CMR

Coding Theory

In communications systems, coding is used to alter the characteristics of a signal to make it more suitable for an intended application. Coding is used to optimize signals for transmission, to improve transmission quality and fidelity, to modifying the signal spectrum, to increasing information content, to provide error detection and/or correction, to provide data security, etc.

Code theorists have developed many different types of codes that can be used to vary one or more signal attributes including position, amplitude, polarity, and signal shape.

Barker codes (shown in Fig. 1) can be used to vary signal polarity to produce low autocorrelation characteristics.

Length	Codes
2	+1 −1	+1 +1
3	+1 +1 −1
4	+1 −1 +1 +1	+1 −1 −1 −1
5	+1 +1 +1 −1 +1
7	+1 +1 +1 −1 −1 +1 −1
11	+1 +1 +1 −1 −1 −1 +1 −1 −1 +1 −1
13	+1 +1 +1 +1 +1 −1 −1 +1 +1 −1 +1 −1 +1

Fig. 1 Barker Codes