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.
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.
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 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.
Topological quantum error-correcting codes are a promising candidate for building fault-tolerant quantum computers. Decoding topological codes optimally, however, is known to be a computationally hard problem. Various decoders have been proposed that achieve approximately optimal error thresholds. Due to practical constraints, it is not known if there exists an obvious choice for a decoder. In this paper, we introduce a framework which can combine arbitrary decoders for any given code to significantly reduce the logical error rates. We rely on the crucial observation that two different decoding techniques, while possibly having similar logical error rates, can perform differently on the same error syndrome. We classify each error syndrome to the decoder which is more likely to decode it correctly using machine learning techniques. We apply our framework to an ensemble of minimum-weight perfect matching (MWPM) and hard-decision re-normalization-group decoders for the surface code in the depolarizing noise model. Our simulations show an improvement of 38.4%, 14.6%, and 7.1% over the pseudothreshold of MWPM in the instance of distance 5, 7, and 9 codes, respectively. Lastly, we discuss the advantages and limitations of our framework and applicability to other error-correcting codes. Our framework can provide a significant boost to error correction by combining the strengths of various decoders. In particular, it may allow for combining very fast decoders with moderate error-correcting capability to create a very fast ensemble decoder with high error-correcting capability.
Low-density parity-check (LDPC) codes have been successfully commercialized in communication systems due to their strong error correction capabilities and simple decoding process. However, the error-floor phenomenon of LDPC codes, in which the error rate stops decreasing rapidly at a certain level, presents challenges for achieving extremely low error rates and deploying LDPC codes in scenarios demanding ultra-high reliability. In this work, we propose training methods for neural min-sum (NMS) decoders to eliminate the error-floor effect. First, by leveraging the boosting learning technique of ensemble networks, we divide the decoding network into two neural decoders and train the post decoder to be specialized for uncorrected words that the first decoder fails to correct. Secondly, to address the vanishing gradient issue in training, we introduce a block-wise training schedule that locally trains a block of weights while retraining the preceding block. Lastly, we show that assigning different weights to unsatisfied check nodes effectively lowers the error-floor with a minimal number of weights. By applying these training methods to standard LDPC codes, we achieve the best error-floor performance compared to other decoding methods. The proposed NMS decoder, optimized solely through novel training methods without additional modules, can be integrated into existing LDPC decoders without incurring extra hardware costs. The source code is available at https://github.com/ghy1228/LDPC_Error_Floor .
Binary cyclic codes achieve good error correction performance and allow the implementation of very simpleencoder and decoder circuits. Among them, BCH codesrepresent a very important class of t-error correcting codes, with known structural properties and error correction capability. Decoding of binary cyclic codes is often accomplished through hard-decision decoders, although it is recognized that softdecision decoding algorithms can produce significant coding gain with respect to hard-decision techniques. Several approaches have been proposed to implement iterative soft-decision decoding of binary cyclic codes. We study the technique based on “extended parity-check matrices”, and show that such method is not suitable for high rates or long codes. We propose a new approach, based on “reduced parity-check matrices” and “spread parity-check matrices”, that can achieve better correction performance in many practical cases, without increasing the complexity.
This dissertation presents a novel approach to soft decision decoding for binary linear block codes. The basic idea of this approach is to achieve a desired error performance progressively in a number of stages. For each decoding stage, the error performance is highly bounded and the decoding is terminated at the stage where either near-optimum error performance or a desired level of error performance is achieved. As a result, more flexibility in the trade-off between performance and decoding complexity is provided. The proposed decoding is based on the reordering of the received symbols according to their reliability measure. In the dissertation, we evaluate the statistics of the noise after ordering. Based on these statistics, we derive two monotonic properties which dictate the reprocessing strategy. Each codeword is decoded in two steps: (1) hard-decision decoding based on reliability information and (2) reprocessing of the hard-decision decoded codeword in successive stages until the desired performance is achieved. The reprocessing is based on the monotonic properties of the ordering and is carried out using a cost function. A new resource test highly related to the reprocessing strategy is introduced to reduce the number of computations for each reprocessing stage. For short codes of lengths N ≤ 32 or medium codes with 32 < N ≤ 64 with rate R ≥ 0.6, near-optimum bit error performance is achieved in two stages of reprocessing with at most a computation complexity of o(K2) constructed code-words, where K is the dimension of the code. For longer codes, three or more reprocessing stages are required to achieve near-optimum decoding. However, most of the coding gain is obtained within the first two reprocessing stages for error performances of practical interest. The proposed decoding algorithm applies to any binary linear code, does not require any data storage and is well suitable for parallel processing. Furthermore, the maximum number of computations required at each reprocessing stage is fixed, which prevents buffer overflow at low SNR. Further reductions of the number of computations based on probabilistic or decomposable properties of the code considered are also investigated. The generalization of the algorithm to other channels is discussed. Finally, the discrete time channel associated with the AWGN model after ordering is greatly simplified. This simplification allows an important reduction of the number of computations required to evaluate the theoretical error performance of any algorithm based on a partial or total ordering.