Multi valued parity generator based on Sudoku tables: properties and detection probability. Issue 14 (1st August 2020)

• Record Type: Journal Article
• Authors: Ghalamdoost Pirbazari, Shahab; Souri, Alireza; Faghih Mirzaee, Reza; Jabbehdari, Sam
• Is Part Of: IET communications. Volume 14:Issue 14(2020)
• Page Start: 2377
• Page End: 2386
• Publication Date: 2020-08-01
• Subjects: error correction codes -- probability -- error detection codes -- formal verification -- parity check codes -- error detection; error detection probability increases -- higher radixes -- multivalued parity generator -- Sudoku tables -- simple yet effective error detection method -- sophisticated error detection techniques -- single parity‐check -- MPGs -- necessary properties -- optional properties -- binary parity generator -- single‐digit errors -- higher probability; Telecommunication systems -- Periodicals; Speech processing systems -- Periodicals; 621.38205
• DOI: 10.1049/iet-com.2019.0247
• Languages: English
• ISSNs: 1751-8628

Abstract

Abstract : Parity‐check is a simple yet effective error detection method. Several other more sophisticated error detection techniques are founded upon single parity‐check (SPC). Exclusive‐OR (XOR) is known as the parity generator in binary logic. This study suggests some multi‐valued parity generators (MPGs), studies their behaviour, and provides a full discussion about their necessary and optional properties. The concept of Sudoku with some customised rules is used to create MPGs, which are the extended versions of binary parity generator in higher radixes. They are capable of revealing all single‐digit errors. Additionally, they can detect incorrect data delivery with high probability when more than one error occurs (with even higher probability than XOR). The probability of error detection is analytically calculated for the occurrence of two to five errors in different bases. The calculations are then experimentally verified by a formal verification method. The authors' investigations show that error detection probability increases in higher radixes, and it is independent of dataword size.