# Symmetrical binary channel

Alice wants to transmit a message to Bob. A symmetrical binary channel is a discrete Canal where Alice transmits a succession of elements of the unit $\ \left\{0,1 \\right\}$ and where the Probabilité of error in the transmission of a symbol is of $p$, for 0 and 1 (from where symmetry). This channel is without memory, i.e. no file of the messages is held.

In Communication, a traditional problem is to send information of a source to a destination via a Channel of communication, in the presence of Bruit. The Codage of channel is the whole of the solutions to this problem which are the correct codes.

## Technical details

### Definition

The idea of the symmetrical binary channel is that it is useful to model the Bruit channel. In this model, each bit of transmitted data is reversed with a probability $p$ and is transmitted without error with the probability complementary to $1-p$. The parameter $p$ determines (i.e. it only defines) the symmetrical channel binary of which it is question.

Without loss of general information, one can suppose that $p \ Leq 1/2$.

### Solutions

A simple solution this to secure against this type of noise is to send several copies of each bit to being transmitted: it is the Code of repetition. To make information redundant is the idea behind the Codage of channel, although its techniques can be much more elaborate (see Familles of codes).

## See too

• Another model of error: binary Channel with error of Bernoulli

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