  Decoder diversity is a powerful error correction framework in which a
collection of decoders collaboratively correct a set of error patterns
otherwise uncorrectable by any individual decoder. In this paper, we propose a
new approach to design the decoder diversity of finite alphabet iterative
decoders (FAIDs) for Low-Density Parity Check (LDPC) codes over the binary
symmetric channel (BSC), for the purpose of lowering the error floor while
guaranteeing the waterfall performance. The proposed decoder diversity is
achieved by training a recurrent quantized neural network (RQNN) to
learn/design FAIDs. We demonstrated for the first time that a machine-learned
decoder can surpass in performance a man-made decoder of the same complexity.
As RQNNs can model a broad class of FAIDs, they are capable of learning an
arbitrary FAID. To provide sufficient knowledge of the error floor to the RQNN,
the training sets are constructed by sampling from the set of most problematic
error patterns - trapping sets. In contrast to the existing methods that use
the cross-entropy function as the loss function, we introduce a
frame-error-rate (FER) based loss function to train the RQNN with the objective
of correcting specific error patterns rather than reducing the bit error rate
(BER). The examples and simulation results show that the RQNN-aided decoder
diversity increases the error correction capability of LDPC codes and lowers
the error floor.
