Caleb Zulawski

Master's Thesis

Learning an End-to-End Physical Layer with Computational Graphs

Read my entire thesis here

The goal of my thesis was to use machine learning, specifically neural networks, to learn a high-performing physical layer for a wireless communication system. I attempted to address a weakness in current modulation schemes; modulation and forward error correction are considered two separate problems. It is possible, however difficult, to design a modulation scheme that nears the Shannon limit, which is where neural networks come into play.

The results were promising. In the end I was able to train a modem that performed slightly outperformed convolutional codes.


The modem was designed as an autoencoder. The inputs to the autoencoder are the symbol bits, and the latent representation is the transmitted symbol. Therefore, the encoder becomes the modulator and the decoder becomes the demodulator.

An autoencoder


The autoencoder modem was able to compete with BPSK protected by one of the convolutional codes used by the LTE standard. The results are shown below.

Note: since convolutional codes do not block-encode, blocks were constructed by taking sets of adjacent bits.

Bit error rate

Block error rate