation E as follows: . °ù £ — Lf 1 is the fc-th group of Q elements of the vector t ^,k ' 1)Ê? Ij d which is the vector of coded (and interleaved) bits of size QK corresponding to the data block, and ¢() is a so-called "labeling" function associating the bits or sequences of bits with a point of a constellation to determine a complex symbol. The bit vector dk can be interpreted as the binary label of the symbol xk. We also note , _ 1 The g-th bit of the symbol label with q = 0, .... Q-1. For “kQ+q ~ To finish, we also set {ag ( a ) = & j, i.e. the set of all symbols of the constellation which have a bit of value Z? (0 or 1) in the g-th position of their binary label. The size of the constellation is । | M — 2^' c"c is therefore formed of M distinct symbols.

[0017] The following details the operations necessary to calculate the outputs of the soft demodulator / modulator: the K extrinsic LLR bit vectors Le(dk), the soft symbols EP and their variance EL. These calculations correspond for example to those described in patent EP 3,528,443 Bl.

[0018] For each set of inputs the flexible demodulator 301 calculates a set of K vectors i.e. K vectors of Q LLR extrinsic bits, which is supplied to the decoder. Note that when Q = 1, the vectors Le ( dk ) are one-dimensional vectors. Several methods are well known to those skilled in the art for calculating these outputs. These methods are more or less complex and are not detailed here.

[0019] From the Æ vectors of Q LLR bits AP L“ provided by the decoder, also noted rta \rt A \ r \ j tJ \] if we wish to show L'a ( «fc) ~ [M ( ak,Q ) “kg J • • • 7 J that the LLR bits are a function of the bits sent dk, it is possible to calculate, by block 303, the K vectors of LLR symbols AP: Lk(a) ~ log[IIÆ(a) / ¾(, aref, ag E (1)

[0020] where logn*(a) = _£^^ vÆ= t K. In choosing equal to the symbol having the binary label jq q] g qQ, we have = a) with "e E are called the probabilities of mass (or equivalently the probability distribution) of the soft symbols a priori. The same vector of LLR symbols AP corresponding to the emitted symbol is denoted La( xk ) and it has a size of M, its entries L%(a) being indexed on the M symbols of the constellation a G E.

[0021] The log-likelihoods corresponding to the input signal are calculated by block 304, for example using the formula hM2 >°ù ^pam ~ for constellations linear type PAM (English acronym for Pulse Amplitude Modulation, or modulations in amplitude of pulse), BPSK (English acronym for Binary Phase Shift Keying, or modulation by binary phase change) or tt / 2-BPSK, and Mam = 1 for the other constellations.

[0022] Block 305 can then calculate K vectors of LLR symbols a posteriori (APP) M, the inputs of which are written: ^k ( ® — fcpAMri ® ) ' ^ref' a (2)

[0023] These are called LLR a posteriori symbols because they include knowledge of the observation in addition to Va priori. These vectors of LLR symbols APP are then provided as input to block 306 which uses them to obtain the mass probabilities of the a posteriori symbols (which are a linear scale probability distribution): A , , _ ___ (3)

[0024] where ( a ) = eLk^ are defined as the LLR APP symbols in linear scale. The K APP soft symbols and their instantaneous variances (APP) are calculated by block 306 from the APP mass probabilities: ^ = ^2^-^1^0) = LJ «l%-( «) - l^l2 (4)

[0025] We note that is finally a function of the symbol at the input of the flexible demodulator and of the a priori information (if present), and that it is parameterized on the variance of the residual input noise v 1. This function is formally denoted by Pd'

[0026] Similarly, the instantaneous variance of the APP soft symbol depends on the symbol and the a priori information through the function yd • ( vj) >-> For some applications, such as equalization in the frequency domain, it is more advantageous to calculate the empirical average APP variance over the block of data ri = (5)

[0027]

[0028] which is an estimate of the statistical expectation of the APP variance viewed as a random variable or, in other words, of the mean square error between the APP soft symbols and the sent symbols. The empirical mean APP variance is therefore a function of all the entries corresponding to a data block, and it is denoted by Identical formulas can be applied using the a priori soft symbol distribution (if 3¾ ( ") is available, after a decoder pass through a turbo-iteration). It is therefore possible to calculate the a priori soft symbols and their instantaneous variance ^ = E aeS year fe (has) (6) v^ = E Æ Ja-x£| 2 n^a) =E f ^ - |xf| 2 .

[0029] It is also possible to calculate their average a priori variance: Lr xJv (7)

[0030] where Kc is the overall size (sum) of all data blocks whose symbols come from the same code word.

[0031] Then block 306 calculates the variance of soft symbols EP vx through an operation called "Gaussian division". v*x is a non-linear function of the inputs, and is calculated as follows: vl: (O = otherwise (8)

[0032] where E is a fixed parameter typically taking values ​​between 1()-3 and 10"4- The variance f»- can also be seen more simply as a function ,,*1^ rx)

[0033] Note that it is possible to use the same formulas by substituting for yd the instantaneous APP variances and à the instantaneous variances of the disturbance to obtain instantaneous EP variances useful in certain applications, as well as the corresponding EP soft symbols.

[0034] Block 306 also calculates through this “Gaussian division” procedure the soft symbols EP according to the following function which is parameterized by vJ,: (9) otherwise

[0035] The calculation of the flexible return signal EP requires a large number of computational passes, with the frequent use of the exponential non-linear function, when calculating the mass probabilities of the symbols a posteriori (equation (3)), and numerous divisions, which may prove too complex to implement, in particular for equipment constrained in terms of cost and consumption.

[0036] In some implementations, the soft demodulator / modulator may provide the equalizer / detector with the outputs xf and ie the soft symbols AP and their mean variance AP, instead of the soft symbols EP and their mean variance EP, for example when the observations are considered not good or not representative, and only the a priori information from the decoder is present (for example, this may be the case after a decoding test made by the decoder).

[0037] Smoothing treatments 307 can advantageously be implemented on the signals x*k and For example, the block 307 can carry out linear filtering operations on the available values ​​of xk and C: those of the current auto-iteration and the previous ones and / or those of the current turbo-iteration and the previous ones, the filters being able to change at each auto or turbo-iteration.

