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Indonesian Journal of Electrical Engineering and Computer Science

Machine learning for decoding linear block codes: case of multi-class logistic regression model

Imrane Chems Eddine Idrissi, Saïd Nouh, El Mehdi Bellfkih, Seddiq El Kasmi Alaoui, Abdelaziz Marzak

Published Oct 1, 2021• 4 citations
Publisher

Abstract

Facing the challenge of enormous data sets variety, several machine learning-based algorithms for prediction (e.g, Support vector machine, multi layer perceptron and logistic regression) have been highly proposed and used over the last years in many fields. Error correcting codes (ECCs) are extensively used in practice to protect data against damaged data storage systems and against random errors due to noise effects. In this paper, we will use machine learning methods, especially multi-class logistic regression combined with the famous syndrome decoding algorithm. The main idea behind our decoding method which we call logistic regression decoder (LRDec) is to use the efficient multi-class logistic regression models to find errors from syndromes in linear codes such as bose, ray-chaudhuri and hocquenghem (BCH), and the quadratic residue (QR). Obtained results of the proposed decoder have a significant benefit in terms of bit error rate (BER) for random binary codes. The comparison of our decoder with many competitors proves its power. The proposed decoder has reached a success percentage of 100% for correctable errors in the studied codes.

DOI
10.11591/ijeecs.v24.i1.pp538-547

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Facing the challenge of enormous data sets variety, several machine learning-based algorithms for prediction (e.g, Support vector machine, multi layer perceptron and logistic regression) have been highly proposed and used over the last years in many fields. Error correcting codes (ECCs) are extensively used in practice to protect data against damaged data storage systems and against random errors due to noise effects. In this paper, we will use machine learning methods, especially multi-class logistic regression combined with the famous syndrome decoding algorithm. The main idea behind our decoding method which we call logistic regression decoder (LRDec) is to use the efficient multi-class logistic regression models to find errors from syndromes in linear codes such as bose, ray-chaudhuri and hocquenghem (BCH), and the quadratic residue (QR). Obtained results of the proposed decoder have a significant benefit in terms of bit error rate (BER) for random binary codes. The comparison of our decoder with many competitors proves its power. The proposed decoder has reached a success percentage of 100% for correctable errors in the studied codes.
Error-correcting codes are used to partially or completely correct errors as much as possible, while ensuring high transmission speeds. Several Machine Learning (ML) models such as Logistic Regression and Decision tree have been applied to correct transmission errors. Among the most powerful ML techniques are aggregation methods which have yielded to excellent results in many areas of research. It is this excellence that has prompted us to consider their application for the hard decoding problem. In this sense, we have successfully designed, tested and validated our proposed EL-BoostDec decoder (hard decision decoder based on Ensemble Learning - Boosting technique) which is based on computing of the syndrome of the received word and on using Ensemble Learning techniques to find the corresponding corrigible error. The obtained results with EL-BoostDec are very encouraging in terms of the binary error rate (BER) that it offers. Practically EL-BoostDec has succeed to correct 100% of errors that have weights less than or equal to the correction capacity of studied codes. The comparison of EL-BoostDec with many competitors proves its power. A study of parameters which impact on EL-BoostDec performances has been established to obtain a good BER with minimum run time complexity.
Abstract In recent days, polar codes have attracted the attention of Industry and Academia. It is one of a linear block error correction codes. Polar codes are one of the capacity achieving algorithms over a wide range of channels, making them very attractive from a theoretical perspective. Polar codes are shown to be instances of concatenated codes. It has been shown that the effect of a polar code can be enhanced by showing the multistage decoding algorithm with log-likelihood based Successive List decoding (SCL). However, SCL decoders are no longer optimal in terms of frame error rate. It is believed that the machine learning based algorithm can improve the FER for the decoded bit. Thus, the logistic regression algorithm is proposed in this paper. The proposed method offers an optimized solution to the decoded bits. The simulation result shows that with sufficient training, this method can provide a lower frame error rate for different code lengths.
