This paper tackles the challenge of detecting unreliable behavior in regression algorithms, which may arise from intrinsic variability (e.g., aleatoric uncertainty) or modeling errors (e.g., model uncertainty). First, we formally introduce the notion of unreliability in regression, i.e., when the output of the regressor exceeds a specified discrepancy (or error). Then, using powerful tools for probabilistic modeling, we estimate the discrepancy density, and we measure its statistical diversity using our proposed metric for statistical dissimilarity. In turn, this allows us to derive a data-driven score that expresses the uncertainty of the regression outcome. We show empirical improvements in error detection for multiple regression tasks, consistently outperforming popular baseline approaches, and contributing to the broader field of uncertainty quantification and safe machine learning systems.

Deep neural networks (DNNs) are very efficient at object recognition but sometimes have an overestimated reliability for erroneous decisions. It is therefore very important to check if the distribution of images to be processed matches that of the training set. This has been studied as out-of-distribution (OoD) detection. This paper proposes an algorithm allowing classification as well as OoD detection, based on the generative classifier (GC) paradigm.While a discriminative classifier (DC) learns p(y|x) to achieve classification and a generative network learns p(x) to achieve OoD detection, the GC learns p(x|y) to achieve classification as well as OoD detection. Since generative models such as variational auto-encoders (VAEs) show good performance for unsupervised OoD detection, we propose to structure the latent variable of a VAE with a gaussian mixture model (GMM) while building a GC. The proposed model1is shown to outperform classical approaches based on DCs for far OoD and generative adversarial network (GAN) based models for near OoD without losing any performance for the classification task.

Radar and wireless communication coexistence is considered in this paper as a possible solution to face the exploding demand and rising congestion in wireless networks. The transmission medium is modeled as an AWGN channel with additive radar interference. Standard constellations are not optimal in this context, and an auto-encoder (AE) is used to design proper constellations and corresponding receiver devices. AE is a powerful tool in neural networks that shares strong similarities with communication systems. This technique is particularly relevant in the lack of an analytical expression of the loss function. In the asymptotic region (high interference regime), the optimal constellation shape is known and the AE always converges toward this optimal solution. In the other regions, the AE is able to yield solutions that outperform the standard configurations. Several demapping alternatives are also considered leading to the conclusion that it is possible to maintain the communication link in the presence of radar interference independently of the interference power. This is a step further compared with previous works in which solutions were limited to low or high interference regimes.

The non-orthogonal multiple access (NOMA) technique is considered as a key component for the next generation cellular system. In downlink NOMA, the constellation of several users are superposed for transmission. The resulting super-constellation needs to be carefully designed for allowing recovering of the data at the receiver side. A deep learning method for constellation optimization is proposed here in the context of downlink NOMA communications. The method is based on an analogy between auto-encoders, a powerful tool in neural networks, and communication systems. Simulation results have verified the effectiveness of this method for both constellation design and optimization of the individual receivers of the users. The optimized encoder/decoder can be successfully combined with iterative error-correction devices such as turbo-codes or LDPC and can be integrated in current communication systems. This technique is quite general and can be used for point-to-point communication as well as for multi-user access under various channel conditions.

This paper studies secure communication based on incremental redundancy (INR) secure hybrid automatic retransmission request (HARQ) protocol over block-fading wiretap channels. The transmitter has no instantaneous channel state information (CSI) available from either main channel or the eavesdropper channel, hence the coding rates cannot be adapted to instantaneous channel conditions. We investigate the outage performance for two schemes of INR secure HARQ protocols: case 1) when there exists two reliable multibit feedback channels from both legitimate receiver and eavesdropper to the transmitter carrying a function of outdated CSI, and case 2) when there is a multibit feedback channel only from legitimate receiver. In both cases, we demonstrate that using the information carried via multibit feedback channels, the transmitter can adapt the coding rates in order to achieve a better secrecy throughput using a smaller number of transmissions comparing to the ACK/NACK feedback channel model. For some parameters, our rate adaptation protocol achieves a strictly positive secrecy throughput whereas it is equal to zero for the protocol with ACK/NACK feedback. We show that for some set of parameters, the loss of secrecy throughput between case 1 and case 2 is very small compared to the gain provided by both protocols.

