  We present a new deep-neural-network (DNN) based error correction code for
fading channels with output feedback, called deep SNR-robust feedback (DRF)
code. At the encoder, parity symbols are generated by a long short term memory
(LSTM) network based on the message as well as the past forward channel outputs
observed by the transmitter in a noisy fashion. The decoder uses a
bi-directional LSTM architecture along with a signal to noise ratio (SNR)-aware
attention NN to decode the message. The proposed code overcomes two major
shortcomings of the previously proposed DNN-based codes over channels with
passive output feedback: (i) the SNR-aware attention mechanism at the decoder
enables reliable application of the same trained NN over a wide range of SNR
values; (ii) curriculum training with batch-size scheduling is used to speed up
and stabilize training while improving the SNR-robustness of the resulting
code. We show that the DRF codes significantly outperform state-of-the-art in
terms of both the SNR-robustness and the error rate in additive white Gaussian
noise (AWGN) channel with feedback. In fading channels with perfect phase
compensation at the receiver, DRF codes learn to efficiently exploit knowledge
of the instantaneous fading amplitude (which is available to the encoder
through feedback) to reduce the overhead and complexity associated with channel
estimation at the decoder. Finally, we show the effectiveness of DRF codes in
multicast channels with feedback, where linear feedback codes are known to be
strictly suboptimal.
