We investigate the application of the factor graph framework for blind joint channel estimation and symbol detection on time-variant linear inter-symbol interference channels. In particular, we consider the expectation maximization (EM) algorithm for maximum likelihood estimation, which typically suffers from high complexity as it requires the computation of the symbol-wise posterior distributions in every iteration. We address this issue by efficiently approximating the posteriors using the belief propagation (BP) algorithm on a suitable factor graph. By interweaving the iterations of BP and EM, the detection complexity can be further reduced to a single BP iteration per EM step. In addition, we propose a data-driven version of our algorithm that introduces momentum in the BP updates and learns a suitable EM parameter update schedule, thereby significantly improving the performance-complexity tradeoff with a few offline training samples. Our numerical experiments demonstrate the excellent performance of the proposed blind detector and show that it even outperforms coherent BP detection in high signal-to-noise scenarios.

Deep learning is envisioned to facilitate the operation of wireless receivers, with emerging architectures integrating deep neural networks (DNNs) with traditional modular receiver processing. While deep receivers were shown to operate reliably in complex settings for which they were trained, the dynamic nature of wireless communications gives rise to the need to repeatedly adapt deep receivers to channel variations. However, frequent re-training is costly and ineffective, while in practice, not every channel variation necessitates adaptation of the entire DNN. In this paper, we study concept drift detection for identifying when does a deep receiver no longer match the channel, enabling asynchronous adaptation, i.e., re-training only when necessary. We identify existing drift detection schemes from the machine learning literature that can be adapted for deep receivers in dynamic channels, and propose a novel soft-output detection mechanism tailored to the communication domain. Moreover, for deep receivers that preserve conventional modular receiver processing, we design modular drift detection mechanisms, that simultaneously identify when and which sub-module to re-train. The provided numerical studies show that even in a rapidly time-varying scenarios, asynchronous adaptation via modular drift detection dramatically reduces the number of trained parameters and re-training times, with little compromise on performance.

Polar codes have promising error-correction capabilities. Yet, decoding polar codes is often challenging, particularly with large blocks, with recently proposed decoders based on list-decoding or neural-decoding. The former applies multiple decoders, while the latter family learns to decode from data. In this work we introduce a novel polar decoder that combines list-decoding with neural-decoding, by forming an ensemble of multiple weighted belief-propagation (BP) decoders trained with different data. We employ the cyclic-redundancy check code as a proxy for combining the ensemble decoders and selecting the most-likely decoded word after inference, while facilitating real-time decoding. We evaluate our decoder over a wide range of polar codes lengths, empirically showing gains of around 0.25dB in frame-error rate. Our complexity and latency analysis shows that the number of operations approaches that of a single BP decoder at high SNR.

Recent years have witnessed growing interest in the application of deep neural networks (DNNs) for receiver design, which can potentially be applied in complex environments without relying on knowledge of the channel model. However, the dynamic nature of communication channels often leads to rapid distribution shifts, which may require periodically retraining. This paper formulates a data-efficient two-stage training method that facilitates rapid online adaptation. Our training mechanism uses a predictive meta-learning scheme to train rapidly from data corresponding to both current and past channel realizations. Our method is applicable to any deep neural network (DNN)-based receiver, and does not require transmission of new pilot data for training. To illustrate the proposed approach, we study DNN-aided receivers that utilize an interpretable model-based architecture, and introduce a modular training strategy based on predictive meta-learning. We demonstrate our techniques in simulations on a synthetic linear channel, a synthetic non-linear channel, and a COST 2100 channel. Our results demonstrate that the proposed online training scheme allows receivers to outperform previous techniques based on self-supervision and joint-learning by a margin of up to 2.5 dB in coded bit error rate in rapidly-varying scenarios.

Deep neural networks (DNNs) allow digital receivers to learn to operate in complex environments. To do so, DNNs should preferably be trained using large labeled data sets with a similar statistical relationship as the one under which they are to infer. For DNN-aided receivers, obtaining labeled data conventionally involves pilot signalling at the cost of reduced spectral efficiency, typically resulting in access to limited data sets. In this paper, we study how one can enrich a small set of labeled pilots data into a larger data set for training deep receivers. Motivated by the widespread use of data augmentation techniques for enriching visual and text data, we propose dedicated augmentation schemes that exploits the characteristics of digital communication data. We identify the key considerations in data augmentations for deep receivers as the need for domain orientation, class (constellation) diversity, and low complexity. Following these guidelines, we devise three complementing augmentations that exploit the geometric properties of digital constellations. Our combined augmentation approach builds on the merits of these different augmentations to synthesize reliable data from a momentary channel distribution, to be used for training deep receivers. Furthermore, we exploit previous channel realizations to increase the reliability of the augmented samples. The superiority of our approach is numerically evaluated for training several deep receiver architectures in different channel conditions. We consider both linear and non-linear synthetic channels, as well as the COST 2100 channel generator, for both single-input single-output and multiple-input multiple-output scenarios. We show that our combined augmentations approach allows DNN-aided receivers to achieve gains of up to 1 dB in bit error rate and of up to$\times 3$in spectral efficiency, compared to regular non-augmented training. Moreover, we demonstrate that our augmentations benefit training even as the number of pilots increases, and perform an ablation study on the different augmentations, which shows that the combined approach surpasses each individual augmentation technique.