[0038] In order to reduce the number of calculations and simplify the type of operations required to implement flexible return in the context of a turbo receiver, without significantly degrading performance in terms of packet error rate (PER) or bit error rate (BER), while reducing or controlling the memory footprint, the inventors filed patent application FR2315402. [Fig.4] represents in the form of a block diagram an embodiment of the method for estimating a return signal described in this patent application.

[0039] This turbo receiver differs from the state of the art on several points allowing its implementation to be simplified and its memory footprint to be limited.

[0040] First, soft APP LLR bits are obtained (at 403) from the LLR extrinsic bits (obtained in 402) and LLR bits AP provided by the decoder. These LLR bits APP are then converted (in 404) into soft symbols APP ^49 using a technique called "bitwise soft mapping" (English term equivalent to generating soft symbols from LLR bits), unlike the prior art which directly calculates LLR symbols APP by implementing functions that are difficult to implement (see equation (2)). This way of proceeding makes it possible to avoid the implementation of the steps described above in equations (1) to (4), in particular the calculation of exponential functions, and is therefore much less complex and costly in terms of computing resources.

[0041] Then, the Gaussian division 405 is carried out using the following cep coefficient: CEP^CEp{^^) = (10) to simplify the calculations.

[0042] The calculation of the soft symbols xk of the output signal can then be written: iT. (x^L^^ i K . ( 1 + ~ CeA Otherwise (H)

[0043] Similarly, the variance of the soft symbols EP of the output signal can be written:

[0044] The use of the EP cep coefficient makes it possible to reduce the operational complexity of the Gaussian division, since equations (11) and (12) do not contain divisions, unlike equations (9) and (8).

[0045] Patent application FR2315402 uses a two-dimensional table 407 to obtain directly and without calculations the value of the cep coefficient as a function of the values ​​of 14 and v%.

[0046] Patent application FR2315402 also uses a one-dimensional table 406 to obtain directly and without calculations the value of the average AP variance v* from the variance of the input samples only.

[0047] Many state-of-the-art articles formulate proposals to simplify the calculations of formula (5), the average APP variance yd, of formula (8), and the average EP variance Kv, and of formula (7).

[0048] Some suggest evaluating the average APP variance y^ by approximating it by its Minimum Square Error (MSE): MSE^ E[ |^( Xe, ) -x|2 ], (1)

[0049] and / or to approximate the average EP variance C by its EQM: MSEX« E[ La;^)-x|2]. (2)

[0050] In all these formulas, the expectations are calculated on the statistics of the symbols sent, and possibly the residual noise and the a priori LLRs (these random variables can be dependent or correlated with each other). Note that the index & is not indicated because the symbols and are considered independent and identically distributed as a function of k. However, these formulas are theoretical and do not reveal as a function of how many and which parameters the metrics should be described, nor how to calculate them in detail. Moreover, the most suitable choice of their parameterization is linked to their use and to technical considerations such as the fact that their calculation, carried out with good precision, can be too complex or require too much time. In the literature it is therefore possible to find different parametric descriptions of equations (13) and (14), as well as different ways of approximating and calculating them..

[0051] One way to do this is to pre-calculate these quantities, and store them in a LookUp Table (LUT) in the receiver's memory. Rather than calculating the quantity of interest, the receiver retrieves it quickly and without intermediate calculations from the lookup table, which reduces the number of calculations to be performed and the time required to obtain the quantity of interest.

[0052] It is therefore necessary to define a method for establishing the lookup tables (LUTs) implemented in the turbo receiver, in particular the two-dimensional table 407 establishing the relationship between, on the one hand, the variance of residual noise at the demodulator input and the average AP variance of a priori soft symbols associated with a priori LLR bits supplied by the decoder, and on the other hand, the EP cep coefficient.

[0053] The purpose of this two-dimensional table is to summarize the "relationship" between its two inputs (the variance of residual noise >1 at the demodulator input and the average AP variance of a priori soft symbols associated with a priori LLR bits provided by the decoder), and an estimate of the EP coefficient cep. We speak of a "relationship" because there is no 1 to 1 correspondence or a function properly speaking between these inputs and the output. The correspondence table must therefore represent in a suitable manner (i.e. the performance of the receiver must not be significantly degraded compared to the exact reference receiver) the complex dependence that may exist between the output, i.e. the average EP variance, and the inputs, i.e. the variance of the residual noise at the demodulator input and the AP LLR bits provided by the decoder. In the absence of a priori (i.e. when = 1, i.e. 0 dB), this table depends only on the chosen constellation.In the presence of a priori, it can also depend, through the input of the coding and decoding parameters.

[0054] Each table is specific to a combination of corrector code (type, size, throughput), decoder parameterization (for example, number of internal turbo iterations for a turbo code or an LDPC code (Low Density Parity Check code, or code with low density parity checking equations), method of calculating the internal metrics of the decoder, etc.) and the constellation used in the system. However, the same table can be used for several different relatively close configurations (for example for close code word sizes).

[0055] When the a priori information from the decoder is available, we distinguish two receiver configurations requiring different processing concerning the calculation of the variance of the soft EP return: - either the turbo receiver does not use self-iterations between the equalizer / detector 201 and the demodulator / modulator 202, which is the case for example for a turbo equalizer / detector of the LMMSE IC type. This turbo receiver is available in several variants depending on the type of soft return used: either the LLR bits AP of the decoder are used to calculate the soft symbols, or the soft return is calculated according to the method of propagation of expectation. In the second case, it is necessary to use a lookup table to estimate the soft symbols EP and their average variance, - either the turbo receiver uses self-iterations between the equalizer / detector 201 and the demodulator / modulator 202, for example in the case of a turbo DFE receiver based on expectation propagation, equivalently called Self Iterated Linear Equalizer based on EP (SILE-EP). In this case it is necessary to use a look-up table to estimate the soft symbols EP and their average variance. This look-up table is generally a function of both the observations and the LLR bits AP coming from the decoder (through the value of the a priori average variance

[0056] First case: turbo receiver without self-iterations

[0057] This case was studied in the article by J. Ma, L. Liu, X. Yuan, L. Ping, “On orthogonal AMP in coded linear vector Systems”, IEEE Transactions on Wireless Communications, September 2019, in the context of MIMO transmissions. A LMMSE turbo-detector IC is presented, which uses a soft feedback EP calculated from the observations of the previous turbo iteration. The article also presents the case of a soft feedback calculated only from the LLR bits AP provided by the decoder.

