# Symmetric channel

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.

#### Comments

#### References

[a1] | R.C. Gallager, "Information theory and reliable communication" , Wiley (1968) |

**How to Cite This Entry:**

Symmetric channel.

*Encyclopedia of Mathematics.*URL: http://www.encyclopediaofmath.org/index.php?title=Symmetric_channel&oldid=12571