IAES Inter national J our nal of Articial Intelligence (IJ-AI) V ol. 15, No. 1, February 2026, pp. 547 ∼ 558 ISSN: 2252-8938, DOI: 10.11591/ijai.v15.i1.pp547-558 ❒ 547 An efcient method to impr o v e machine lear ning decoders using automor phisms gr oup Imrane Chemseddine Idrissi, Said Nouh, El Mehdi Bellfkih, Mohammed El Assad, Abdelaziz Marzak Department of Mathematics and Informatics, F aculty of Science Ben M’ sick, Hassan II Uni v ersity of Casablanca, Casablanca, Morocco Article Inf o Article history: Recei v ed Oct 29, 2023 Re vised No v 14, 2025 Accepted Jan 10, 2026 K eyw ords: Automorphisms group Bose-Chaudhuri-Hocquenghem codes Error correcting code Machine learning for decoding Multilayer perceptron Syndrome decoding ABSTRA CT The decoding of error -correcting codes (ECCs) is a critical aspect of communication systems, yet traditional decoding techniques can often be computationally demanding or inef fecti v e for certain codes, necessitating inno v ati v e approaches. In this study , we introduce a h ybrid approach that combines machine learning and automorphism techniques to optimize the decoding process. Specically , we train multilayer pe rceptron (MLP) models to learn the mapping between error syndromes and their corresponding errors. While these models e xhibit r ob us t learning capabilities, their performance sometimes does not reach 100%. T o mitig ate this limitation, we e xploit the automorphism group of the code —a set of structure-preserving transformations—to con v ert the errors that the MLP struggles to decode into ones it can process more ef fecti v ely . W e use a minimum number of p permutations, pre-calculating and storing all possible automorphisms to ensure computational ef cienc y . Our e xperimental results re v eal that this h ybrid approach substantially enhances the decoding performance of the MLP model, presenting a promising a v enue for decoding ECCs. Importantly , this approach is not limited to MLP models and can be applied to an y machine learning model with a learning s core less tha n 100%, broadening its applicability and impact. By inte grating machine le arning with traditional algebraic coding theory , we propose a ne w paradigm that holds the potential to re v olutionize the design of decoding systems, making them more ef cient and ef fecti v e. This is an open access article under the CC BY -SA license . Corresponding A uthor: Imrane Chemseddine Idrissi Department of Mathematics and Informatics, F aculty of Science Ben M’ sick Hassan II Uni v ersity of Casablanca Casablanca, Morocco Email: imran.chems@gmail.com 1. INTR ODUCTION Communication channels are pi v otal in transmitting information between a transmitter and a recei v er across v arious applications, from telecommunication systems to computer netw orks and wireless communication systems. Understanding communication channels is k e y to grasping the limitations and possibilities of communication systems and designing ef cient and rob ust techniques for encoding and decoding information [1]. A communication channel is the medium through which information tra v els from the transmitter to the recei v er . Communication channels are broadly cate gorized into tw o types: wired and wireless. W ired channels encompass copper cables, optical bers, and coaxial cables, while wireless channels in v olv e transmitting information through airw a v es using radio frequenc y (RF) or optical signals [2]. J ournal homepage: http://ijai.iaescor e .com Evaluation Warning : The document was created with Spire.PDF for Python.
