Abstract

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.

Keywords: Convolutional codes; Decoding; Noise energy function; Simulated annealing; Recurrent neural networks

Article Outline

1. Introduction

2. Theoretical background

2.1. Encoding and transmission procedure

2.2. Decoding procedure

2.3. Minimisation of the noise energy function

2.4. Solutions for the problem of global minima

2.4.1. Application of simulated annealing

2.4.2. A special class of codes

3. Application of the GDA

3.1. GDA implementation

3.2. GDA application and investigation

3.3. RNN decoding procedure

4. Decoding methodologies

4.1. Hard-decision decoding mode

4.2. Soft-decision decoding mode

4.3. A special class of codes

5. Conclusions

Appendix A. Derivation of the general gradient term

Appendix B. RNN decoder complexity and speed

Appendix B.1. Number of additions

Appendix B.2. Number of multiplications

References