Error-correcting codes improve the reliability of data exchanged between transmitters and receivers; achieving efficient and fast decoding is a major challenge. In this work, we propose an efficient, fast, and high-performing decoder named FastSyndISD. The first version of the proposed decoder uses hashing techniques to quickly find the information set that allows for error correction directly from the syndrome of the received word. Hashing information sets significantly reduce space complexity, instead of all correctable errors, compared to HSDec, LRDec, and EL-BoostDec. The second version utilizes a machine learning model (decision tree) to quickly find the information set that enables error correction directly from the syndrome of the received word. This second version does not require storing a hash table, since the information set is determined by a decision tree classifier model. The performance of the proposed decoder FastSyndISD is very encouraging regarding its bit error rate (BER). Indeed, it succeeds in correcting all errors whose weights are equal to or less than the correction capacity of the analyzed codes. Furthermore, a comparison with various other decoders highlights its effectiveness. A detailed study of its space complexity, its time complexity, and the factors influencing its performance has also been conducted, aiming to achieve an optimal BER while reducing computational time and memory usage. This comparison proves the significant success of the proposed decoder.
Modern communication systems require robust, adaptable and high performance decoders for efficient data transmission. Support Vector Machine (SVM) is a margin based classification and regression technique. In this paper, decoding of Bose Chaudhuri Hocquenghem codes has been approached as a multi-class classification problem using SVM. In conventional decoding algorithms, the procedure for decoding is usually fixed irrespective of the SNR environment in which the transmission takes place, but SVM being a machinelearning algorithm is adaptable to the communication environment. Since the construction of SVM decoder model uses the training data set, application specific decoders can be designed by choosing the training size efficiently. With the soft margin width in SVM being controlled by an equation, which has been formulated as a quadratic programming problem, there are no local minima issues in SVM and is robust to outliers.
The decoding of error-correcting codes (ECCs) is a critical aspect of communication systems, yet traditional decoding techniques can often be computationally demanding or ineffective for certain codes, necessitating innovative approaches. In this study, we introduce a hybrid approach that combines machine learning and automorphism techniques to optimize the decoding process. Specifically, we train multilayer perceptron (MLP) models to learn the mapping between error syndromes and their corresponding errors. While these models exhibit robust learning capabilities, their performance sometimes does not reach 100%. To mitigate this limitation, we exploit the automorphism group of the code—a set of structure-preserving transformations—to convert the errors that the MLP struggles to decode into ones it can process more effectively. We use a minimum number of p permutations, pre-calculating and storing all possible automorphisms to ensure computational efficiency. Our experimental results reveal that this hybrid approach substantially enhances the decoding performance of the MLP model, presenting a promising avenue for decoding ECCs. Importantly, this approach is not limited to MLP models and can be applied to any machine learning model with a learning score less than 100%, broadening its applicability and impact. By integrating machine learning with traditional algebraic coding theory, we propose a new paradigm that holds the potential to revolutionize the design of decoding systems, making them more efficient and effective.
Error syndromes for heavy hexagonal code and other topological codes such as surface code have typically been decoded by using Minimum Weight Perfect Matching– (MWPM) based methods. Recent advances have shown that topological codes can be efficiently decoded by deploying machine learning (ML) techniques, in particular with neural networks. In this work, we first propose an ML-based decoder for heavy hexagonal code and establish its efficiency in terms of the values of threshold and pseudo-threshold for various noise models. We show that the proposed ML-based decoding method achieves ~ 5 × higher values of threshold than that for MWPM. Next, exploiting the property of subsystem codes, we define gauge equivalence for heavy hexagonal code, by which two distinct errors can belong to the same error class. A linear search-based method is proposed for determining the equivalent error classes. This provides a quadratic reduction in the number of error classes to be considered for both bit flip and phase flip errors and thus a further improvement of ~ 14% in the threshold over the basic ML decoder. Last, a novel technique based on rank to determine the equivalent error classes is presented, which is empirically faster than the one based on linear search.