[0058] The authors of this article noticed that the Mean Square Error of the EP returns of formula (14) can be used to have good predictions of the receiver performance in the case of large code words. The predictions are poorer for small or medium code words (of the order of a few hundred bits). Indeed, in the article, the MSEr. is evaluated at the input of the soft demodulator / modulator by generating symbols Xe obtained by a model with a white complex additive Gaussian noise of zero mean and variance v*: xe = x+ne where zf~XN(0,v$.). (3)

[0059] The LLR bits AP if from the decoder are considered as a simple function of Xe and Ve, because the extrinsic LLRs calculated by the soft demodulator / modulator do not take into account the a priori information coming from the previous turbo iteration, and are calculated only from Xe. Thus, with this assumption, the MSE of the EP symbols becomes a function of the single parameter and is denoted here as MSEX.( rj). This function can be evaluated by a Monte Carlo method, and tabulated in a lookup table as a function of 'x If this approach allows Indeed, while it reduces the implementation complexity of calculations, its drawback is that it only works well for long code words.

[0060] Second case: turbo-receiver with self-iterations

[0061] This case occurs for example in the case of a turbo DFE EP receiver. It is more complex than the previous one since the variance of the APP symbols is a function of both the current observations, the variance of the associated residual noise and the LLR AP bits provided by the decoder during the previous decoding iteration, i.e. the previous turbo-iteration.

[0062] Several approaches have been proposed in the literature to provide an alternative estimate to equation (5), calculated through equations (4).

[0063] A trivial approach would be to use the APP MSE of formula (13) by computing the expectation on the statistics of the sent symbols and the Gaussian noise, as in equation (16), but considering the LLR bits AP coming from the decoder as inputs to the function. In this case the APP MSE becomes a function with a multidimensional input depending on the LLR bits AP and the variance of the residual noise only, denoted MSE^^Z / , y® ) • This approach has the problem that if, for a BPSK constellation, only one LLR bits AP is needed, the vector L“ has Q = log^M entries for higher order constellations. Therefore, a direct tabulation of the APP variance as a function of the LLR values ​​is not efficient, since the dimension of the table will be Q + 1 and either a large memory or a large number of interpolation polynomials will be required to correctly represent this function.Moreover, the MSE APP depends on X of these iadc LLR bits AP vectors. We must therefore find a method to associate a single vector _£,“of LLR bits AP with the Æ vectors, under penalty of seeing the dimension of the table climb to QK + 1. .

[0064] The research community has carried out a number of works to address these issues. The article by S. §ahin, A. M. Cipriano, C. Poulliat and M.-L. Boucheret, "Evolution Analysis of Iterative BICM Receivers with Expectation Propagation over ISI Charnels" 2019 IEEE International Symposium on Information Theory (ISIT), Paris, France, 2019, pp. 166-170 uses tools from state evolution (which refers to an asymptotic performance prediction method, where "asymptotic" means that the method has an accuracy that improves as the sizes of the data blocks and code words tend to infinity) and analysis of extrinsic information transfer (EXIT) diagrams for the performance prediction of a turbo DFE EP receiver implemented in the frequency domain. The average APP variance is predicted using a function / where II is obtained fromof Vx by the Gaussian capacity curve (i.e. with a signal having purely Gaussian statistics without any constraints) calculated offline with the Monte Carlo method, and Ia is used to derive a Consistent Gaussian Approximation (CGA, where the random variable is approximated by a real Gaussian random variable that has a parametric description in terms of a single real parameter) of the LLR bits AP J? injected into the receiver model. However, the CGA becomes increasingly poorer as the number of turbo iterations increases, even in the case of a BPSK constellation. For higher-order constellations, the CGA of the LLRs may not be sufficiently accurate, even with few turbo iterations.In the asymptotic regime (where very long codewords of tens of thousands of bits are usually found), the prediction method proposed in this paper gives good accuracy, but this is not the case for short codewords. Moreover, for constellations other than BPSK and QPSK, if the CGA of the LLR AP bits is not sufficiently accurate, the calculation of and Ia will require multidimensional lookup tables.

[0065] To account for the finite size effects of the codewords, some work on a LMMSE-IC turbo receiver for MIMO communications with LTE turbo codes uses two-dimensional lookup tables to jointly model detection and decoding. These tables are generated based on a CGA for LLRs, and use the average mutual information Ia as input. They are generated by taking into account the finite size of the codes, but this method suffers from the inaccuracies related to the modeling of LLRs by a CGA.

[0066] In other works, the MSE EP of equation (14) is calculated with the Monte Carlo method. The LLR bits AP are generated according to a CGA, and therefore with a mean and a variance determined bijectively by the value Ia- The random variables are parameterized according to the a priori mutual information Ia- Thus, by averaging the MSE EP of equation (14) over the sent symbols, the noise, and the LLR bits AP, the MSE EP becomes a function of only two variables, denoted MSE^ir^ IA). This method also suffers from the consistent Gaussian assumption for the LLR bits AP on the coded bits generated by the turbo-decoder. Furthermore, to be able to use it, it is necessary to find a way to associate the LLR bits AP actually generated by the turbo-decoder for an entire codeword with a single value Ia-

[0067] Other works, such as those in the article by S. §ahm, A. M. Cipriano, C. Poulliat and M.-L. Boucheret, "Iterative Decision Feedback Equalization Using Online Prediction" IEEE Access, vol. 8, pp. 23638-23649, 2020, study the use of prediction in the context of EP-based time-domain DFE turbo equalization. This article shows that, in order to calculate the MSE APP of equation (13), the use of the Average AP variance of soft symbols generated with AP bit LLRs is more robust than other metrics, such as maximum likelihood estimation of the LLR mean. The values ​​of the average AP variances v* are generated according to formula (7) from AP bit LLRs generated as realizations of consistent Gaussian random variables (CGA is used). There is a one-to-one correspondence between the CGA used to generate AP bit LLRs and the average AP variance v£. Thus, the APP MSE of equation (13) is estimated by averaging over the sent symbols, the noise, and the AP binary LLRs. The APP MSE therefore becomes a function of only two variables, and is denoted MSE^ ( v£, Ç( ). This method also suffers from the inaccuracies associated with the use of CGA for LLRs.

