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

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.

A new efficient modified back propagation algorithm with adaptive learning rate is proposed to increase the convergence speed and to minimize the error. The method eliminates initial fixing of learning rate through trial and error and replaces by adaptive learning rate. In each iteration, adaptive learning rate for output and hidden layer are determined by calculating differential linear and nonlinear errors of output layer and hidden layer separately. In this method, each layer has different learning rate in each iteration. The performance of the proposed algorithm is verified by the simulation results.

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 channel characteristics. Two types of tested data have been used; randomly generated data and a practical data that have been extracted from a funded project entitled by ECEM. From the achieved simulation results, the work that is based on SAT shows promising results in reducing the PAPR effect reached up to 80% over the work in the literature and our previously published work. This means that this work gives an extra reduction up to 15% of our previously published work. However, this achievement will be under the cost of complexity. This penalty could be optimized by imposing the NN to the SAT work in order to enhance the wireless systems performance.

- by Thomas Britz
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- Linear error correcting codes, Matroid, Codeword Support, Linear Subcodes

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.