Theory and application of neural networks for 1/n rate convolutional decoders

In this paper a detailed mathematical model of a 1/n rate conventional convolutional decoder system, based on neural networks (NNs) applications and the gradient descent algorithm, has been developed and analysed. The general expression for the noise energy function, needed for the recurrent neural networks (RNNs) decoding, is derived. Then, the expressions for the gradient descent updating rule are derived and the NN decoder was designed. Based on the developed theory, a simulator of the decoder was implemented. Simulation results have confirmed that the RNN decoder is capable of performing very close to the Viterbi decoder and works extremely well for some specially structured convolutional codes. In particular, decoding capabilities of RNN decoders are investigated in the case when simulated annealing (SA) technique has been used. It is also shown that there are certain codes that do not require SA and can achieve performance comparable to the Viterbi algorithm.