"Real" Slepian-Wolf Codes
Bikash Kumar Dey, Sidharth Jaggi, and Michael Langberg

TL;DR
This paper proves that real-linear codes can achieve the Slepian-Wolf rate region for i.i.d. sources, introducing novel decoding methods and techniques relevant to information theory and compressed sensing.
Contribution
It provides a new achievability proof using real-linear codes and demonstrates their effectiveness for Slepian-Wolf coding, connecting to broader applications.
Findings
Real-linear codes achieve the Slepian-Wolf rate region.
Typicality decoding is equivalent to solving an integer program.
Minimum entropy decoding achieves exponentially small error probability.
Abstract
We provide a novel achievability proof of the Slepian-Wolf theorem for i.i.d. sources over finite alphabets. We demonstrate that random codes that are linear over the real field achieve the classical Slepian-Wolf rate-region. For finite alphabets we show that typicality decoding is equivalent to solving an integer program. Minimum entropy decoding is also shown to achieve exponentially small probability of error. The techniques used may be of independent interest for code design for a wide class of information theory problems, and for the field of compressed sensing.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsCoding theory and cryptography · Cellular Automata and Applications · Error Correcting Code Techniques