[0068] Thus, patent application FR2315402 proposes to determine the correspondence tables between, on the one hand, the variance of residual noise at the demodulator input and the average AP variance of a priori soft symbols associated with a priori LLR bits provided by the decoder, and on the other hand, the EP cep coefficient by means of a computer simulation. This implementation makes it possible to use real AP LLR bits generated by a decoder rather than by a consistent Gaussian approximation, thus avoiding the problems linked to the parametric modeling of the probability density of the LLRs at the decoder output.

[0069] There is therefore a need for the definition of a method for determining correspondence tables implemented from a simulation. Summary of the invention

[0070] To this end, the present invention describes a method for determining a correspondence table between, on the one hand, a variance of input samples of a flexible demodulator and an a priori variance, AP, average v? of a priori flexible symbols associated with LLR bits AP supplied by a decoder, and on the other hand an EP coefficient cep used to calculate a signal xk and its associated variance at the output of a modulator in a turbo receiver.

[0071] The method according to the invention comprises the following steps: - a first step of implementing a computer simulation to determine, for a plurality of variance values ​​of the sets of LLR bits AP and corresponding average AP variance Vx, - a second classification step, for each variance value of the LLR bits AP in boxes defined by the corresponding average AP variance values ​​y?, - a third step of implementing a computer simulation to generate a two-dimensional correspondence table of APP variances having as inputs the variance and the average AP variance Vx, and as output an average a posteriori variance (or average APP variance) using the correspondences between average AP variance vf and variance calculated during the first step on the one hand, and the correspondences between LLR bits AP and average AP variance Vj calculated during the second step on the other hand, - a fourth step of calculating the cep coefficient for a plurality of variance values ​​and average AP variance using the two-dimensional correspondence table calculated during the third step with:

[0072] , ,P TA- El x, x'

[0073] According to an embodiment of the method for determining a correspondence table according to the invention, the first step of implementing a computer simulation to determine, for a plurality of variance values ​​of the sets of LLR bits AP and of corresponding average AP variances Vx comprises, for each variance value: - a sub-step of generating a symbol vector with k = 1, generated according to a particular modulation and coding scheme, - a sub-step of adding a noise of variance vx to the symbols x*, to form a vector of input samples X^ with k = 1, K, - a soft demodulation sub-step of the input samples xk, in order to obtain extrinsic LLR bits L^d^, - a sub-step of decoding the extrinsic LLRbits Le{dk\ in order to obtain LLR bits AP r (al - a sub-step of calculating LLR symbols AP logn^la) from the LLR bits AP for each a belonging to the constellation of the modulation and coding scheme, - a sub-step of calculating mass probabilities H*.( a ) of the symbols a of the constellation of the modulation and coding scheme, from the LLR symbols AP lOgnk ( a ), - a sub-step of calculating soft symbols AP x% and calculating their instantaneous variance from the mass probabilities a), - a sub-step of calculating an average AP variance measure from the variances v^.

[0074] According to an embodiment of a method for determining a correspondence table according to the invention, the third step of implementing a computer simulation to generate a two-dimensional APP variance correspondence table having as inputs a variance Vx and an average AP variance ?x, and as output an average APP variance includes: - a sub-step of generating a symbol vector with k = 1, K, generated according to a particular modulation and coding scheme, - a sub-step of adding a noise of variance ^x to the symbols to form a vector of observations with k = 1, ..., K, - a sub-step of choosing a realization of LLR bits AP La{d) as a function of V? in the classification of LLR bits AP carried out during the second step, a sub-step of calculating LLR symbols AP logll^a ) from the LLR bits AP Ljjd), for each a belonging to the constellation of the scheme of

[0075]

[0076]

[0077]

[0078]

[0079]

[0080] modulation and coding, - a sub-step of calculating likelihoods Ffe(a) from the input samples Xe and the variance ^x, - a sub-step of calculating LLR symbols APP Lk{a) with: - a sub-step of converting the LLR symbols APP Lk(a) into probability mass of the symbols APP AÆ( «) according to the formula: A / S y - sub-steps of calculating APP soft symbols and calculating their instantaneous variances ydxk, according to the formulas: / _ 'VJ< 1___ 'k' ~ £^8 / «) ~ ' = Jal 2 HAS t ( <z) -1F, fx,k "Æi * ■ F k I - a sub-step of calculating the average APP variance j for the iteration f'xVV n, with: - a sub-step of carrying out Na iterations of the previous sub-steps, with Na > 1, and determining an average APP variance yd from the average APP variances wLA ' aA 7 According to one embodiment of a method for determining a correspondence table according to the invention, the sub-step of determining a variance Mean APP from Mean APP Variances Mean APP includes calculating the average of the largest mean APP variance values ​​( n ), with Nh <Na-

[0081] According to different embodiments of a method for determining a correspondence table according to the invention, the LLR bits AP can be signed or unsigned.

[0082] The invention also relates to a computer program product comprising program code instructions recorded on a computer-readable medium, for implementing the steps of the method for determining a correspondence table according to an embodiment of the invention when said computer program is executed on a computer. It also relates to a computer-readable recording medium, on which is recorded a computer program comprising program code instructions for executing the steps of the method for determining a correspondence table according to an embodiment of the invention. Brief description of the drawings

[0083] The invention will be better understood and other characteristics, details and advantages will appear more clearly on reading the following description, given without limitation, and thanks to the appended figures, given by way of example.

[0084] [Fig.l] [Fig.l] represents very roughly the key elements of a transmission chain for digital radio communications equipment.

[0085] [Fig.2] [Fig.2] represents very roughly the key elements of a reception chain for a turbo receiver.

