  This paper proposes a method for designing error correction codes by
combining a known coding scheme with an autoencoder. Specifically, we integrate
an LDPC code with a trained autoencoder to develop an error correction code for
intractable nonlinear channels. The LDPC encoder shrinks the input space of the
autoencoder, which enables the autoencoder to learn more easily. The proposed
error correction code shows promising results for one-bit quantization, a
challenging case of a nonlinear channel. Specifically, our design gives a
waterfall slope bit error rate even with high order modulation formats such as
16-QAM and 64-QAM despite one-bit quantization. This gain is theoretically
grounded by proving that the trained autoencoder provides approximately
Gaussian distributed data to the LDPC decoder even though the received signal
has non-Gaussian statistics due to the one-bit quantization.
