An algorithm for scaling and single residue error correction in residue number systems

Author

Su, Chien-Chun ; Lo, Hao-Yung

Author_Institution

Dept. of Electr. Eng., Nat. Tsing-Hua Univ., Hsin-Chu, Taiwan

Volume

39

Issue

8

fYear

1990

fDate

8/1/1990 12:00:00 AM

Firstpage

1053

Lastpage

1064

Abstract

An algorithm for scaling and single residue digit error correction is proposed. This algorithm is fully based on mixed radix conversion (MRC). The redundant digits of MRC can be used to establish a lookup table to correct single residue digit errors. By using this algorithm the error correction and scaling operation can be unified in one hardware, thereby reducing the complexity of these implementations. The scaling error e_s is analyzed and found to be limited to the interval of -1<e_s<1. Since scaling is often required in the computations of digital signal processing (DSP), which is the main application of RNS, and error-correction circuit with scaling (ECCS) will by very efficient in the fault-tolerant systems for the DSP applications. Two examples for the application of the proposed ECCS are given

Keywords

digital arithmetic; digital signal processing chips; error correction; fault tolerant computing; number theory; RNS; digital signal processing; error-correction circuit with scaling; fault-tolerant systems; lookup table; mixed radix conversion; redundant digits; residue number systems; scaling error; single residue digit error correction; Digital signal processing; Error analysis; Error correction; Error correction codes; Fault tolerant systems; Filters; Hardware; Random access memory; Signal processing algorithms; Table lookup;

fLanguage

English

Journal_Title

Computers, IEEE Transactions on

Publisher

ieee

ISSN

0018-9340

Type

jour

DOI

10.1109/12.57044

Filename

57044