[0086] [Fig.3] [Fig.3] schematically represents the structure of a flexible demodulator / modulator with expectation propagation according to the state of the art.

[0087] [Fig.4] [Fig.4] schematically represents the structure of a flexible demodulator / modulator with expectation propagation according to patent application FR2315402.

[0088] [Fig.5] [Fig.5] is a block diagram of an embodiment of a method for determining a correspondence table according to the invention.

[0089] [Fig.6] [Fig.6] represents, in the form of a block diagram, an embodiment of the first step of the method for determining a correspondence table according to the invention.

[0090] [Fig.7] [Fig.7] represents, in the form of a block diagram, an embodiment of the second step of the method for determining a correspondence table according to the invention.

[0091] [Fig.8] [Fig.8] represents, in the form of a block diagram, an embodiment of the third step of the method for determining a correspondence table according to the invention.

[0092] [Fig.9] [Fig.9] represents three examples of variance correspondence tables APPs obtained by different embodiments of the invention.

[0093] [Fig. 10] Figure 10 represents three examples of correspondence tables of the EP cep coefficients obtained by different embodiments of the invention.

[0094] Identical references may be used in different figures when they designate identical or comparable elements. Description of the embodiments

[0095] The invention relates to the definition of a method for determining a correspondence table between, on the one hand, the variance of residual noise at the demodulator input and the average AP variance Vy of a priori soft symbols associated with a priori LLR bits provided by the decoder, and on the other hand, the EP coefficient cep used to implement the Gaussian division in a soft modulator of a turbo receiver. Subsequently, it is called the cpp correspondence table.

[0096] The method is defined in the form of a block diagram in [Fig.5].

[0097] It firstly comprises a first step 501 of determining, for a plurality of values ​​of variances of sets of LLR bits AP and of corresponding average AP variances.

[0098] This step is implemented by a computer simulation carried out by any digital calculation means, typically a microprocessor, but also a DSP (English acronym for Digital Signal Processor), an FPGA (English acronym for Field Programmable Gate Array), an ASIC (English acronym for Application-Specific Integrated Circuit), or any combination of these means or hardware components.

[0099] This step consists of using a simulation chain to generate a priori (AP) LLR bits from the decoder and, for each set of AP LLR bits, calculating the corresponding average AP variances Vx, then storing these quantities in two databases: one for the AP LLR bits, and the other for the average AP variances. In these databases, the set of AP LLR bits and the correspondents are associated with the realization of the symbols sent and the noise used to generate the observations.

[0100] Step 501 comprises a set of sub-steps represented in [Fig.6] in the form of a block diagram.

[0101] First, a vector (or block) of K symbols x is generated according to a particular modulation and coding scheme (MCS). The symbols are designated xk, with k = 1, K. This step is implemented by a modulation and coding block 601, which generates sequences of bits coded by an error-correcting coder whose configuration is compatible with that of the turbo receiver decoder (i.e. same code type, for example turbo code or LDPC code, same code word size and throughput configuration, etc.), and modulated according to a constellation corresponding to the constellation implemented by the turbo receiver. Optionally, the coded bits can be interleaved, punctured and / or repeated (this is the case in particular for rate matching in the 3GPP standard). It is possible for a code word to occupy several blocks of symbols.

[0102] At 602, a noise of variance >4 is added to the symbols x, for example a white noise following a Gaussian model. The resulting noisy samples are called input samples, and are denoted Xe. The variance »4 can also be seen as the variance of the samples Xe conditioned on the fact that the emitted symbols are equal to x, and therefore models the variance of the residual noise which affects the emitted symbols x at the input of the soft demodulator. In the following we will use a more concise name by also calling >4 the variance of the input samples (of the soft demodulator).

[0103] In order to determine sets of LLR bits AP and average AP variances Vy associated with a plurality of variance values ​​'4, the simulation steps must be executed for each targeted value of >4.

[0104] For a given value *4, a large number N r of input vectors x4' can be generated. By large, we mean several hundred or even several thousand vectors, for example Nr = 5000 or more.

[0105] Step 501 then comprises a soft demodulation sub-step 603 of the input samples Xe, in order to determine extrinsic LLR bits Lg^d^ , with k = 1, ..., K. This block is identical to block 402 of Figure 4, and must implement the same calculation algorithm as that implemented in the turbo receiver. It takes as input a vector of input samples Xe and the corresponding variance *4.

[0106] Step 501 then comprises a decoding sub-step 604, by a decoder accepting the soft inputs and providing soft outputs (in English SISO for Soft Input Soft Outputf of the LLR extrinsic bits L^d^), after implementing deinterlacing, depunching, and / or summation processing when the inverse operations have been carried out in block 601. The sequence and the exact content of these processings depend on the communications system in question, and on the way in which the transmitter is implemented.

[0107] Since the decoder operates by code words, when a code word covers several input sample vectors, which can happen for long code words, it is necessary to save the extrinsic LLR bits calculated from multiple input sample vectors Xe to implement decoding. Conversely, for short codewords, multiple codewords can be covered by a single input sample vector.

[0108] The rest of the simulation can be carried out:

[0109] - either by considering each of the code words independently, in order to determine an average AP variance specific to each code word,

[0110] - either by considering blocks of decoded LLR bits of homogeneous size K with the size of the input sample vectors, in order to determine an average AP variance vÇ for each input sample vector emitted.

[0111] In the remainder of the description, the first choice has been retained, but the method can easily be adapted to operate according to the second choice.

[0112] Step 504 of the method according to the invention therefore produces coded LLR bits (which can be extrinsic or APP from the point of view of the code), considered as LLR bits AP For all 'cs ct for all the input sample vectors occupied by the code word.

[0113] For each code word, the LLR bits AP are saved in the database 611, and the associated average AP variance v£ is saved in the database 612. These databases make it possible to keep a memory of the correspondence link between a set of LLR bits AP of a code word and its corresponding average AP variance. For example, the two quantities can be saved at the same entry index in the two databases, so that it is possible to identify the value of the average AP variance in 612 from a set of LLR bits AP selected in the database 611, and vice versa.