548 ❒ ISSN: 2252-8938 The performance of a communication channel is profoundly af fected by the presence of nois e and other impairments that can de grade the quality and reliability of the transmitted information [3]. Noise sources include thermal noise, shot noise, and interference from other signals, whereas channel impairments may comprise f ading, multipath propag ation, and signal attenuation [4]. The concept of channel capacity , introduced by Shannon, sets a fundamental limit on the maximum rate at whi ch information can be transmitt ed reliably o v er a communication channel [1]. This limit is dependent on the channel’ s signal-to-noise ratio (SNR) and bandwidth, which are crucial f actors in determining the performance of communication systems [3]. Error -correcting codes (ECCs) and modulation techniques are e xtensi v ely emplo yed to enhance the reliability and ef cienc y of communication systems in the presence of channel noise and impairments [5]. Modern communication systems also incorporate adapti v e techniques, such as adapti v e modulation and coding, to optimize their performance based on v arying channel conditi ons [6]. In conclusion, comprehending communication channels and their characteristics is essential for designing and optimizing communication systems to achie v e reliable and ef cient transmission of information across v arious applications and en vironments. Since all channels are noisy and unreliable, transmitting binary data o v er the aforementioned channels can cause errors in messages by changing 0 to 1, or vice v ersa. Here, ECCs mak e it possible to e xtract the original binary data from the altered binary data due to noise. In other w ords, the primary objecti v e of ECCs is to enable reliable digital communication o v er unreliable channels, as sho wn in Figure 1. Figure 1. Communication model As an e xample, we discuss the fundamental idea behind ECC: communication o v er unreliable channels. T o reduce the probability of altering the original messages, we add redundanc y , making the transmitted messages easier to distinguis h from each other . There are v arious classes of ECC; ho we v er , the main goal of an y ECC is to rec o v er the original message using dif ferent types of techniques, such as algebraic, heuristic, meta-heuristic, or machine learning techniques. The use of machine learning to enhance communication netw orks is not a ne w concept. The information theory and machine learning communities ha v e long shared a neb ulous belief that the y are one and the same since the y emplo y similar statistical techniques to address comparable issues. This belief w as rst e xpressed by MacKay [7]. ECCs, as sho wn in Figure 2 can be broadly classied into tw o major f amilies: block codes and con v olutional codes. These tw o f amilies ha v e distinct char acteristics and are used in dif ferent applications depending on their specic adv antages. Block codes and con v olutional codes are tw o classes of ECCs used in digital communication systems. Block codes operate on x ed-size blocks of data, encoding each block independently and correcting errors upon decoding [1]. Examples of block codes include Hamming codes, Reed-Solomon codes, and Bose-Chaudhuri-Hocquenghem (BCH) codes, each with specic error -correction capabilities and applications [8], [5]. Con v olutional codes, on the other hand, w ork on continuous streams of data, using a dif ferent encoding scheme in v olving con v olving the data stream with generator polynomials [9]. The y are widely used in digital communication systems and often combined with block codes for enhanced error -correction performance [7], [5]. Int J Artif Intell, V ol. 15, No. 1, February 2026: 547–558 Evaluation Warning : The document was created with Spire.PDF for Python.
Int J Artif Intell ISSN: 2252-8938 ❒ 549 In our research paper , we ha v e or g anized our e xploration of decoding methods into distinct sec tions. W e be gin with a re vie w of e xisting approaches, including algebraic dec o de rs, heuristic and meta-heuristic decoders, and machine learning decoders, in section 2. Ne xt, in section 3, we introduce no v el machine learning techniques, focusing on the multilayer perceptron (MLP) decoder and its enhanced v ersion, the impro v ed multilayer perceptron decoder (MLPDec) with an automorphism set. Section 4 presents empirical ndings, including performance comparisons with other methods, while the section 5 summarizes our k e y ndings and suggests future research directions. Figure 2. Error correcting codes classication 2. RELA TED W ORK ECCs are essential tools in modern digital communication systems, pro viding a means to detect and correct er rors that may occur during data transmission. Among v arious ECCs, BCH codes stand out for their capability to correct multiple errors while maintaining relati v ely lo w comple xity . BCH codes are a class of c yclic ECCs with the abilit y to correct multiple errors in a data block. The y were independently disco v ered by Bose and Chaudhuri, and by Hocquenghem in the early 1960s. Since then, BCH codes ha v e been widely used in v arious communication and storage systems due to their e xcellent error -correcting capabilities and ef cient decoding algorithms. In ECCs, man y approaches ha v e been de v eloped to impro v e the coding and decoding process. Decoders can be classi ed based on decoding algorithms into four major classes: algebraic, heuristic, meta-heuristic, and machine learning decoders (Figure 3). These classications can help to cate gorize decoding algorithms based on their properties, computational approaches, and adaptability . Each type of decoder has its adv antages and disadv antages, and the choice between them depends on the specic requirements of the application and the desired trade-of fs between performance, comple xity , adaptability , and implementation [5]. Figure 3. Error correcting codes techniques 2.1. Algebraic decoders These decoders are based on algebraic techniques and rely on the underlying mathematical structure of the ECC. The y use deterministic algorithms to nd and correct errors. Examples of algebraic decoding techniques include Berlekamp-Masse y , Peterson, and Euclidean algorithms for BCH and Reed-Solomon codes. Algebraic decoders typically ha v e well-dened performance and comple xity characteristics b ut may An ef cient method to impr o ve mac hine learning decoder s using ... (Imr ane Chemseddine Idrissi) Evaluation Warning : The document was created with Spire.PDF for Python.
