scholarly journals Self Checking Design Technique for Numerical Computations

VLSI Design ◽  
1998 ◽  
Vol 5 (4) ◽  
pp. 385-392 ◽  
Author(s):  
F. S. Vainstein
Keyword(s):  
Error Detection ◽  
Substantial Reduction ◽  
Design Technique ◽  
Numerical Computations ◽  
Field Extensions ◽  
Class A ◽  
Error Detection And Correction ◽  
Algebraic Concepts ◽  
Class Of Functions ◽  
Multiple Error

The objective of this paper is to develop an efficient method for testing of numerical computations based on algebraic concepts such as transcendental degree of field extensions.A class of polynomially checkable functions is introduced, and for computation of the functions from this class a new method for error detection/error correction is proposed. This class of functions is shown to be large. The proposed method can also be extended to testing of computations of functions which are not polynomially checkable.The preliminary results show great potential of this approach. In particular the proposed approach will lead to substantial reduction in hardware overhead required for multiple error detection and correction, as compare to the check sum method and other existing techniques.

scholarly journals Multiple Error Correction in Redundant Residue Number Systems: A Modified Modular Projection Method with Maximum Likelihood Decoding

2022 ◽  
Vol 12 (1) ◽  
pp. 463
Author(s):  
Mikhail Babenko ◽  
Anton Nazarov ◽  
Maxim Deryabin ◽  
Nikolay Kucherov ◽  
Andrei Tchernykh ◽  
...  
Keyword(s):  
Error Detection ◽  
Chinese Remainder Theorem ◽  
Number System ◽  
Maximum Likelihood Decoding ◽  
Number Systems ◽  
Residue Number Systems ◽  
Error Detection And Correction ◽  
Residue Number ◽  
Weighted Number ◽  
Multiple Error

Error detection and correction codes based on redundant residue number systems are powerful tools to control and correct arithmetic processing and data transmission errors. Decoding the magnitude and location of a multiple error is a complex computational problem: it requires verifying a huge number of different possible combinations of erroneous residual digit positions in the error localization stage. This paper proposes a modified correcting method based on calculating the approximate weighted characteristics of modular projections. The new procedure for correcting errors and restoring numbers in a weighted number system involves the Chinese Remainder Theorem with fractions. This approach calculates the rank of each modular projection efficiently. The ranks are used to calculate the Hamming distances. The new method speeds up the procedure for correcting multiple errors and restoring numbers in weighted form by an average of 18% compared to state-of-the-art analogs.

scholarly journals The natural defense system and the normative self model

F1000Research ◽  
2016 ◽  
Vol 5 ◽  
pp. 797 ◽  
Author(s):  
Philippe Kourilsky
Keyword(s):  
Immune System ◽  
Error Detection ◽  
The Body ◽  
The Self ◽  
Infectious Agents ◽  
Defense System ◽  
Defensive Function ◽  
Natural Defense ◽  
Error Detection And Correction ◽  
Multiple Error

Infectious agents are not the only agressors, and the immune system is not the sole defender of the organism. In an enlarged perspective, the ‘normative self model’ postulates that a ‘natural defense system’ protects man and other complex organisms against the environmental and internal hazards of life, including infections and cancers. It involves multiple error detection and correction mechanisms that confer robustness to the body at all levels of its organization. According to the model, the self relies on a set of physiological norms, and NONself (meaning : Non Obedient to the Norms of the self) is anything ‘off-norms’. The natural defense system comprises a set of ‘civil defenses’ (to which all cells in organs and tissues contribute), and a ‘professional army ‘, made of a smaller set of mobile cells. Mobile and non mobile cells differ in their tuning abilities. Tuning extends the recognition capabilities of NONself by the mobile cells, which increase their defensive function. To prevent them to drift, which would compromise self/NONself discrimination, the more plastic mobile cells need to periodically refer to the more stable non mobile cells to keep within physiological standards.

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