Optimization Coding Theory and Multithreshold Algorithms
V.V. Zolotarev, Y.B. Zubarev, G.V. Ovechkin
This work sets out the basic principles of modern error-correction coding optimization theory, before moving on directly to consider multithreshold decoding (MTD) algorithms. 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.
It reviews the capabilities of symbolic codes, discovered by the authors, and the corresponding, simple-toimplement special symbolic MTD decoders, which are easier and more efficient than all other known methods of decoding non-binary codes. Concatenated parallel-type arrangements and other configurations that enhance the efficiency of MTD are proposed. The efficiency limits of real codes with a code rate close to channel capacity, i.e. when R≈C, are evaluated. The effectiveness and complexity of error-correction procedures in software and hardware implementation are assessed.
This work will be of interest to experts in the field of coding theory, communication system developers, and undergraduate and postgraduate students in relevant disciplines.
First published in Switzerland in 2015 by ITU
Coding Theory as a Simple Optimal Decoding near Shannon's Bound
V.V. Zolotarev
Optimization Theory of error-correcting coding - is a new "quantum mechanics" of information theory
Theoretical and applied results of modern coding theory are presented as a problem of search global extremum of the functionals in the discrete spaces.
Various methods of simple error correction are considered for maximum possible noise level. It is shown that the multithreshold decoders (MTD), different versions of the Viterbi algorithms (VA) and other new coding methods successfully have solved at high technological level the main problem of information theory – a simple and effective decoding in close vicinity to the Shannon's bound.
This new «quantum mechanics» of information theory is named Optimization Theory (OT) of error-correcting coding.
For specialists in the field of communication systems, engineers, undergraduate, graduate and postgraduate students of mathematics and radio engineering departments.
Publisher: Hot Line - Telecom, 2019
Problems and Discoveries of the Optimization Theory for Coding near Shannon's Bound (OT in illustrations)
N.A. Kuznetsov, V.V. Zolotarev, Y.B. Zubarev, G.V. Ovechkin, R.R. Nazirov, S.V. Averin
The theoretical and applied results of the modern noiseproof coding theory are summarized in a popular form, using extensive illustrative material as a problem of searching for the global extremum of the functional in discrete spaces.
The authors propose the simplest algorithms for decoding of all channels classes with independent character distortions and with a linear of the code length complexity. The decoding error probabilities correspond to the best possible veracity levels, which is provided usually only by optimal full searching error correction methods in noisy channels. It is extremely important also that these highest characteristics of algorithms developed by Optimization Theory (OT) can be achieved even very close to the Shannon’s bound.