550 ❒ ISSN: 2252-8938 ha v e limited adaptability to dif ferent channel conditions or code structures. Some recent de v elopments and optimizations in algebraic decoding techniques highlight ongoing ef forts to impro v e ef cienc y and performance of algebraic decoders in v arious communication systems and applications. A no v el algebraic decoding technique for BCH codes using Gr ¨ obner bases is proposed. The proposed algorithm of fers ef cient and e xible decoding process while also pro viding a better understanding of mathematical properties of BCH codes. Li and Salehi [10] presents algebraic soft-decision decoding algorithm for concatenated Reed-Solomon codes. The proposed algorithm reduces the decoding comple xity while maintaining good performance in the presence of noise and channel impairments. Puchinger et al. [11] presents an enhanced algebraic-ge o m etry decoding technique for Hermitian codes, which impro v es decoding performance while simplifying the decoding procedure. F or Reed-Solomon codes, there is a no v el algebraic soft-decision decoding algorithm that seeks to increase error -correcting ef cienc y while lo wering decoding comple xity and computing cost [12]. 2.2. Heuristic and meta-heuristic decoders Heuristic decoders utilize simplied problem-solving strate gies, often relying on rules of thumb or educated guesses to approximate optimal solutions during the decoding process. These approaches are particularly attracti v e due to their relati v ely lo w computational comple xity when compared to algebraic decoders. While the y can yield good performance in man y scenarios, their ef fecti v eness is hea vily inuenced by the quality of the chosen heuristic, and the y may f ail to achie v e optimal decoding performance in more comple x or noisy en vironments. Notable e xamples of heuristic decoders include chase decoding and generalized minimum distance (GMD) decoding algorithms, which are commonly applied to Reed-Solomon codes. In contrast, meta-heuristic decoders emplo y more generalized and e xible optimization frame w orks capable of solving a broad class of decoding problems. These methods are inspired by natural processes and include algorithms such as particle sw arm optimization, simulated annealing, and genetic algorithms. The primary adv antage of meta-heuristic approaches lies in their adaptability to v arious code structures and dynamic channel conditions, allo wing for impro v ed performance in non-ideal or e v olving transmission en vironments. Ne v ertheless, the increased performance often comes at the cost of higher computational comple xity and the necessity for careful parameter tuning to achie v e satisf actory results. An illustr ati v e e xample is the articia l reliabilities based decoding genetic algorithm (ArDecGA) decoder , which applies genetic algorithm principles to the decoding of BCH codes. This method searches the solution space of candidate code w ords, e v olving them iterati v ely based on tness scores that reect ho w closely each candidate approximates the correct code w ord [13]. Another ef cient decoding f amily includes the hard and soft decoder (HSDec) [14] and hard weights decoder (HWDec) [15], which prioritize decoding speed and simplicity . These decoders are particularly benecial in lo w-l atenc y , real-time systems, although their reliance on hash tables can result in signicant memory requirements—posing potential limitations in embedded or resource-constrained applications. Ov erall, these decoding strate gies represent a v aluable spectrum of alternati v es to traditional methods. The continued de v elopment of heuristic and meta-heuristic decoders highlights the dynamic nature of ECC research, sho wcasing no v el trade-of fs between decoding accurac y , computational demands, and system constraints. 2.3. Machine lear ning decoders In recent years, deep learning has become increasingly inuential in the eld of ECC decoding. Among the most studied cases are deep learning-based decoders for BCH codes, which in v olv e training neural netw orks to learn the mapping between noisy recei v ed code w ords and their corresponding original code w ords. These netw orks, typically composed of multiple layers with non-linear acti v ation functions, are capable of identifying intricate patterns within data that traditional methods may o v erlook. T o ef fecti v ely train these neural models, lar ge datasets consisting of noisy input code w ords and their kno wn transmitted outputs must be generated. The learning process