Symmetric channel

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A communication channel whose transition function possesses some kind of symmetry. A homogeneous discrete time memoryless channel with finite alphabets and of input and output letters, respectively, and defined by a matrix of transition probabilities is called a symmetric channel if


where is the number of elements of , . The most studied example of a memoryless symmetric channel is the binary symmetric channel with matrix of transition probabilities

For symmetric channels, many important information-theoretic characteristics can either be calculated explicitly or their calculation can be substantially simplified in comparison with non-symmetric channels. For example, for a memoryless symmetric channel with matrix of the form (*) the capacity (cf. Transmission rate of a channel) is given by the equation

For references see ,

cited under Communication channel.



[a1] R.C. Gallager, "Information theory and reliable communication" , Wiley (1968)
How to Cite This Entry:
Symmetric channel. Encyclopedia of Mathematics. URL:
This article was adapted from an original article by R.L. DobrushinV.V. Prelov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article