  In this paper, we introduce the syndrome loss, an alternative loss function
for neural error-correcting decoders based on a relaxation of the syndrome. The
syndrome loss penalizes the decoder for producing outputs that do not
correspond to valid codewords. We show that training with the syndrome loss
yields decoders with consistently lower frame error rate for a number of short
block codes, at little additional cost during training and no additional cost
during inference. The proposed method does not depend on knowledge of the
transmitted codeword, making it a promising tool for online adaptation to
changing channel conditions.