is centered around minimizing the error between the predicted and actual code w ords. Once trained, the netw ork can generalize this mapping to ne w , unseen data by selecting the most probable code w ord, enhancing decoding reliability under v ariable noise conditions. A signicant benet of such models is their adaptability to a wide range of channel conditions and noise characteristics. Ho we v er , this adaptability comes at the cost of substantial computational resources, particularly during the training phase, and a strong dependence on the quality and size of the dataset used. Se v eral w orks ha v e been proposed to enhance the ef fecti v eness of these models. F or e xample, Nachmani et al. [16] introduces multiple n e ural architectures and training techniques that outperform traditional algebraic decoders in high-noise scenarios. Similarly , Kim et al. [17] e xplores v arious learning Int J Artif Intell, V ol. 15, No. 1, February 2026: 547–558 Evaluation Warning : The document was created with Spire.PDF for Python.
Int J Artif Intell ISSN: 2252-8938 ❒ 551 strate gies and netw ork structures applicable to multiple code f amilies. These studies collecti v ely demonstrate promise of machine l earning approaches in impro ving decoding performance, particularly when traditional algorithms f ace performance de gradation due to comple x or unpredictable noise patterns. Another inuential study analyze the use of deep neural netw orks for channel decoding, comparing their method ag ainst classical approaches [18]–[20]. Their results underscore both the strengths and limitations of neural decoders—sho wing impro v ed performance b ut also pointing to challenges in scalability and interpretability . Extending this research, Cammerer et al. [21] presents a deep learning strate gy for polar codes, le v eraging partitioning methods to manage longer code lengths ef cientl y . Though the focus is on polar codes, the proposed techniques are lik ely transferable to BCH code decoding, suggesting broader applicability of these inno v ations. In addition to deep neural netw orks, other machine learning models such as logistic re gression decoders (LRDec) ha v e been e xplored. The LRDec model [22] uses list decoding and combines algebraic and combinatorial strate gies to achie v e rob ust performance, particularly under high-error conditions. Nonetheless, its computational b urden increases with code length and error density , presenting practical trade-of fs. Be yond classical settings, recent de v elopments ha v e also e xtended machine learning and error correction into the quantum domain. Chao and Reichardt [23] propose a quantum error correction approach that requires only tw o ancillary qubits, of fering a lightweight and practical frame w ork for quantum systems. Kribs et al . [24] introduce operator quantum error correction as a theoretical frame w ork for managing errors in quantum computations. Meanwhile, T erhal [25] highlights the critical role of quantum error correction in maintaining coherence within quantum memory architectures. In summary , the body of recent research illustrates the substantial progress made in m achine learning-based decoding. Whether through deep neural netw orks or h ybrid techniques lik e LRDec, modern approaches are pushing the boundaries of error correction. These methods sho w signicant promise in increasing decoding ef cienc y and rob ustness while also introducing ne w challenges in terms of computational cost and model comple xity . 3. PR OPOSED DECODERS 3.1. Machine lear ning techniques Machine learning algorithms, specically MLP neural netw orks, ha v e transformed data pr o c essing and analysis by enabling v arious applications across dif ferent elds. One signicant application is data decoding, where MLPs, a cate gory of articial neural netw orks (ANNs) as sho wn in Figure 4, ha v e become widely adopted due to their capability to ef fecti v ely m o de l comple x, nonlinear relationships between inputs and outputs. In our study , the initial focus w as on de v eloping a model with optimal performance using MLP by selecting appropriate model parameters during the training phase for linear BCH codes. The rst step in creating a decoder model for linear BCH codes in v olv es dening the inputs (X) and outputs (Y) [22]. Figure 4. Machine learning algorithms classication An ef cient method to impr o ve mac hine learning decoder s using ... (Imr ane Chemseddine Idrissi) Evaluation Warning : The document was created with Spire.PDF for Python.
