Linear error correcting codes Research Papers (original) (raw)

This study introduces an Artificial Neural Network (ANN) framework to address the two-dimensional Poisson's equation within a rectangular domain. It places a focus on the training process of a neural network with three layers,... more

This study introduces an Artificial Neural Network (ANN) framework to address the two-dimensional Poisson's equation within a rectangular domain. It places a focus on the training process of a neural network with three layers, incorporating hidden neurons. The feedforward ANN is trained using MATLAB, which calculates weights for all neurons within the network structure. These acquired weights are subsequently applied in the trained network model to make predictions for the desired output of a specific partial differential equation. The architecture of the ANN consists of three layers: one input layer, one hidden layer, and one output layer. In this study, we specifically employ an ANN configuration with 50 hidden neurons. The training process is executed using MATLAB, utilizing the Levenberg-Marquardt algorithm (LMA) for optimization. Furthermore, the study encompasses the development of surface and contour plots that illustrate the computational solution of the partial differential equation. Additionally, error functions are graphed to assess the effectiveness of the ANN model.

Machine learning and deep learning algorithms have proved to be a powerful tool for developing data-driven signal processing algorithms for challenging engineering problems. This paper studies the modern machine learning algorithm for... more

Machine learning and deep learning algorithms have proved to be a powerful tool for developing data-driven signal processing algorithms for challenging engineering problems. This paper studies the modern machine learning algorithm for modeling nonlinear devices like power amplifiers (PAs) for underwater acoustic (UWA) orthogonal frequency divisional multiplexing (OFDM) communication. The OFDM system has a high peak to average power ratio (PAPR) in the time domain because the subcarriers are added coherently via inverse fast Fourier transform (IFFT). This causes a higher bit error rate (BER) and degrades the performance of the PAs; hence, it reduces the power efficiency. For long-range underwater acoustic applications such as the long-term monitoring of the sea, the PA works in full consumption mode. Thus, it becomes a challenging task to minimize power consumption and unnecessary distortion. To mitigate this problem, a receiver-based nonlinearity distortion mitigation method is prop...

A theoretical formulation of a fast learning method based on a pseudoinverse technique is presented. The efficiency and robustness of the method are verified with the help of an Exclusive OR problem and a dynamic system identification of... more

A theoretical formulation of a fast learning method based on a pseudoinverse technique is presented. The efficiency and robustness of the method are verified with the help of an Exclusive OR problem and a dynamic system identification of a linear single degree of freedom mass–spring problem. It is observed that, compared with the conventional backpropagation method, the proposed method has a better convergence rate and a higher degree of learning accuracy with a lower equivalent learning coefficient. It is also found that unlike the steepest descent method, the learning capability of which is dependent on the value of the learning coefficient ν, the proposed pseudoinverse based backpropagation algorithm is comparatively robust with respect to its equivalent variable learning coefficient. A combination of the pseudoinverse method and the steepest descent method is proposed for a faster, more accurate learning capability.

We present generalisations of several MacWilliams type identities, including those by Klve and Shiromoto, and of the theorems of Greene and Barg that describe support weight enumerators of the code. One of our main tools is a... more

We present generalisations of several MacWilliams type identities, including those by Klve and Shiromoto, and of the theorems of Greene and Barg that describe support weight enumerators of the code. One of our main tools is a generalisation of a decomposition theorem due to Brylawski. 1

A new work has been proposed in this paper in order to overcome one of the main drawbacks that found in the Orthogonal Frequency Division Multiplex (OFDM) systems, namely Peak to Average Power Ratio (PAPR). Furthermore, this work will be... more

A new work has been proposed in this paper in order to overcome one of the main drawbacks that found in the Orthogonal Frequency Division Multiplex (OFDM) systems, namely Peak to Average Power Ratio (PAPR). Furthermore, this work will be compared with a previously published work that uses the neural network (NN) as a solution to remedy this deficiency. The proposed work could be considered as a special averaging technique (SAT), which consists of wavelet transformation in its first stage, a globally statistical adaptive detecting algorithm as a second stage; and in the third stage it replaces the affected peaks by making use of moving average filter process. In the NN work, the learning process makes use of a previously published work that is based on three linear coding techniques. In order to check the proposed work validity, a MATLAB simulation has been run and has two main variables to compare with; namely BER and CCDF curves. This is true under the same bandwidth occupancy and ...