[0114] The remainder of step 501 of the method for determining a cef correspondence table according to an embodiment of the invention corresponds to flexible modulation processing 605 of the LLR bits AP La(d^ provided by the decoder for the entire code word.

[0115] This flexible modulation first comprises the calculation 606 of LLRs symbols AP logll^( « ) from the LLR bits AP using the formula: [01161 108^) = -^^(0)1.,(¼). € Vk=L...,K

[0117] Then, in 607, the mass probabilities 1^(a) of the a priori symbols are calculated, for each index k and in linear scale, according to the formula:

[0118] n*O) =^0) / ^ / 1^ VaeZ, € € yk=L...,K.

[0119] Finally, soft symbols AP and their instantaneous variance vpxJi are calculated at 608 and 609 according to the formulas of equation (6).

[0120] Step 501 of the method for determining a cep correspondence table according to an embodiment of the invention then comprises a sub-step of calculating the average AP variance v£ over the entire code word by the formula given in equation (7).

[0121] These sub-steps make it possible to establish the value of the average AP variance on a code word realization, for an average AP variance of input samples Vx, and for the set of LLR AP bits generated by the decoder for this same code word. The set of LLR AP bits is saved in the database 611 and the average AP variance in the database 612, taking care to keep the link between these two quantities. These sub-steps are iterated several times for each value of Vx, in order to constitute significant databases 611 and 612, i.e. which contain a significant number of realizations of LLR AP bits and average AP variances, in the range of significant values ​​for this quantity for the given Vx and for the operating points targeted by the communication system.To enrich these databases it is possible, for any Vx, to repeat the simulation for modulation and coding schemes having the same constellations but different coding rates, in order to cover a wide spectrum of values ​​of the average AP variance and the AP LLR bits.

[0122] Step 501 therefore makes it possible to associate sets of LLR AP bits and average AP variances with input sample variance values, and to save these values.

[0123] Two types of LLR AP bits can be generated and stored: - unsigned (or uninformed) AP LLR bits: in this case, no knowledge about the coded bits sent is necessary, and the LLR database only stores the AP LLR bits as calculated by the decoder. These LLRs are realizations of an ergodic stochastic process where the bits sent are random, the probability density (PDF) of the LLR AP bits is an even function, that is, positive and negative LLR values ​​have the same probabilities; - signed (or informed) AP bit LLRs: in this case, knowledge of the coded bits sent is available. If j (j} is the AP LLR of bit dk„, the signed AP bit LLR stored in the database is Q _ pj. These LLRs are realizations of a PDF that would be generated by sending only bits equal to 1, since the LLRs of bits 0 have their sign reversed.

[0124] These two types of LLR produce different look-up tables. For modulation and coding schemes with medium or low spectral efficiency, cep coefficient look-up tables generated with signed AP bit LLRs give better performance. For modulation and coding schemes with medium or high spectral efficiency, cep coefficient look-up tables generated with unsigned AP bit LLRs give better performance. It is important to simulate a sufficiently high number of realizations of over the entire significant range of v£ values, this range depending on the choice of modulation and coding scheme. In addition, the distribution of LLRs at the decoder output may also depend on the coding rate.The inventors observed that LLRs generated using a modulation and coding scheme associated with a given code rate also give very good results for modulation and coding schemes using the same modulation with a different code rate. Thus, a single effort per constellation can be made for the generation of the look-up tables (as long as the codeword sizes are not too different).

[0125] The method for determining a correspondence table of the vine stocks according to an embodiment of the invention then comprises a classification step 502, for each variance value of the LLR bits AP in boxes defined by the corresponding average AP variance values ​​v?.

[0126] This step aims to group the LLR bits AP into bins defined by the values ​​v^. For this, a grid of values ​​is fixed. Advantageously, this grid is given in logarithmic scale (base 10 or base 2 for example), for example a scale going from -24.5 dB to 0 dB with a step of 0.5 dB.

[0127] For each box L v ) of the value grid, the database 612 L'»' yn+ V constructed at the end of the first step 501 of the method according to the invention is traversed to identify all the values ​​of the average variance AP located in the box. The indexes of vp eyj are used to extract the corresponding LLR bit AP vectors in the database 611 constructed in the first step 501. These vectors are therefore associated with the n-th box of identified by the central value of the interval of the box L, „ i.e. C, . i / o. This way of proceeding makes it possible to construct a database of LLR vectors indexed on vJ.

[0128] Figure 7 schematically represents the operations carried out in an embodiment of the second step 502 of the method for determining a vine table according to the invention.

[0129] We see the grid 701 of values ​​of v^. For each box of the grid, such as box 702, the database 612 is searched to determine the corresponding indexes in the base 611 of the LLR bits AP. These LLR bits AP are then associated with box 702.

[0130] At the end of this step, each box contains realizations of LLR bits AP leading to realizations which differ at most from the size of the box (in our case 0.5 dB). If the size of the box is small, the realizations of the LLR bits AP lead to substantially the same v£. It is important to note that the realizations of the LLR bits AP of the same box can come from different noise variances Vx. This classification of the LLR bits AP is specific to a type of modulation and a type of LLR bits AP (signed or unsigned).

[0131] The method for determining a correspondence table of the vine stocks according to an embodiment of the invention then comprises a third step 503 of implementing a computer simulation to generate a two-dimensional correspondence table having as inputs a variance and an average AP variance Vx, and as output an average APP variance y^. This will subsequently be referred to as a correspondence table of the APP variances. This step is implemented using the correspondences between average AP variance v* and variance vx calculated during step 501 on the one hand, and the correspondences between LLR bits AP and average AP variance calculated during step 502 on the other hand.

[0132] An advantageous embodiment of this APP variance correspondence table consists in establishing it in the logarithmic domain, base 10 or 2, due to the large dynamic range of the input quantities. The grid step for v* must be the same as that of the LLR bits AP database indexed on the average AP variance v£. For it can be different, the choice of a small step leading to a greater memory occupation but making it possible not to have to use interpolation routines between the points of the correspondence table, a large step requiring the addition of interpolation routines to the outputs of the table.

