Error Detection and Correction.

1. Error Detection

1.1. Definition*: Identifying errors in data transmission or storage.

1.1.1. Types

1.1.1.1. Parity Check

1.1.1.1.1. Definition: Adding a parity bit to data for error detection.

1.1.1.2. Checksum

1.1.1.2.1. Definition: Sum or hash function used to verify data integrity.

1.1.1.3. CRC

1.1.1.3.1. Definition: Polynomial-based method for error detection.

2. Error Correction

2.1. Definition*: Fixing detected errors to ensure data integrity.

2.1.1. Types:

2.1.1.1. Single-bit

2.1.1.1.1. refers to a situation where only one binary digit (bit) within a data unit changes its value, either from 0 to 1 or vice versa, due to noise, interference, or other factors.

2.1.1.2. Hamming code

2.1.1.2.1. Definition: Error correction code using parity bits.

3. Polynomials

3.1. Polynomials play a crucial role in error detection and correction, particularly in techniques like Cyclic Redundancy Check (CRC). In CRC, a polynomial is used to generate a checksum or remainder, which is then appended to the data. The polynomial division process helps in error detection.

4. Cyclic code.

4.1. are a class of linear block codes used in error detection and correction. These codes possess a unique property: if a codeword is cyclically shifted, the result is another valid codeword. This property simplifies encoding and decoding processes.