Binary extinction channel

Model of the BEC

The term binary erasure channel (short BEC of English. Binary erasure channel ) has been in the information theory first proposed by Peter Elias used. It denotes a memory-free information-theoretical channel that receives a bit (0 or 1) at the input and outputs a bit (0 or 1) or a transmission error E at the output. In the three possible output values ​​it differs from the binary symmetrical channel , which can only assume two output states.

Describes the probability of the occurrence of a transmission error E , then the probability of the error-free reception of a bit sent via the BEC is . This probability is independent of the value of the bit sent and its position. ${\displaystyle p_{e}}$ ${\displaystyle 1-p_{e}}$

The channel capacity of the BEC is . ${\displaystyle 1-p_{e}}$

literature

• Martin Bossert: Introduction to communications technology. Oldenbourg Verlag, Munich 2012, ISBN 3-486-70880-5 , p. 130 ff.
• Jürgen Göbel: Information theory and coding methods. Basics and Applications, 1st edition, VDE Verlag GmbH, Berlin 2007, ISBN 978-3-8007-2935-7 .

Web links

• Vincent Kerbaol: Binary Erasure Channel ( Memento June 14, 2004 in the Internet Archive )
• Lecture notes Kanalcodierung I (accessed January 22, 2018)
• Coding Theory (accessed January 22, 2018)