Review of the book «Proceedings on the Self-Checking Embedded Control Circuits Synthesis Theory Based on Binary Redundant Codes»

Proceedings on the Self-Checking Embedded Control Circuits Synthesis Theory Based on Binary Redundant Codes. Vol. 1. Moscow, Nauka publ., 2020, 611 p. ISBN 978-5-02-040758-9.Proceedings on the Self-Checking Embedded Control Circuits Synthesis Theory Based on Binary Redundant Codes. Vol. 2. Moscow, Nauka publ., 2021, 527 p. ISBN 978-5-02-040757-2.The first volume of the book includes papers devoted to three main areas of research in the field of synthesis of self-checking discrete systems: study of features of classical sum codes (Berger codes), modular sum codes, as well as their modifications proposed by the authors of the articles; study of features of codes for which check bits are obtained using convolutions modulo М = 2 of a part of data bits (polynomial codes and classical Hamming codes); research of the Boolean Complement method for organisation of self-checking discrete systems based on redundant binary codes. Materials are provided on detailed characteristics of error detection in data bits of redundant binary codes under the condition of errorfree check bits, descriptions of methods for constructing previously unknown modified sum codes and features of methods for synthesizing self-checking discrete systems based on binary redundant codes.The second volume of the book includes papers in the field of constructing binary sum codes weighted bits and transitions between bits occupying adjacent positions in data vectors of code words, as well as the results of studying their characteristics and methods of synthesising coding equipment. The issues of application of features of codes in organisation of self-checking discrete systems are considered. The reader will find on the pages of this volume materials on detailed characteristics of error detection in data bits of weight-based sum codes provided that the check bits are error-free, descriptions of methods for constructing previously unknown weight-based sum codes and features of methods for synthesising self-checking discrete systems based on them.The book can be useful for developers, researchers and engineers working in the field of technical diagnostics of discrete systems and synthesis of systems with fault detection, as well as students studying computer science, computer technology and automation.

The Concurrent Error-Detection Systems Organization Based on the Boolean Complement Method with the Preliminary Transformation of Operating Functions into Check Vectors of Berger Codes

The article describes a new way of concurrent error-detection (CED) systems organization using the Boolean complement method, which involves the use of pre-compression of signals from the diagnostic object using encoders of classical sum codes (Berger codes). Control of compressed signals is carried out using the constant-weight "1-out-of-4" code. In comparison with the known methods of the CED systems organization, it is possible to implement a self-checking digital device using one such circuit, and this significantly reduces the structural redundancy. The article suggests using the encoders of modified Berger codes with improved error detection characteristics as a compression scheme.

BERGER CODES IN CONCURRENT ERROR-DETECTION SYSTEMS, IMPLEMENTED ON THE BASIS OF BOOLEAN COMPLEMENT METHOD

The article deals with the previously unknown characteristics of the error detection by using classical Berger codes based on their multiplicities and types (unidirectional, symmetrical and asymmetrical), which can be applied in the concurrent error-detection (CED) systems synthesis, for example, through the use of Boolean complement method. The article shows that Berger codes do not detect a certain amount of both symmetrical, unidirectional and asymmetrical errors in code words. This differs from the previously identified characteristics of the error detection only in data vectors of Berger codes (in this case, any symmetrical errors are not detected, and any unidirectional and asymmetrical errors are detected, which is used in the synthesis of systems with fault detection). The share of undetectable er-rors from their total number for Berger codes with data vector lengths r = 4,…,7 is less than 2%, and for Berger codes with data vector lengths r = 8,…,15 it is less than 0.5%. The use of classical sum codes is effective in the CED systems synthesis, including the Boolean complement method, in which both data and check bits of code words are calculated using the diagnostic object itself

The features of the concurrent error-detection systems of combinational logic circuits based on the search for groups of symmetrically-independent outputs construction

The authors of the article found that in the use of classical sum codes (Berger codes) and a some of their modifications in the combinational circuits testing organization it is possible to detect both unidirectional and part of non-unidirectional errors in the data vectors. It is shown that it is possible to search for such groups of outputs of combinational circuits where only symmetrical errors occur due to stuck at-faults of elements of the internal structure of the circuits. Such groups of outputs are designated as symmetrically-independent outputs (SI-groups of outputs). The conditions of belonging of the group of outputs of the combinational circuits to the SI-groups of outputs are determined. It is shown that each SI-group of outputs can be controlled using a separate testing subsystem based on the code with the detection of any non-symmetrical errors (in particular, and any non-symmetrical errors up to certain multiplicities). The ways of searching for SI-groups of outputs in the combinational circuits testing organization are presented