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 $\backslash \; \{0,1\; \backslash \}$ 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 $p\; \backslash \; Leq\; 1/2$.

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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