Iterative decoding is an efficient error-correction tool based on the exchange of extrinsic probabilities between the constituent decoders. In this paper, the properties of the mutual information between the extrinsic LLR at the output of two constituent decoders are analyzed with application to turbo and LDPC codes. This is a bridge between information-theoretic analysis and practical implementations. It is proved here that the mutual information between extrinsics is a lower bound of the mutual information between each extrinsic and the transmitted message. In addition, an efficient online evaluation is provided in the paper with accuracy validated through numerical experiments. As an application, the mutual information between extrinsics is used for designing efficient stopping criterion and error detection rules at the decoder side. Two online methods for the estimation of optimal scaling factor to be applied to the extrinsic LLR are also derived. In contrast with most references, an analytical expression is obtained that does not require estimation of the actual transmitted bits. All results in the paper are derived for Gaussian distributed LLR with independent mean and variance.

This paper considers the Broadcast Channel with Confidential Message (BCCM) where the sender attempts to send altogether a common message to two receivers and a confidential message to one of them. The achievable rate regions are derived for the power-constrained Gaussian BCCM with finite input alphabet using various transmission strategies. Namely, time sharing, superposition modulation and superposition coding are used as broadcast strategies. For superposition modulation and superposition coding, the maximal achievable rate regions are obtained by maximizing over both constellation symbol positions and the joint probability distribution. The maximization of the secrecy rate for wiretap channels is also studied as a particular case of the BCCM problem. We compare the considered transmission strategies in terms of percentage gains in achievable rates. We concentrate on the impact of the finite alphabet constraint on achievable rates, and show that this constraint may change well known results obtained in the Gaussian case. We show also that the secrecy constraint can change the shape of the achievable rate region in superposition modulation used in some standards when symbols are equiprobable. On a more practical side, it is shown that a performance close to the optimum can be obtained by strategies with reduced complexity.

This paper investigates the maximization of the secrecy-achievable rate region for the Gaussian broadcast channel with confidential message (BCCM) using finite input constellations. The maximization is done jointly over symbol positions and their joint probabilities. The secrecy-achievable rate regions are given for various broadcast strategies which differ in their complexity of implementation. We compare these strategies in terms of improvement in achievable rates and we study the impact of finite input alphabet on the secrecy-achievable rates. It is shown that finite alphabet constraints may change well known results holding in the Gaussian case.

This paper studies the problem of finding the optimal route of a stream between the transmitter and the receiver in an ad hoc network while minimizing the total power consumption. The criterion is the minimum power, and the fact that the stream must reach its destination is used as a constraint. Compared to previous approaches, we introduce more flexibility by allowing the stream to be split between several intermediate destinations, and we do not use the specific approximations (mainly high SNR) required to make the problem convex. Therefore, the main difficulty is due to the non convexity of the problem. In this contribution, we address a simple situation (flat fading channels, constant during the optimization process, simple transmitters and receivers) in order to demonstrate some properties of the problem. Finally, we propose an algorithm which, at least in some cases, is able to overcome the non convexity. Illustrations of the path followed by the algorithm demonstrates that it is able to find the global optimum even is difficult cases.

Iterative decoding is considered in this paper from an optimization point of view. Starting from the optimal maximum likelihood decoding, a (tractable) approximate criterion is derived. The global maximum of the approximate criterion is analyzed: the maximum likelihood solution can be retrieved from the approximate criterion in some particular cases. The classical equations of turbo-decoders can be obtained as an instance of an hybrid Jacobi/Gauss-Seidel implementation of the iterative maximization for the tractable criterion. The extrinsics are a natural consequence of this implementation. In the simulation part, we show a practical application of these results.

Iterative decoding was not originally introduced as the solution to an optimization problem rendering the analysis of its convergence very difficult. In this paper, we investigate the link between iterative decoding and classical optimization techniques. We first show that iterative decoding can be rephrased as two embedded minimization processes involving the Fermi-Dirac distance. Based on this new formulation, an hybrid proximal point algorithm is first derived with the additional advantage of decreasing a desired criterion. In a second part, an hybrid minimum entropy algorithm is proposed with improved performance compared to the classical iterative decoding. Even if this paper focus on iterative decoding for BICM, the results can be applied to the large class of turbo-like decoders.

