Slepian–Wolf coding
In and , the Slepian–Wolf coding, also known as the Slepian–Wolf bound, is a result in discovered by and in 1973. It is a method of theoretically two correlated .
Distributed coding is the coding of two, in this case, or more dependent sources with separate and a joint . Given two statistically dependent i.i.d. finite-alphabet random 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 
and 
for 
and 
respectively, where and are the entropies of and . However, with joint decoding, if vanishing error probability for long sequences is accepted, the Slepian–Wolf theorem shows that much better compression rate can be achieved. As long as the total rate of and is larger than their joint entropy 
and none of the sources is encoded with a rate smaller than its , distributed coding can achieve arbitrarily small for long sequences.
A special case of distributed coding is compression with decoder side information, where source is available at the decoder side but not accessible at the encoder side. This can be treated as the condition that 
has already been used to encode , while we intend to use 
to encode . In other words, two isolated sources can compress data as efficiently as if they were communicating with each other. The whole system is operating in an asymmetric way (compression rate for the two sources are asymmetric).
This bound has been extended to the case of more than two correlated sources by in 1975, and similar results were obtained in 1976 by and with regard to lossy coding of joint Gaussian sources.