Classification of error-control codes

The error-control codes can be classified to various signs. The structure of codes classification is resulted on figure 1.2. On a way of formation the error-control codes are subdivided on block and continuous codes. Formation of the block codes provides splittingof transferred digital sequencesinto separate blocks which move to encoder input. To each such block on an encoder output there corresponds the block of code symbols which work is defined by a rule named as the coding algorithm. Formation of the continuous codes is carried out continuously in time, without division into blocks as defines the name of this code class.

Block codes historically have been discovered and studied earlier, at beginning of coding theory development. In a class of continuous codes it is necessary to note the convolutional codes which exceed on characteristics of the block codes, and, for this reason, find wide application in a transmission systems.

Many codes carry names of scientists which have discovered and investigated them.Such example is the continuous Fink-Hagelbarger’s code offered by Soviet scientist L. Fink and German expert R. Hagelbarger. Long time this code was in the literature as indicative example of a continuous code with simple encoding/decoding algorithms, but after elaborating the convolutional code has given way to them. For the description of procedures of coding/decoding both block and convolutional codes usually use an adequate mathematical apparatus.For the description of linear codes the well developed linear algebra is used. Formation of nonlinear codes is made with application of nonlinear procedures. Such approach allows to construct in some cases nonlinear codes with a number of special properties. In the error-control coding theory the problem of realisation complexity of encoding/decoding procedure and in particular decoding procedure is important. Therefore some classes of codes (Hamming codes, Bose-chaudhuri-Hochquenghem codes, Reed-Solomon codes etc.) have been developed together with the decoding algorithms connected with structural properties of these codes.And on contrary the elaborating of a new decoding algorithms for convolutional codes (Viterbi algorithm, sequential decoding, threshold decoding) initiated searches of corresponding codes. Distinctive advantages of error-control codes induced searches of new approaches to realization of ways to increase of noise immunity and efficiency of transmission systems. On figure 1.2 new methods of encoding/decoding (coded modulation, turbo-codes, time-space coding) are noted accordingly.