A Syndrome Based Decoding of Linear Codes Using Deep Learning Method

Subject Areas : Multimedia Processing, Communications Systems, Intelligent Systems

Ali Moradi ¹ , Mohammad Tahghighi Sharabyan ²

1 - MSc Student, Faculty of Electrical and Computer Engineering, Zanjan Branch, Islamic Azad University, Zanjan, Iran
2 - Assistant Professor, Faculty of Electrical and Computer Engineering, Zanjan Branch, Islamic Azad University, Zanjan

Received: 2021-05-18 Accepted : 2021-07-24 Published : 2021-06-22

Keywords: Coding, deep learning, Convolutional neural networks,

Abstract :

Introduction: The development of digital communication with high reliability has been made possible in the first place by designing codes that allow the receiver to recover the received message efficiently and correctly in noisy channel conditions. Coding theory has progressed tremendously over the past seven decades, and we now see near-optimal codes for relatively long codes. The private codes have reached the Shannon capacity limit using the belief propagation algorithm. Although this shows acceptable performance for relatively long codes, for medium and short codes, the belief propagation algorithm performs poorly. Hence, we are still facing challenges with short codes, which are of paramount importance currently in digital communication thanks to the spread of the Internet of Things. With the emergence of deep learning models that have obtained good results in various fields such as object recognition and speech recognition, the use of neural networks in the field of coding has been revived. Among these, convolutional networks, which play an essential role in the success of deep learning models, have been favored by researchers in the field of coding.Method: To increase the coding accuracy of short-length LDPC (Low-Density Parity Check Codes) based on the sign equation and reduce its computational complexity, the combined architecture of a one-dimensional convolutional network, and recurrent neural network was used. To determine the solution of the sign equation, the error pattern detection method was utilized. For this purpose, first, a one-dimensional convolutional network with three main layers was used, each layer containing sublayers of convolution and integration. Then, the output of the convolutional network was applied to the return network of the GRU. The GRU return network with three times the length of the codeword was used with the ReLU activation function.Findings:We consider Maximizer Posterior Probability or MAP as the comparison metric. The comparison between the combined model of the one-dimensional convolutional network and the return network with the pure return network model shows that for the 64-length LDPC code in reducing the bit error rate, the combined model of the convolutional network and the GRU network performs better. The bit error rate in different noise conditions is 0.5 to 0.8 dB less than the rate of maximum likelihood coder.Discussion and Conclusion:In the last few years, in the encoding method of linear codes based on the syndrome equation, methods based on deep learning are used to solve the equation of the symbol and also to detect the error pattern. We showed that convolutional networks have the potential to improve the performance of such networks.

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