552 ❒ ISSN: 2252-8938 Initially , a list of all possible errors of length ‘n’ with a weight less than or equal to ‘t’ (the error -correcting capability of the code) must be created. This list encompasses all the classes of the model. Moreo v er , to dif ferentiate between correctable and uncorrectable errors, a null v alue w as added as output for uncorrectable errors in the list, and the recei v ed w ord (with a detectable weight error) w as mark ed as uncorrectable. The objecti v e here is to preserv e the inte grity of the w ord if the error weight is greater than the code’ s error -correcting capability . By incorporating this approach, our model not only identies the errors b ut also dif ferentiates between correctable and uncorrectable errors, which is crucial for maintaining the inte grity of the transmitted data. This methodology ensures that the decoder model de v eloped is rob ust and ef cient in correcting errors in linear BCH codes. 3.2. Multilay er per ceptr on decoder The MLP is a foundational architecture in neural netw orks, comprising an input layer , one or more hidden layers, and an output layer . The hidden layers emplo y nonlinear acti v ation functions, such as rectied linear unit (ReLU) or sigmoid, which empo wer t he netw ork to capture comple x, non-linear relationships within the data. This mak es MLPs particularly adept at handling noisy or incomplete inputs. Furthermore, the feedforw ard nature of the MLP architecture ensures ef cient training and enables generalization to unseen data—a crucial fea ture in decoding applications. In the conte xt of ECCs, Nachmani et al. [16]. demonstrated the successful application of MLP s to the decoding of linear codes, underscoring their ef fecti v eness in real-w orld communication systems. W e propose a no v el MLP architecture for hard decoding of BCH codes. The model learns the mapping between syndromes and correct able errors to enable error correction i n noisy communication channels. This approach le v erages MLP pattern recognition capabiliti es while preserving BCH structural properties for rob ust decoding. F or training, input data X consists of syndromes for BCH ( n, k , t ) codes, where each x i has length n − k . Output data Y contains binary error v ectors of length n , with each y i indicating error positions. The training set is constructed by enumerating all correctable errors and pairing them with their respecti v e syndromes. – Input data ( X ): syndromes generated from BCH( n, k , t ) codes, where each instance x i is of length n − k . – Output data ( Y ): binary error v ectors of length n , where each instance y i indicates a correctable error pattern. The mapping can thus be formalized as: ( X = x i ) → ( Y = y i ) Once the training dataset is assembled, the MLP model is tr ained to approximate the function that maps syndromes to error v ectors. The model comprises multiple layers, where each layer contains a set of neurons connected to the pre vious and ne xt layers. During training, the model iterati v ely updates its weights to minimize the prediction error using backpropag