Error-control codes in transmission systems

In theory of modern transmission systems the considerable attention to coding methods of information is given.

Coding – the operation of an identification of the symbols or groups of symbols from one code by symbols or groups of symbols to other code. Necessity of coding arises, first of all, from requirement to adapt a message form to the given communication channel or to any other device intended for transformation or storage of the information. The typical block diagram of digital telecommunication system is resulted on figure 1.1. The source produces messages which it is necessary to transfer through the channel of a telecommunication systems. It can be discrete messages (data, cable messages etc.) or continuous messages (speech, audio, TV, etc.), transformed to the digital signals. The real messages containredundancy and for matching of the information source with a transmitting channel usually the source encoder is used. Together with decoder they form source codec. The source coding methods were studied in Module №2. The primary goal of any telecommunication system is the information transmitting with given fidelity and rate. These requirements are in contradict and increasing of information rate leads to decreasing of the noise immunity and transmitting fidelity. In agree with well known Shannon theorems, as is wished considerable increase of fidelity of information transfer if a transmitting rate through channel R _ch does not exceed the channel capacity C _ch basically is possible. It is reached by using of the enough long error-correcting codes.

error-control code is the code which allow to detect and correct errors arising from messages transition in the communication channels. With this purpose the redundancy is entered into structure of an error-correcting codes. Codec of error-control code (channel encoder and decoder) is shown on figure 1.1.

In real conditions the length of a code is limited by admissible complexity of coding/decoding devices. Therefore the result from using of error-control codes depends on the code parameters and restrictions on realization of the channel codec.

The modern theory offers a wide set of error-control codes, various on structure, construction principles and error detection and correction capability. In the subsequent chapters the important classes of the codes with effective coding/decoding algorithms are considered.