Deep neural networks (DNNs) allow digital receivers to operate in complex environments by learning from data corresponding to the channel input-output relationship. Since communication channels change over time, DNN-aided receivers may be required to retrain periodically, which conventionally involves excessive pilot signaling at the cost of reduced spectral efficiency. In this paper, we study how one can obtain data for retraining deep receivers without sending pilots or relying on specific protocol redundancies, by combining self-supervision with active learning concepts. We focus on the recently proposed ViterbiNet receiver, which integrates into the Viterbi algorithm a DNN for learning the channel. To enable self-supervision, we use the soft-output Viterbi algorithm to evaluate the decision confidence for each of the detected symbols in a given word. Then, to overcome learning with erroneous data, we choose a subset of the recovered symbols to be used for retraining via active learning. The proposed method selects decision-directed data whose confidence is not too low to result in inaccurate labeling, yet not too high to preserve sufficient diversity of the data. We demonstrate that self-supervised symbol-level training yields a performance within a small gap of the Viterbi algorithm with instantaneous channel knowledge.

Error correction codes are an integral part of communication applications, boosting the reliability of transmission. The optimal decoding of transmitted codewords is the maximum likelihood rule, which is NP-hard due to the curse of dimensionality. For practical realizations, sub-optimal decoding algorithms are employed; yet limited theoretical insights prevent one from exploiting the full potential of these algorithms. One such insight is the choice of permutation in permutation decoding. We present a data-driven framework for permutation selection, combining domain knowledge with machine learning concepts such as node embedding and self-attention. Significant and consistent improvements in the bit error rate are introduced for all simulated codes, over the baseline decoders. To the best of the authors' knowledge, this work is the first to leverage the benefits of the neural Transformer networks in physical layer communication systems.

Ensemble models are widely used to solve complex tasks by their decomposition into multiple simpler tasks, each one solved locally by a single member of the ensemble. Decoding of error-correction codes is a hard problem due to the curse of dimensionality, leading one to consider ensembles-of-decoders as a possible solution. Nonetheless, one must take complexity into account, especially in decoding. We suggest a low-complexity scheme where a single member participates in the decoding of each word. First, the distribution of feasible words is partitioned into non-overlapping regions. Thereafter, specialized experts are formed by independently training each member on a single region. A classical hard-decision decoder (HDD) is employed to map every word to a single expert in an injective manner. FER gains of up to 0.4dB at the waterfall region, and of 1.25dB at the error floor region are achieved for two BCH(63,36) and (63,45) codes with cycle-reduced parity-check matrices, compared to the previous best result of [1].

Tail-biting convolutional codes extend the classical zero-termination convolutional codes: Both encoding schemes force the equality of start and end states, but under the tail-biting each state is a valid termination. This paper proposes a machine-learning approach to improve the state-of-the-art decoding of tail-biting codes, focusing on the widely employed short length regime as in the LTE standard. This standard also includes a CRC code.First, we parameterize the circular Viterbi algorithm, a baseline decoder that exploits the circular nature of the underlying trellis. An ensemble combines multiple such weighted decoders, each decoder specializes in decoding words from a specific region of the channel words’ distribution. A region corresponds to a subset of termination states; the ensemble covers the entire states space. A non-learnable gating satisfies two goals: it filters easily decoded words and mitigates the overhead of executing multiple weighted decoders. The CRC criterion is employed to choose only a subset of experts for decoding purpose. Our method achieves FER improvement of up to 0.75dB over the CVA in the waterfall region for multiple code lengths, adding negligible computational complexity compared to the circular Viterbi algorithm in high SNRs.

High quality data is essential in deep learning to train a robust model. While in other fields data is sparse and costly to collect, in error decoding it is free to query and label thus allowing potential data exploitation. Utilizing this fact and inspired by active learning, two novel methods are introduced to improve Weighted Belief Propagation (WBP) decoding. These methods incorporate machine-learning concepts with error decoding measures. For BCH(63,36), (63,45) and (127,64) codes, with cycle-reduced parity-check matrices, improvement of up to 0.4dB at the waterfall region, and of up to 1.5dB at the error-floor region in FER, over the original WBP, is demonstrated by smartly sampling the data, without increasing inference (decoding) complexity. The proposed methods constitutes an example guidelines for model enhancement by incorporation of domain knowledge from error-correcting field into a deep learning model. These guidelines can be adapted to any other deep learning based communication block.