ation and gradient descent techniques. T o e v aluate the ef fecti v eness of the MLP model, we conducted a series of e xperiments analyzing the impact of dif ferent acti v ation functions and architectural depths. Specically , we compared models utilizing the sigmoid functi on and the ReLU, both with single and double hidden layers. These v ariations allo w us to assess ho w acti v ation choices and netw ork depth inuence decoding performance. The comparati v e results of these e xperiments are summarized in a table, of fering insight into optimal congurations for specic BCH code parameters. 3.3. The impr o v ed multilay er per ceptr on decoder using automor phsim set In our study , we aim to enhance the MLP technique by incorporating mathematical automorphism groups, which can potentially impro v e the decoding performance. Automorphism groups ha v e been pre viously used in the conte xt of ECCs, of fering signicant benets in terms of code symmetry and reducing decoding comple xity . By harnessing the capabilities of MLPs and the intrinsic properties of automorphism groups, we aim to de v elop a decoding method that is both more ef cient and rob ust. Pre vious research has e xplored the application of automorphism groups in decoding, specically studying the role of permutation automorphisms in the decoding of linear codes [26]. Building upon these foundational studies and inte grating automorphism groups with MLPs, our proposed approach, as illustrated in Figure 5, presents the potential to push the boundaries of e xisting decoding techniques and contrib ute to the adv ancement of machine learning-based decoding methods. W e propose to enhance the decoding process by incorporating the sets of automorphism groups for BCH codes. W e le v erage permutations generated by the automorphism group to impro v e decoding accurac y Int J Artif Intell, V ol. 15, No. 1, February 2026: 547–558 Evaluation Warning : The document was created with Spire.PDF for Python.
Int J Artif Intell ISSN: 2252-8938 ❒ 553 by applying them iterati v ely until the correct decoding i s achie v ed. The initial step in v olv es generating automorphism group permutations, which are the set of transformations that preserv e the properties of the BCH codes. The Algorithm 1 outlines the decoding procedure for the multi-layer perceptron with automorphism (MLP Aut) decoding and the requirements for its implementation. Algorithm 1 The algorithm of decoding by the MLP Aut decoder Requir e: A ut = { σ i : σ i ( C ) = C } , d ( H amming distance ) , t = ⌊ d − 1 2 ⌋ Requir e: MLP-nR the multilayer perceptron model M ← R eceiv edM essag e M c ← M σ ← σ I d while (T rue) do M sg Auto ← σ ( M ) M sg M od ← M LP − nR ( M sg Auto ) dist ← d ( M sg M od, M c ) if ( S y ndr ome ( M s g M od ) ! = 0 or dist > t ) then σ ← σ i ▷ chose permutation M ← M sg M od else M es D ec ← σ − 1 ( M sg M od ) br eak end if end while Figure 5. MLP Aut diagram An ef cient method to impr o ve mac hine learning decoder s using ... (Imr ane Chemseddine Idrissi) Evaluation Warning : The document was created with Spire.PDF for Python.
