In information theory and communication, the Slepian–Wolf coding, also known as the Slepian–Wolf bound, is a result in distributed source coding discovered by David Slepian and Jack Wolf in 1973. It is a method of theoretically coding two lossless compressed correlated sources.
Distributed coding is the coding of two, in this case, or more dependent sources with separate encoders and a joint decoder. Given two statistically dependent i.i.d. finite-alphabet random sequences X and Y, the Slepian–Wolf theorem gives a theoretical bound for the lossless coding rate for distributed coding of the two sources as shown below:
If both the encoder and the decoder of the two sources are independent, the lowest rate it can achieve for lossless compression is
A special case of distributed coding is compression with decoder side information, where source
This bound has been extended to the case of more than two correlated sources by Thomas M. Cover in 1975, and similar results were obtained in 1976 by Aaron D. Wyner and Jacob Ziv with regard to lossy coding of joint Gaussian sources.