[0133] For each box 0*, vJ), a large number of realizations of mean APP variance measurements must be carried out, so as to make the measurement statistically reliable. With Na the number of realizations of the mean APP variance calculated for each box, for example Na = 5000.

[0134] For each box of the two-dimensional grid, therefore for each value of v% and the procedure for generating Na variance average APP is described in relation to [Fig.8]. The idea is to inject: - on the one hand observations created according to a Gaussian model having a variance 'l,

[0135]

[0136]

[0137]

[0138]

[0139] - on the other hand LLR bits AP representative of the receiver decoding functions, recovered from a database indexed on v£, in a module 800 which performs the exact calculations of a flexible EP modulator, and which provides average APP variances as output. The average APP variances thus created are representative of the behavior of the flexible EP modulator and can be processed to form a correspondence table representing the behavior of the flexible modulator with respect to the average APP variances. Step 503 of the method for determining a correspondence table of the vines of the invention therefore comprises, for a plurality Na of embodiments: - a sub-step 801 of generation of a vector of symbols xk, with k = 1, ... A. in accordance with a particular modulation and coding scheme, - a sub-step 802 of adding a noise ne of variance to the symbols x\ to form a vector of observations x^ with k = 1, ..., K. The samples Xe are independent and identically distributed, and follow the Gaussian model described in equation (15). They are generated in a manner comparable to what is done during the first step 510, - a sub-step of choosing a realization of the LLR bits AP La(d} in the box of the database 803 constructed during step 502 of the method, indexed by the value The size of the LLR bits AP can be adapted to the size of the block of input samples. If the number of vectors of the LLR bits AP in the box is less than Na, it is possible to reselect vectors of LLR bits AP previously chosen, for example by looping over the available vectors. These LLR bits AP can be signed or unsigned, - a sub-step 804 for calculating LLR symbols AP Lk(a) - logll^.( a ), in an identical manner to that described in connection with block 606 of [Fig.5], - a sub-step 805 for calculating likelihoods a ) from the input samples Xe and the variance of the residual noise according to the formula: Vit (d ) ~ , tZ E 2L. where kp^ = 2 for constellations of type PAM, BPSK, n / 2-PKSK, and Apam = 1 otherwise, - a sub-step of calculation 806 of LLR symbols APP Lk(a) with: Lk(a) = Vk(a)+Lk(a), - a sub-step 807 of converting the LLR symbols APP Lk(a) into mass probability of the symbols APP At(a) according to the formula given in equation (3), 808 calculation sub-steps, for each of APP flexible symbols and calculation 809 of their instantaneous variances according to the given formulas to equation (4), a sub-step of calculation 810 of the realizations of the variance AP average over the entire index codeword with formula (5).

[0140] The achievements Na, are stored in the box

[0141]

[0142]

[0143]

[0144]

[0145]

[0146]

[0147]

[0148] fl) of the two-dimensional correspondence table, subsequently called 1¾ H) denotes a two-dimensional broad-mean APP variance lookup table, whether obtained using signed or unsigned AP LLR bits. The MSE of the APP soft symbols in equation (13) can therefore be seen as a function of *1 and il, and be estimated by averaging the APP variance realizations averaged over a large number Na as follows: The MSEx;.(v£, v£) can be used as an estimator of the mean APP variance y^. Let us denote by p4°) / y / ' pe \ the same set p* ( yP, y^ ) but with the elements classified in decreasing order according to the increasing index n. The y^(n) are all between 0 and 1 for constellations with energy normalized to 1. Thus, According to an advantageous embodiment of the invention, the average APP variance is estimated by taking the average of the N largest values ​​y^ ( n ) in p / (o) ( yp j for each *1: ^( / / )^(11,11). This y^) can be used as an estimator of the mean APP variance y^. This embodiment produces increasingly conservative APP variance estimates as Ω decreases. It can be applied to lookup tables made from signed or unsigned LLR AP bits. The resulting APP variance lookup tables depend on the modulation and coding scheme constellation, as well as the code parameters for generating the LLR AP bits.

[0149] Figure 9 gives an example with three APP variance lookup tables that can be used to estimate the mean APP variance. All three tables were calculated using Na = 5000.

[0150]

[0151]

[0152]

[0153]

[0154]

[0155]

[0156]

[0157] Table 901 is generated with unsigned AP LLR bits. Table 902 is generated with signed AP LLR bits. Table 903 is generated with signed AP LLR bits, selecting the 28 highest average APP variance values ​​(only when prior information is present). It is observed that when unsigned AP LLR bits are used for the generation of the APP variance lookup table 901, the APP MSE is quite high for small values ​​of v£ and This is because the AP LLR bits may be inconsistent with the observation, since no knowledge about the sent bit is used. Therefore, the soft modulator, which has safe observations and at the same time safe AP information that is sometimes inconsistent, calculates a very pessimistic APP variance. When signed AP LLR bits are used to generate the APP variance lookup table 902, the sign of the LLRs is determined by the bits sent. Thus, in general, when an observation is good (small), the AP LLR bits do not conflict with them, especially when is small. The APP variance is small in this case. Finally, the case using signed AP bits LLR and = 128 gives mean APP variance estimates 903 a little more pessimistic than those of the APP 902 variance correspondence table. The method of determining a correspondence table of the vines according to a mode embodiment of the invention finally comprises a step 504 of calculating the cep coefficient for a plurality of variance values ​​and average AP variance Vy. Let us note a correspondence table of the APP variance, whatever the how it is implemented. Then the correspondence table of the EP cep coefficients is derived by calculating: (16) The preferred implementation of this lookup table uses linear scale output and logarithmic scale inputs. Figure 10 shows examples of such a Cep correspondence table, in the case of 8-PSK modulation, always for Na = 5000 realizations. The three cases illustrated correspond to those of Figure 9, namely a two-dimensional correspondence table of EP coefficients generated with: unsigned AP LLR bits (1001), signed AP LLR bits (1002), and signed AP LLR bits and an estimate on the Nh = 128 highest values ​​of average APP variance (1003) (only when the a priori information is present).

