Types of redundancy.

Types of redundancy.

The effect of interference can lead to the following results: 1) “1” -> “0”, 2) “0” -> “1”, 3) “1” -> “x”, 4) “0” -> “x ". X - indefinite signal, 3), 4) - erasing, 1), 2) - inversion. There can be situations of 1) and 2) equiprobable, i.e. distortions are symmetric, and maybe asymmetrical, when either 1) or 2) the type of errors prevails. Suppose message α is transmitted. As a result, infa was distorted, and the message β was obtained. The task is to retrieve the transmitted message α from the received message β. This problem is solved by introducing redundancy. There are temporary, spatial and combined redundancy. Under redundancy understand the use of large resources for message transmission than the minimum necessary. Temporal redundancy is the repeated repetition of one total ... source and array processing ... In the simplest case, this processing comes down to a simple vote. Spatial redundancy is the introduction of additional bits in the information word according to certain rules. Receiver, knowing these rules and applying them to the received message. Can detect or correct a certain number of errors. This application of both spatial and temporal redundancy.

An example of temporal redundancy: a code with repetition (2S + 1) times, voting takes place at the receiving end and S = 1, 2, ... the majority of them make a decision about the transmitted message. If S = 1, then the code is called “treble code”. Let us evaluate the efficiency: let it be necessary to transfer “0”; P <½. At the receiving end:

P = 3p ² (1-p) + p ³ = p [3p (1-p) + p ² ] is the probability that an incorrect decision will be made => P <p. The general conclusion: the use of code with repetition reduces the likelihood of making the wrong decision. The <probability of a single error, the more effective the code, than> S, the more effective the code. However, loss of time, reduction in transmission speed.

An example of spatial redundancy: let the message be transmitted α = a ₁ , a ₂ , ..., a _k . Before transmitting the message, add another digit to it, such that α '= a ₁ , a ₂ , ..., a _k a _{k +1} . ∑ _{i = 1} ^{k +1} (+) a _i = 0. α = 101101, α '= 1011010. At the receiving end, β 'is obtained, having k + 1 digit and calculating the sum of direct discharges. If this sum is 0, then it is assumed with great confidence that β '= α'. If not. It is reported that there is an error in the message. This procedure is called parity check. (+): simplicity, Θ: time. This code has only a detecting ability and is not able to correct the error.

k = 16. Found and corrected the error. 16 useful and 4 additional.