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Distributed source coding (DSC) is a method for compressing related but non-communicating information sources. The Slepian-Wolf theorem, proposed in 1973, sets a theoretical limit for lossless compression in DSC. While the theorem has not been practically achieved, scientists are attempting to reach the limit by maximizing the separation distance between the two coded signals.
In communication and information theory, distributed source code (DSC) is a crucial problem that describes the compression of information sources that are related in multiples but cannot communicate with each other. DSC enables relationship paradigms in video coding that swap the complexity of encoders and decoders, representing a conceptual shift in video processing. A multi-source correlation can be modeled between the channel codes and the decoder sides, allowing distributed source coding to shift computational complexity between the encoder side and the decoder side. This provides an appropriate framework for applications that have a sender that is subjected to complexity stresses, such as a sensor network or video compression.
Two men named Jack K. Wolf and David Slepian proposed a theoretical lossless compression limit for distributed source encoding, which is now called the Slepian-Wolf theorem or limit. The limit was proposed in terms of entropy with related sources of information in the year 1973. One of the things they were able to present is that two separate and isolated sources are able to compress data efficiently and as if both the sources communicated directly with each other. Later in 1975, a man named Thomas M. Cover extended this theorem to an instance of more than two sources.
In distributed source coding, multiple dependent sources are encoded with separate decoders and joint encoders. The Slepian-Wolf theorem, which represents these sources as two different variables, assumes that two separate and related signals came from different sources and were not communicating with each other. These are the encoders and their signals are transferred to a receiver, which is the decoder capable of performing the joint decoding process of both information signals. The theorem attempts to resolve what the probability rate of the receiver decoding an error is and approaches zero, which is represented as its joint entropy. As both Wolf and Slepian demonstrated in 1973, even if correlated signals are encoded separately, the combined rate is sufficient.
While this theorem theoretically postulates that this is achievable in distributed source encoding, the limits of the theory have not been realized or even closely approached in practical applications. Two other scientists, Ramchandran and Pradhan, attempted to figure out how to reach this theoretical limit and prove the plausibility of the Slepian-Wolf theorem. They have attempted this by providing a particular solution for the two coded signals having a maximum separation distance.
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