A Method for Operational Diagnosis of Data Represented in a Residue Number System
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A METHOD FOR OPERATIONAL DIAGNOSIS OF DATA REPRESENTED IN A RESIDUE NUMBER SYSTEM V. A. Krasnobayev1 and S. A. Koshman2
UDC 681.04
Abstract. Two methods for diagnosing data represented in a residue number system (RNS) are considered. It is shown that the main drawback of these methods is a considerable time of diagnosing RNS-based data. The proposed method makes it possible to reduce the time of diagnosing errors in RNS-based data, which increases the efficiency of diagnosis. The use of the method of operational diagnosis of data increases the overall efficiency, which indicates the expediency of its application in computing systems of nonpositional code structures in RNSs. Keywords: residue number system, data control, operativeness of diagnosing data, nonpositional code structure, alternative aggregate of a number. INTRODUCTION In the general case, by diagnosing data in a residue number system (RNS) we understand the process of determining distorted residues in a redundant nonpositional code structure (NCS) of the form A RNS = ( a1 || a 2 ||
K || a i -1 || a i || a i + 1 || K || a n || K || a n + k ) , where n and k are numbers of information and control bases mi ( i = 1, n + k ) , respectively, in the ordered ( mi < mi +1 ) RNS. An NCS is diagnosed after data control for the subsequent possible correction of errors. To control, diagnose, and correct errors in an NCS, a definite information redundancy should be introduced. The ( RNS) degree R of information redundancy that determines the correcting abilities of a code is estimated by the value d min of ( RNS) the minimum code distance (MCD). In RNS, the value of MCD is specified by the relation d min = k +1 [1]. With one (RNS) (RNS) control base, the value of the MCD d min = 2 . According to coding theory, when MCD d min = 2 , the fact of
distortion of only one of residues (one-fold error) of the code word in RNS is reliably determined in a code structure. To (RNS) correct, for example, a one-fold error, it is necessary to provide the fulfillment of the condition d min = 3. As is noted in [2–5], by virtue of the influence of RNS properties on data processing, sometimes there is the possibility to correct one-fold (in one NCS residue) errors in data by introducing the minimal ( k = 1) information code redundancy. One of cases of correction stipulated by the RNS property such as the independence of NCS residues is the correction of errors of only the final result of computation [1, 2]. A typical example of such a situation is the possibility of implementing an error correction procedure in the presence of one control base without stopping the process of intermediate computations (in the computational process dynamics (CPD)). To implement such a procedure, it is necessary to diagnose intermediate results of computations using of the concept of the alternative aggregate (AA) of a number in RNS [1]. 1
V. N. Karazin Kharkiv National University, Kharkiv, Ukraine, [email protected]. 2Kharkiv Petro Vasylenko National Technical University of Agriculture, Kharki
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