Представлены теоретические и прикладные результаты современной теории кодирования как задачи поиска глобального экстремума функционала в дискретных пространствах. Рассмотрены различные методы простой коррекции ошибок при максимально допустимом уровне шума. Показано, что многопороговые декодеры, различные версии алгоритма Витерби и новые методы кодирования успешно решают на высоком технологическом уровне главную проблему теории информации – простое и эффективное декодирование вблизи границы Шеннона.

Для специалистов в области систем связи, инженеров, студентов старших курсов, а также аспирантов математических и радиотехнических факультетов.

Theoretical and practical results of modern coding theory are presented as the problem the global extremum search of functionals in discrete spaces. The Optimization Theory (OT) for coding is taken as approach for simple error correction under such conditions, when the code rate R is directly close to the channel capacity C : R?C.
It is shown that the multithreshold decoders (MTD), different versions of the Viterbi algorithm and the new codes that are created on the OT basis provide a simple highly reliable correction of the digital streams at such noise levels, which correspond to the successful solution with a high technological level the main problems of information theory, formulated 70 years ago: - simple and effective decoding in vicinity to the Shannon's bound.
New paradigms of OT and opportunities of divergent coding, symbolic algorithms for MTD and decoders with direct metrics control are considered in ensuring such a level of encoding efficiency which is really identical to the optimal exhaustive search methods, but at the minimum possible linear with a code length complexity of decoding.
The technology of modern developments is described in the new version of application researches of error-correcting coding theory.
The MTD and OT studies were supported in Russia by the RFFI with grants: 05-07-00024в, 08-07-00078а, 15-37-50568, 14-07-00859, 15-07-06348.
For specialists in the field of communication systems, engineers, students, and post-graduate students of mathematics and radio engineering faculties.