[0158] The EP coefficient is generally close to zero when is small, i.e., when the a priori information is reliable, and the EP soft symbols are quite close to the APP soft symbols. However, especially for unsigned AP LLR bits, the coefficient is high even for low vJ and , thus showing the effect of conflicting AP information (as explained previously, for the APP variance lookup table).

[0159] In practice, only the EP coefficient lookup table is used in the turbo receiver. This table has the advantage of having a linear scale output, smooth behavior, and controlled dynamics depending on the constellation. In principle, it is possible to implement it by approximating it for example with polynomials. This implementation can be interesting if the polynomials are not too high in degree, which would reduce the memory footprint by increasing the calculations. However, if the fast storage memory of the receiver is sufficient, it is more advantageous to store the values ​​of the EP coefficient lookup table on a sufficiently dense input grid, so as not to have to interpolate the values, or to use a simple linear interpolation.

[0160] The method for determining a correspondence table of the EP cep coefficients according to the invention applies to the determination of correspondence tables for a turbo receiver such as that described in patent application FR2315402. Such a table is specific to a constellation. It also applies to any other type of turbo receiver as long as it requires the establishment of a reliable relationship between the variance Vx of input samples, the average variance AP Vx of soft symbols AP obtained from LLR bits established by the decoder, and the cep coefficient.

[0161] The invention relates to the method of determining the tables itself, as well as to the tables determined from the method.

[0162] It also relates to a computer program product comprising code instructions for executing the method, and to a recording medium, or storage device, such as for example a CD, a USB key (English acronym for Universal Serial Bus, or universal serial bus) or an SSD memory (English acronym for Solid State Drive), comprising the code instructions for executing the computer program product.

Claims

Claims

1. Method for determining a correspondence table between, on the one hand, a variance of input samples of a soft demodulator (204) and an a priori variance, AP, average Vx of a priori soft symbols associated with LLR bits AP supplied by a decoder (203), and on the other hand a coefficient EP used to calculate a signal x*k and its associated variance at the output of a modulator (205) in a turbo receiver, characterized in that the method comprises the following steps: - a first step (501) of implementing a computer simulation to determine, for a plurality of variance values *1, sets of LLR bits AP and corresponding average variance AP, - a second step (502) of classifying, for each variance value ^r, the LLR bits AP into boxes defined by the corresponding average variance AP values,- a third step (503) of implementing a computer simulation to generate a two-dimensional correspondence table of the APP variances having as inputs the variance and the mean AP variance and as output an a posteriori variance, APP, mean y^, using the correspondences between mean AP variance v? and variance *1 calculated during the first step (501) on the one hand, and the correspondences between LLR bits AP and mean AP variance Vx calculated during the second step (502) on the other hand, - a fourth step (504) of calculating the coefficient cep for a plurality of values of variance and mean AP variance v£, using the two-dimensional correspondence table calculated during the third step (503), with: cEP(vln) -,

2. Method for determining a correspondence table according to claim 1, in which the first step (501) of implementing a computer simulation to determine, for a

3. plurality of variance values of the sets of LLR bits AP and corresponding average AP variances comprises, for each variance value Ÿx: - a sub-step of generation (601) of a vector of K symbols xk with...K.generated in accordance with a particular modulation and coding scheme, - a sub-step of adding a noise (602) of variance to the symbols to form a vector of input samples *1, with k = I, ..., K, - a soft demodulation sub-step (603) of the input samples in order to obtain extrinsic LLR bits - a decoding sub-step (604) of the extrinsic LLR bits sLe(dk), in order to obtain LLR bits AP - a sub-step of calculating (606) LLR symbols AP logüt( a) from the LLR bits AP for each aa belonging to the constellation of the modulation and coding scheme, - a sub-step of calculating (607) the mass probabilities nfc(a) of the symbols a of the constellation of the modulation and coding scheme, from the LLR symbols AP logHk(a), - a sub-step of calculating (608) soft symbols AP x^ and calculating (609) their instantaneous variance from the mass probabilities nfc(a), - a sub-step of calculating (610) a measure of average AP variance v% from the variances v?k. Method for determining a correspondence table according to one of the preceding claims, in which the third step (503) of implementing a computer simulation to generate a two-dimensional correspondence table having as inputs a variance and an average AP variance and as output an average APP variance comprises: - a sub-step of generation (801) of a vector of K symbols xk with k — 1, .... A. generated in accordance with a particular modulation and coding scheme, - a sub-step of adding noise (802) of variance *1 to the XL symbols to form a vector of observations with . ,K, - a sub-step of choosing a realization of LLR bits AP LAd) according to the classification (803) of the LL R bits AP carried out during the second step (502), - a sub-step of calculation (804) of LLR symbols AP logll^( « ) from the LLR bits AP For each aa belonging to the constellation of the modulation and coding scheme, - a sub-step of calculating (805) likelihoods ^((z) from the input samples Xe and the variance - a calculation sub-step (806) of LLR symbols APP with: ^(«) = ^(«) + Lk{a}, - a sub-step of conversion (807) of the LLR symbols APP Lk (a) into mass probability of the symbols APP Àk (a) according to the formula: HAS Æ (has) y. sub-steps of calculating (808) soft symbols APP and calculating (809) their instantaneous variances sel we formulate them: èk(a) - a sub-step of calculation (810) of the average APP variance For iteration 11. with: yM y. vd - a sub-step of carrying out Na iterations of the previous sub-steps, with Na > 1, and determining an average APP variance from the average APP variances s

4. Method for determining a correspondence table according to the preceding claim, in which the sub-step of determining an average APP variance from the average APP variances comprises calculating the average of the largest average APP variance values yd(n), with

5. Method for determining a correspondence table according to one of the preceding claims, in which the LLR bits AP are signed.

6. Method for determining a correspondence table according to one of claims 1 to 4, in which the LLR bits AP are unsigned.

7. Computer program product comprising program code instructions recorded on a computer-readable medium, for implementing the steps of the method for determining a correspondence table according to one of claims 1 to 6 when said computer program is executed on a computer.

8. A computer-readable recording medium on which is recorded a computer program comprising program code instructions for executing the steps of the method for determining a correspondence table according to one of claims 1 to 6.

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