Аннотация
The results obtained during the 25-year evolution of the error-correction coding optimization theory (OT) and multithreshold decoding (MTD) methods, which have been created on its basis, are presented.These iterative algorithms, with each symbol correction iteration, always find decisions of strictly increasing likelihood, and can achieve optimum results that would normally require exhaustive search of all possible code words.Research results on MTDs and other error-correction methods for binary and non-binary codes used to send messages over channels with binary, symbolic errors and erasures are presented.It is shown MTDs simply decode very long codes, which are the only ones capable of supporting the effective implementation of error correction at high channel noise levels.Assessments of software implementation complexity show the advantage of MTD over other methods in terms of the number of operations per bit with comparable efficiency.It reviews the capabilities of symbolic codes, discovered by the authors, and the corresponding, simple to implement special symbolic MTD decoders, which are easier and more efficient than all other known methods of decoding non-binary codes.The methodological basis of the OT and the new paradigms for successful research into the theory and applied issues of error-correction coding are discussed.General conclusions are formulated on the study, and directions for further development of work on MTD are suggested.