The paper first recalls the Blahut Arimoto algorithm for computing the capacity of arbitrary discrete memoryless channels, as an example of an iterative algorithm working with probability density estimates. Then, a geometrical interpretation of this algorithm based on projections onto linear and exponential families of probabilities is provided. Finally, this understanding allows also to propose to write the Blahut-Arimoto algorithm, as a true proximal point algorithm. it is shown that the corresponding version has an improved convergence rate, compared to the initial algorithm, as well as in comparison with other improved versions.

We propose a new decoding algorithm based on a cascade structure for impulsive noise correction in multicarrier systems such as orthogonal frequency division multiplexing (OFDM) based systems. This new cascade structure based algorithm has the advantage to lead on one hand to a reduced complexity implementation in an OFDM demodulator and on the other hand to overcome the lacks of other algorithms dedicated for impulsive noise correction. To do so, we start the derivation by investigating closed-form analytical expressions of the a priori probabilities used in hypotheses tests that are necessary for the different steps needed for the execution of the cascade structure based decoding algorithm. Such closed-form expressions for the a priori probabilities, result in efficient setups of the threshold values used for the execution of the decoding algorithm. Furthermore, we show that this cascade structure can be applied to efficiently cancel the impulsive noise in OFDM systems. As the clipping event, present in OFDM systems, can be seen as an additive impulsive noise, we prove that after introducing some minor modifications, we can apply the proposed cascade structure to significantly reduce the peak to average power ratio (PAPR) level in such systems. Simulation results are given to illustrate the usefulness of the proposed algorithm results in practical OFDM based communication systems such as Hiperlan 2.

OFDM systems traditionally perform channel estimation relying on known training sequences. However in wireless systems, performance and mobility can be further enhanced by operating semiblind channel estimation refinement between reference symbols. A channel tracking method based on a maximum a posteriori (MAP) version of the expectation-maximization (EM) algorithm and on a block representation of the channel variations has been proposed. It performs better than already existing recursive algorithms with the additional advantage of a linear arithmetic complexity. In this paper, we study the matrix governing the behaviour of this method. This leads to a practical rule for choosing optimally (with respect to the convergence rate) the unique parameter of the method. The proposed iterative procedure is applicable to both single carrier and OFDM systems. Simulations are presented in the context of 5 GHz WLANs, showing the practical interest of the method.

This paper presents a new view of the Bose-Chaudhuri-Hocquengem (BCH) code through the addition of some flexibility to the syndromes distribution in the transmitted sequence. In order to get this flexibility, we derive a necessary condition (NC) on the syndromes distribution for decoding BCH codes, which includes the already known Hartmann-Tzeng proposition. This NC is essentially deduced from the decoding process of BCH code, and is related to the locator polynomial and the requested constraints to guarantee a maximal error-correction capacity. The obtained results have the advantage to be applicable for any considered field (finite or not). Furthermore, we prove that when the correction capacity is equal to 2 or 3, the obtained NC becomes also sufficient. This result is very useful in some practical transmission systems such as orthogonal frequency-division multiplexing systems. Once the pilot tones considered in such systems verify the necessary and sufficient condition, it becomes possible to both reduce the peak-to-average-power rate and correct the impulse noise, present in such multicarrier systems. The usefulness of the presented analysis and the exploitation of the derived condition on the pilot tones distribution is illustrated by simulation results in the case of the Hiperlan2 system

OFDM systems traditionally perform channel coefficients estimation relying on known training sequences. However in wireless systems, performance and mobility can be further enhanced by operating semi-blind channel estimation refinement between reference symbols. A channel tracking method based on a MAP version of the expectation-maximization (EM) algorithm and on a block representation of channel variations has been proposed. It performs better than already existing recursive algorithms but have a quadratic complexity. In this paper, we propose a simplified MAP algorithm which has a linear complexity and we examine its convergence properties. This simplification is an adaptation of the one step late technique to the EM algorithm for MAP estimation. The proposed algorithm is applicable to both single carrier and OFDM systems. Simulations are presented in the context of 5 GHz WLANs, showing that this algorithm perform as well as the MAP version of the EM algorithm in the mobile environment, without any loss in performance in the static situation

