Neural Rate-Adaptive LDPC Decoding for the Slepian-Wolf Problem

Distributed source coding (DSC) enables efficient compression of correlated sources by performing independent encoding and joint decoding. Slepian-Wolf coding plays a central role in DSC, as it allows near-lossless compression of correlated data at rates asymptotically approaching the joint entropy.Traditional approaches to constructive Slepian-Wolf coding employ algebraic binning techniques using channel codes, with decoding performed via algorithms such as belief propagation (BP). While effective, these methods suffer from high computational cost and suboptimal compression performance. We propose the first constructive learned Slepian-Wolf decoder for rate-adaptive coding, using a single multi-rate Transformer model. The architecture is inspired by neural channel decoding, but addresses the unique challenges of syndrome-based Slepian-Wolf coding based on side information. Furthermore, we incorporate the proposed rate-adaptive neural Slepian-Wolf decoder into a novel neural layered Wyner-Ziv code design for the quadratic Gaussian case and into a new layered Wyner-Ziv design for distributed stereo image coding. For Slepian-Wolf coding of binary sources, our neural decoder improves the compression performance over traditional BP decoding by up to 11%. In our monolithic and layered Wyner-Ziv designs, we are between 0.05 and 0.2 bits/sample away from the estimated ideal rate bound, while entropy coding needs an additional 0.4-1.2 bits/sample compared to the proposed Slepian-Wolf codec. Moreover, our stereo image coding design reduces the coding rate by 9-19% in low rate settings compared to the state-of-the-art with minimal loss in image quality. Finally, the proposed decoder is 15 times faster than BP decoding on a GPU.