Application of neural networks and support vector machines in coding theory and practice

Abstract

In this chapter a mathematical model of a K'/n rate conventional convolutional encoder/decoder system was developed to be applied for decoding based on the gradient descent algorithm. For the system a general expression for the noise energy function, which is required for the recurrent neural networks decoding, is derived. The derivative is based on the representation of the encoding procedure as a mapping of a K'-dimensional message into n-dimensional Euclidean encoded bit set vector. The universal nature of derivative is demonstrated through its application for particular cases of a general 1/n rate code, a 1/2 encoder, and a 2/3 rate encoder. In order to eliminate the local minimum problem presented in the recurrent neural network, another global optimisation technique called support vector machine is investigated. Preliminary simulation results have been carried out, showing its potential to be applied as an alternative method to decode convolutional codes.