Open Access

Julia Rechberger

• When we browse via WiFi on our laptop or mobile phone, we receive data over a noisy channel. The received message may differ from the one that was sent originally. Luckily it is often possible to reconstruct the original message but it may take a lot of time. That’s because decoding the received message is a complex problem, NP-hard to be exact. As we continue browsing, new information is sent to us in a high frequency. So if lags are to be avoided and as memory is finite, there is not much time left for decoding. Coding theory tackles this problem by creating models of the channels we use to communicate and tailor codes based on the channel properties. A well known family of codes are Low-Density Parity-Check codes (LDPC codes), they are widely used in standards like WiFi and DVB-T2. In practical settings the complexity of decoding a received message can be heavily reduced by using LDPC codes and approximative decoding algorithms. This thesis lays out the basic construction of LDPC codes and a proper decoding using the sum-product algorithm. On this basis a neural network to improve decoding is introduced. Therefore the sum-product algorithm is transformed into a neural network decoder. This approach was first presented by Nachmani et al. and treated in detail by Navneet Agrawal in 2017. To find out how machine learning can improve the codes, the bit error rates of the trained neural network decoder are compared with the bit error rates of the classic sum-product algorithm approach. Experiments with static and dynamic training datasets of diverse sizes, various signal-to-noise ratios, a feed forward as well as a recurrent architecture show how to tune the neural network decoder even further. Results of the experiments are used to verify statements made in Agrawal’s work. In addition, corrections and improvements in the area of metrics are presented. An implementation of the neural network to facilitate access for others will be made available to the public.