"Real" Slepian-Wolf Codes

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.