Multi Valued Parity Generator based on Sudoku Tables: Properties and Detection Probability

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.