A parallel between Reed-Solomon codes in the complex field and multicarrier transmission using orthogonal frequency-division multiplexing (OFDM) is first presented. This shows that when the signal is sent over some channel composed of Gaussian plus impulsive noise, the impulsive noise can be removed by a procedure similar to channel decoding, using information carried by the "syndrome." This result is first derived in a simple situation (oversampled discrete multitone, additive channel), which is merely of theoretical interest. In any case, consecutive zeros, in the output of the OFDM modulator, do not correspond to real subcarriers. Pilot tones are transmitted for synchronization or channel-estimation purposes. These pilot tones are generally scattered among the information ones. Our approach is to use these pilot tones as syndromes, in order to correct impulsive noise. We show that the correction capacity is conditioned by the position of these pilot tones in the transmitted sequence. A protection subsystem based on hypotheses tests is introduced after the decoding operation in order to detect malfunctions of this decoder. The efficiency of this technique is corroborated with simulations in the slightly modified Hiperlan2 context. Other extensions are then provided in order to increase the practical usefulness of the method.

Our work focuses on semi-blind equalization techniques when applied to GMSK-based mobile communication systems. Starting from the works developed in (F. Alberge et al, SPAWC'99), a new semi-blind block algorithm is proposed to provide reliable communication through a typical mobile multi-path channel. The algorithm is shown to have performance similar to that of the Viterbi algorithm in a fixed setting, while being more efficient in time-varying situations.

The similarity between Reed Solomon codes in the complex field and multicarrier (OFDM) systems can be useful to correct impulse noise. This similarity is best seen when the input of the IFFT in the OFDM modulator has some consecutive zeros. However, this case is merely of theoretical interest, since consecutive zeros, in the OFDM modulator, do not correspond to real subcarriers. However in many cases, pilot tones are generally scattered among the information subcarriers. Our approach is to use these pilot tones as syndromes in order to correct impulse noise. This paper presents a number of interesting results relating on the distribution of pilot tones in the emitted sequence, where we have a necessary condition under which a maximal correction capacity is guaranteed. This necessary condition is also sufficient in the two simple cases, where the correction capacity is 2 or 3. Efficiency of this technique is illustrated by simulations in the practical context of Hiperlan2.

In this contribution, we propose a cascade structure to improve the impulse noise cancellation algorithm that we have already presented in F. Abdelkefi, P. Duhamel and F. Alberge [2002]. The new structure of this decoding algorithm is easy to implement and reliable (several parameters can be obtained theoretically rather than tuned experimentally). We also show that this decoding algorithm can be used for eliminating impulse noise and for reducing the peak-to-average power ratio (PAPR) level. The efficiency of this technique is corroborated by simulations in the practical context of Hiperlan2.

In OFDM systems, pilot tones are emitted for synchronization or channel estimation purposes. These pilot tones are generally scattered among the information ones. Our approach is to use these pilot tones as syndromes, in order to correct impulse noise. We previously proposed (see Abdelkefi, F. et al., ISSPA, 2001) a decoding algorithm in three steps: (1) estimate the amount of impulse noise; (2) seek the location; (3) correct the errors. A protection subsystem was introduced after the decoding operation in order to detect malfunction. Indeed, we added a control step which is able to estimate carefully whether the decoding procedure has worked correctly. We now explain this a posteriori control which is based on the hypothesis test. This approach is new in impulse noise cancellation in multicarrier transmission. The efficiency of this technique is also corroborated with simulations in the practical context of HIPERLAN/2.

A block algorithm is presented to solve the joint blind channel identification and blind symbol estimation problem. It is based on a deterministic maximum likelihood (DML) method. A partial prior on the symbols is incorporated into the DML criterion in order to improve the estimation accuracy. We propose a test which permits to circumvent the local minima problem and which is pertinent for a large class of criteria. The structure of the block algorithm is well-suited for deriving recursive and adaptive versions. We prove that, in the noiseless case, the obtained recursive algorithm converges only towards the global minimum. Numerical results show that the prior on the symbols improves the accuracy of the estimators and brings robustness to the lack of channel diversity. At the same time, this method introduces fewer local minima than the use of a full prior.

Adaptive acoustic echo cancellation in stereophonic teleconferencing is a very demanding application. The characteristics are: a very large number of coefficients, non-stationary input (speech), (slowly) time-varying systems to be identified, plus the specific property that both stereo signals are intrinsically very correlated. Basic versions of stochastic gradient algorithms have difficulties in meeting these requirements. We show that, in a multichannel framework, only a combination of techniques can result in an algorithm which convergence is governed by a quasi-diagonal matrix. Simulations with data recorded in a conference room demonstrate the improvement in convergence of our algorithm compared to the LMS.