554 ❒ ISSN: 2252-8938 4. RESUL TS AND DISCUSSION In this section, we present an o v ervie w of the e xperimental results conduct ed o v er an additi v e white Gaussian noise (A WGN) channel. The focus is on e v aluating the performance of tw o decoding models: the standard MLPDec and its enhanced v ersion. The impro v ed model incorporates automorphism group techniques and is referred to as multi-layer perceptron automorphism decoder (MLP AutDec). W e compare both models under v arious BCH code congurations to assess their decoding accurac y . The results demonstrate the impact of automorphisms on enhancing error correction capabilities. 4.1. Multilay er per ceptr on decoder r esults The rst w ork to create our decoders for dif ferent BCH codes is to create a model decoder using MLP with dif ferent parameters. T able 1 pro vides a comparison of dif ferent models trained on BCH (31,21,5) with v arious congurations, including the number of layers, neurons per layer , ac ti v ation functions, iteration numbers, and corresponding training scores. The same for the code BCH (31,26,5), the results of training score are gi v en in T able 2. T able 1. Scores for BCH (31-21-5) Models training BCH (31,21,5) Layer neurones Acti v ation function Iteration number’ s Score (%) MLP-2nR 2*n Relu 10 000 57 MLP-2nL 2*n Logistic 10 000 51 MLP-nR n Relu 10 000 51 MLP-nL n Logistic 100 000 49 MLP-nR n Relu 100 000 54 T able 2. Scores for BCH (31-26-5) Models training BCH (31,26,5) Layer neurones Acti v ation function Iteration number’ s Score (%) MLP-nR n Relu 10 000 100 MLP-n4R [n/4] Relu 100 000 100 MLP-n6R [n/6] Relu 100 000 93 MLP-n8R [n/8] Relu 100 000 58 When considering e x ecution comple xity , it is advisable to select the model with the fe west neurons and the simplest acti v ation function, in this case, the MLP-nL (MLP with ’n’ neurons and logistic acti v ation function). This model has the lo west e x ecution comple xity compared to others, as it has the fe west neurons, and the logistic acti v ation function is generally computationally less e xpensi v e than ReLU. Ho we v er , it is important to note that the choice of model should not be based solely on e x ecution comple xity . The accurac y and performance of the model are equally important f actors. Therefore, it is essential to consider the trade-of f between e x ecution comple xity and model performance. In this case, the idea is to enhance the performance of the models by using automorphism groups. 4.2. P erf orming multilay er per ceptr on decoder with automor phism set MLP A ut As outlined in the pre vious section, this part presents se v eral e xperiments that combine the standard MLPDec with a subgroup of automorphisms denoted as S g , where the length of the group is represented by Len ( S g ) = p . The main objecti v e is to determine the minimum number of automorphisms p required to achie v e optimal decoding performance for each MLP model. Experimental results indicate that performance impro v es as p increases b ut e v entually reaches a saturation point be yond which further g ains are minimal. Figure 6 illustrates the bit error rate (BER) performance for the BCH (15,7,5) code under v arious v alues of p . The a n a lysis sho ws that when p ≥ 3 , the model achie v es stable performance in terms of BER, with a notable impro v ement in SNR g ain. This stabilization suggests that a small number of well-selected automorphisms can signicantly enhance the decoder’ s accurac y without e xcessi v e computational cost. Extending the analysis to other codes, such as BCH (31,26,3) and BCH (31,21,5), further supports the positi v e impac t of inte grating automorphism groups with MLPDec. Figures 7 and 8 display the BER performance for these codes, demonstrating that the impro v ed decoder (MLP Aut) consistently outperforms or matches the original MLPDec. Specically , the MLP Aut model achie v es con v er gence at p = 5 for BCH (31,21,5) and at p = 6 for BCH (31,26,3), indicating that a small automorphism set is suf cient for performance enhancement. Int J Artif Intell, V ol. 15, No. 1, February 2026: 547–558 Evaluation Warning : The document was created with Spire.PDF for Python.