Index 74 Preface The three subjects of the title (codes, matroids, and permutation groups) have many interconnections. In particular, in each case, there is a polynomial which captures a lot of information about the structure: we have the... more

Index 74 Preface The three subjects of the title (codes, matroids, and permutation groups) have many interconnections. In particular, in each case, there is a polynomial which captures a lot of information about the structure: we have the weight enumerator of a code, the Tutte polynomial (or rank polynomial) of a matroid, and the cycle index of a permutation group. With any code is associated a matroid in a natural way. A celebrated theorem of Curtis Greene asserts that the weight enumerator of the code is a specialisation of the Tutte polynomial of the matroid. It is less well known that with any code is associated a permutation group, and the weight enumerator of the code is the same (up to normalisation) as the cycle index of the permutation group. There is a class of permutation groups, the so-called IBIS groups, which are closely associated with matroids. More precisely, the IBIS groups are those for which the irredundant bases (in the sense of computational group theory) are t...

With every linear code is associated a permutation group whose cycle index is the weight enumerator of the code (up to a trivial normalisation). There is a class of permutation groups (the IBIS groups) which includes the groups obtained... more

With every linear code is associated a permutation group whose cycle index is the weight enumerator of the code (up to a trivial normalisation). There is a class of permutation groups (the IBIS groups) which includes the groups obtained from codes as above. With every IBIS group is associated a matroid; in the case of a group from a code, the matroid differs only trivially from that which arises directly from the code. In this case, the Tutte polynomial of the code specialises to the weight enumerator (by Greene's Theorem), and hence also to the cycle index. However, in another subclass of IBIS groups, the base-transitive groups, the Tutte polynomial can be derived from the cycle index but not vice versa. I propose a polynomial for IBIS groups which generalises both Tutte polynomial and cycle index.

Since the 1963 article [8] by FJ MacWilliams, coding theorists have paid considerable attention to the support (Hamming) weight distribution of linear codes. In later years, this interest has increased due to results such as those by Wei... more

Since the 1963 article [8] by FJ MacWilliams, coding theorists have paid considerable attention to the support (Hamming) weight distribution of linear codes. In later years, this interest has increased due to results such as those by Wei [16] on rth generalised Hamming weights, Kløve [6] ...

A B S T R A C T: This paper presents the artificial neural network (ANN) model for predicting the lift coefficient aerodynamic performance of a NACA 64-210 airfoil in rain conditions. In order to determine the capability of the ANN... more

A B S T R A C T: This paper presents the artificial neural network (ANN) model for predicting the lift coefficient aerodynamic performance of a NACA 64-210 airfoil in rain conditions. In order to determine the capability of the ANN technique on estimating the prediction value for lift coefficient, a wind-tunnel experiment is referred to in this study. in the experiment, 75 samples of data concerned with the airfoil lift coefficient in rain are selected. The MATLAB ANN toolbox is employed for the modeling purpose with some justifications. The Le-venberg-Marquardt (trainlm), mean squared error (MSE), tangent sigmoid (tansig) for feedforward back-propagation networks is adopted as the training algorithm, performance and transfer functions, respectively. With three nodes in the input layer and one node in the output layer, eight network structures are chosen with different numbers of nodes in the hidden layer which are 3-1-1, 3-3-1, 3-6-1, 3-7-1, 3-1-1-1, 3-3-3-1, 3-6-6-1 and 3-7-7-1 structures. It is found that the 3-7-7-1 network structure gives the best prediction results of the lift coefficients of the airfoil in rain conditions. Finally, the effects of rain modeling parameters on the lift coefficients of the airfoil in rain conditions are discussed through a comparison between the experimental and the best 3-7-7-1 structure predicted results.

Levenberg-Marquardt back-propagation training method has some limitations associated with over fitting and local optimum problems. Here, we proposed a new algorithm to increase the convergence speed of Backpropagation learning to design... more

Levenberg-Marquardt back-propagation training method has some limitations associated with over fitting and local optimum problems. Here, we proposed a new algorithm to increase the convergence speed of Backpropagation learning to design the airfoil. The aerodynamic force coefficients corresponding to series of airfoil are stored in a database along with the airfoil coordinates. A feedforward neural network is created with aerodynamic coefficient as input to produce the airfoil coordinates as output. In the proposed algorithm, for output layer, we used the cost function having linear & nonlinear error terms then for the hidden layer, we used steepest descent cost function. Results indicate that this mixed approach greatly enhances the training of artificial neural network and may accurately predict airfoil profile.

This paper considers the prototyping of linear block codes encoder and decoder for sound data using National Instruments LabView software. Linear block codes can be defined by two parameters, which are code size n and information bit size... more

This paper considers the prototyping of linear block codes encoder and decoder for sound data using National Instruments LabView software. Linear block codes can be defined by two parameters, which are code size n and information bit size k. LabView is an easy to use, multipurpose software which has many features for designing and prototyping. This research is a preliminary research on channel coding implementation on LabView. In this research, Reed-Muller codes are used to implement the design. 16-bit sound data are used as test subjects for block code encoding, decoding, and error correction. The result shows that the design works well. The design can correct single bit error in any positions. Authors’ next project is to implement cyclic and more advanced code for error correcting implementation in LabView.