Concept explainers
Suppose a codding scheme is devised that maps
Example 1
Example 2
Example 3
Example 4
Example 1: Parity check – Consider
Example 2: Repetition Codes – Multiple errors can be detected (but not corrected) in a scheme in which a
Example 3: Maximum Likelihood Decoding- Multiple errors can be detected and corrected if each
Example 4: Error Detection and Correction – Suppose
Where
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Elements Of Modern Algebra
- Suppose that the check digit is computed as described in Example . Prove that transposition errors of adjacent digits will not be detected unless one of the digits is the check digit. Example Using Check Digits Many companies use check digits for security purposes or for error detection. For example, an the digit may be appended to a -bit identification number to obtain the -digit invoice number of the form where the th bit, , is the check digit, computed as . If congruence modulo is used, then the check digit for an identification number . Thus the complete correct invoice number would appear as . If the invoice number were used instead and checked, an error would be detected, since .arrow_forwardWrite out the addition and multiplication tables for 4.arrow_forward
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