  In this work, a deep learning-based method for log-likelihood ratio (LLR)
lossy compression and quantization is proposed, with emphasis on a single-input
single-output uncorrelated fading communication setting. A deep autoencoder
network is trained to compress, quantize and reconstruct the bit log-likelihood
ratios corresponding to a single transmitted symbol. Specifically, the encoder
maps to a latent space with dimension equal to the number of sufficient
statistics required to recover the inputs - equal to three in this case - while
the decoder aims to reconstruct a noisy version of the latent representation
with the purpose of modeling quantization effects in a differentiable way.
Simulation results show that, when applied to a standard rate-1/2 low-density
parity-check (LDPC) code, a finite precision compression factor of nearly three
times is achieved when storing an entire codeword, with an incurred loss of
performance lower than 0.1 dB compared to straightforward scalar quantization
of the log-likelihood ratios.
