In this letter, we introduce a new syndrome-based decoder where a deep neural network (DNN) estimates the error pattern from the reliability and syndrome of the received vector. The proposed algorithm works by iteratively selecting the most confident positions to be the error bits of the error pattern, updating the vector received when a new position of the error pattern is selected. Simulation results for the (63,45) and (63,36) BCH codes show that the proposed approach outperforms existing neural network decoders. In addition, the new decoder is flexible in that it can be applied on top of any existing syndrome-based DNN decoder without retraining.
In this letter, we introduce a new syndrome-based decoder where a deep neural network (DNN) estimates the error pattern from the reliability and syndrome of the received vector. The proposed algorithm works by iteratively selecting the most confident positions to be the error bits of the error pattern, updating the vector received when a new position of the error pattern is selected. Simulation results for the (63,45) and (63,36) BCH codes show that the proposed approach outperforms existing neural network decoders. In addition, the new decoder is flexible in that it can be applied on top of any existing syndrome-based DNN decoder without retraining.
Short-length codes have been the subject of recent studies mainly due to the need for specific communication requirements expressed by emerging technologies. However, for the most promising code class (BCH), decoding is complex when using traditional decoders. In this context, projects that use neural networks for this purpose appear as interesting alternatives. That said, in this article, the decoder project proposed in the literature that applies the neural network to estimate the error pattern considering the received vector syndrome extends to the BCH codes of length n less than or equal to 31. In addition, a new decoder is introduced, one that iteratively estimates the most reliable positions to be the erroneous bits of the error pattern previously predicted by a neural network. The results presented show that, for all the analyzed codes, the new decoder reaches the maximum theoretical performances.
Deep neural network (DNN)-based channel decoding is widely considered in the literature. The existing solutions are investigated for the case of hard output, i.e. when the decoder returns the estimated information word. At the same time, soft output decoding is of critical importance for iterative receivers and decoders. In this paper, we focus on the soft-output DNN-based decoding problem. We start with the syndrome-based approach proposed by Bennatan et al. (2018) and modify it to provide soft output in the additive white Gaussian noise (AWGN) channel. The new decoder can be considered as an approximation of the maximum a-posteriori (MAP) decoder with smaller computation complexity. We discuss various regularization functions for joint DNN-MAP training and compare the resulting distributions for [64], [45] (extended Bose-Chaudhuri-Hocquenghem) eBCH code. Finally, to demonstrate the soft-output quality we consider the turbo-product code with [64], [45] eBCH codes as row and column codes. We show that the resulting DNN-based scheme is very close to the MAP-based performance and significantly outperforms the solution based on the Chase decoder. We come to the conclusion that the new method is prospective for the challenging problem of DNN-based decoding of long codes consisting of short component codes.
We present a novel framework for applying deep neural networks (DNN) to soft decoding of linear codes at arbitrary block lengths. Unlike other approaches, our framework allows unconstrained DNN design, enabling the free application of powerful designs that were developed in other contexts. Our method is robust to overfitting that inhibits many competing methods, which follows from the exponentially large number of codewords required for their training. We achieve this by transforming the channel output before feeding it to the network, extracting only the syndrome of the hard decisions and the channel output reliabilities. We prove analytically that this approach does not involve any intrinsic performance penalty, and guarantees the generalization of performance obtained during training. Our best results are obtained using a recurrent neural network (RNN) architecture combined with simple preprocessing by permutation. We provide simulation results that demonstrate performance that sometimes approaches that of the ordered statistics decoding (OSD) algorithm.
In modern communication systems, multiple types of error-correcting codes can be utilized for different transmission scenarios. Therefore, the receiver should include the decoder compatible with multiple codes used in the transmission scheme, which results in the increase of the resources required for its implementation. In this paper, we investigate the possibility of training a single syndrome-based DNN decoder to solve the problem of unified decoding. We observe, that the syndrome-based approach allows to extend the unified decoding capabilities to the codes with considerably larger lengths in comparison to the initially described by Wang et al. (2018) method. Through numerical experiments, we show that the model trained for decoding a pair of moderate lengths codes (BCH and CRC-Aided Polar) achieves performance results comparable with classical decoding solutions, while sharing the same architecture and the set of trainable weights. We note, that the unification of a syndrome-based DNN decoder does not lead to large performance degradation, in comparison to the decoder trained on a single code. The approach described in the paper is promising in terms of reducing the hardware resources required to implement the decoder.
Recently, Machine Learning has been considered for use in various communications subsystems, providing an alternative paradigm for addressing core problems in the physical (PHY) and medium access control (MAC) layers. Several methods and neural network topologies have been proposed for channel decoding targeting short and moderate length codes. In this paper, we consider the Syndrome-based Deep Learning Decoder and propose a modification in order to enable iterative operation. The proposed modifications perform iterations of the original decoder, which are unrolled to build a larger network. The unrolled iterations are subsequently trained jointly. Moreover, the proposed iterative functionality is incorporated within the learning process by accounting for the error of each iteration in the loss function. By sharing the weights between the iterations, we show that it is possible to reduce the storage requirements of the original decoder by a factor of 2.6x for BCH(63,45), while approaching maximum-likelihood decoding performance. Finally, simulation results are provided for several code lengths and rates, which demonstrate the error-correcting capability of the proposed iterative decoder.
Quantum error correction codes (QECC) are a key component for realizing the potential of quantum computing. QECC, as its classical counterpart (ECC), enables the reduction of error rates, by distributing quantum logical information across redundant physical qubits, such that errors can be detected and corrected. In this work, we efficiently train novel end-to-end deep quantum error decoders. We resolve the quantum measurement collapse by augmenting syndrome decoding to predict an initial estimate of the system noise, which is then refined iteratively through a deep neural network. The logical error rates calculated over finite fields are directly optimized via a differentiable objective, enabling efficient decoding under the constraints imposed by the code. Finally, our architecture is extended to support faulty syndrome measurement, by efficient decoding of repeated syndrome sampling. The proposed method demonstrates the power of neural decoders for QECC by achieving state-of-the-art accuracy, outperforming for small distance topological codes, the existing end-to-end neural and classical decoders, which are often computationally prohibitive.