Int J Artif Intell ISSN: 2252-8938 ❒ 555 Figure 6. BER performance for BCH (15,7,5) code Figure 7. BER performance MLPDec and MLP Aut for BCH (31,26,3) code Figure 8. BER performance MLPDec and MLP Aut for BCH (31,21,5) code The con v er gence v alues for each tested BCH code are summarized in T able 3. This ta b l e conrms tha t the inte gration of automorphism groups enhances model con v er gence and decoding performance with relati v ely fe w permutations. Identifying these thresholds pro vides a practical guideline for balancing performance g ains with computational ef cienc y . Incorporating the ndings from this section, it is e vident that automorphisms play a signicant role in enhancing the performance of machine learning-based decoders. These results suggest that automorphism sets, when carefully selected, of fer a scalable and ef fecti v e strate gy for impro ving error correction. As decoding systems e v olv e, such h ybrid techniques may pa v e the w ay for more rob ust and ef cient implementations in communication systems. T able 3. Minimum automorphism count p for model con v er gence BCH code Con v er gence at p = 3 BCH (15,7,5) p = 3 BCH (31,26,3) p = 6 BCH (31,21,5) p = 5 4.3. Comparison with competitors Figures 9 and 10 pro vide a comparati v e analysis of three distinct models: HSDec, HWDec, and MLPDec, all applied to a (31,21,5) and (31,26,3) codes. Notably , HSDec and HWDec sho w closely aligned performances across v arious SNR le v els, suggesting a shared ef cac y in error correcti on. In contrast, MLPDec (p =5) in Figure 9 and MLPDec (p =6) in Figure 10 demonstrates a s ubstantial performance adv antage o v er both HSDec and HWDec, especially as SNR increases. This disparity in performance indicates that MLPDec, when enriched with v e automorphisms (p =5)- and (p =6) (Figures 9 and 10), e xcels in error correction and noise mitig ation for this specic code. The e vident adv antage of MLPDec in higher SNR scenarios highlights its potential to signicantly impro v e the BER and o v erall reliability of data transmission. Also, the results ha v e sho wn that the presence of automorphisms in the MLPDec model, seems to confer a substantial adv antage in handling noise and impro ving error correction. An ef cient method to impr o ve mac hine learning decoder s using ... (Imr ane Chemseddine Idrissi) Evaluation Warning : The document was created with Spire.PDF for Python.
556 ❒ ISSN: 2252-8938 Figure 9. BER comparison of HSDec, HWDec, and MLPDec for BCH (31,21,5) code Figure 10. BER comparison of HSDec, HWDec, and MLPDec for BCH (31,26,3) code 5. CONCLUSION In this research paper , we introduced a no v el approach for decoding linear ECCs by utilizing MLPs and automorphism groups. Our res u l ts indicate that our proposed decoder signicantly outperforms all e xisting machine learning decoders with a learning score of less than 100 percent. This underscores the ef fecti v eness of inte grating automorphism groups and deep learning t o enhance the performance of ECCs, particularly BCH codes. This research not only opens up ne w a v enues for e xploration b ut also holds practical implications for designing more ef cient error correction systems. Ultimately , our w ork contrib utes to the progression of the eld of ECCs and of fers a promising strate gy for optimizing the performance of linear codes. Optimizing the decoder in terms of performance and comple xity remains a pi v otal aspect of ECC research. Although our current study presents a promising approach for optimizing the performance of linear codes using MLPs and automorphism groups, there is still scope for impro v ement in both performance and comple xity . As such, we see a clear path for future research aimed at further rening our decoder . Specically , we plan to e xplore adv anced deep learning techniques and assess the po t ential of amalg amating our approach with other error correction methods. Our objecti v e is to continually push the boundaries of error correction performance and de v elop ne w , ef cient solutions for real-w orld applications. FUNDING INFORMA TION Authors state no funding in v olv ed. A UTHOR CONTRIB UTIONS ST A TEMENT This journal uses the Contrib utor Roles T axonomy (CRediT) to recognize indi vidual author contrib utions, reduce authorship disputes, and f acilitate collaboration. Name of A uthor C M So V a F o I R D O E V i Su P Fu Imrane Chemseddine Idrissi ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ Said Nouh ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ El Mehdi Bellfkih ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ Mohammed El Assad ✓ ✓ ✓ ✓ Abdelaziz Marzak ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ C : C onceptualization I : I n v estig ation V i : V i sualization M : M ethodology R : R esources Su : Su pervision So : So ftw are D : D ata Curation P : P roject Administration V a : V a lidation O : Writing - O riginal Draft Fu : Fu nding Acquisition F o : F o rmal Analysis E : Writing - Re vie w & E diting Int J Artif Intell, V ol. 15, No. 1, February 2026: 547–558 Evaluation Warning : The document was created with Spire.PDF for Python.