ERROR DETECTION & CORRECTION

Error detection codes in digital communication are techniques used to identify errors or corruption that may occur during the transmission of data. These codes help ensure the integrity of the transmitted information by detecting and potentially correcting errors. Here are some common error detection codes:

1. Parity Bit:Even Parity: An extra bit is added to the data such that the total number of ones (including the parity bit) is even.
2. Odd Parity: The total number of ones, including the parity bit, is odd.During transmission, if the received data has an incorrect parity (even when it should be odd, or vice versa), an error is detected.
3. Checksums:A checksum is a sum or hash value computed from the data. The sender calculates the checksum and sends it along with the data. The receiver recalculates the checksum upon receiving the data and compares it with the received checksum. If they don't match, an error is detected.
4. Cyclic Redundancy Check (CRC):CRC is a more sophisticated error detection technique. It involves polynomial division, where the sender and receiver both have a generator polynomial. The sender appends a CRC code (remainder) to the data before transmission. The receiver performs the same polynomial division and checks if the remainder matches the received CRC code. A mismatch indicates an error.
5. Hamming Code:Hamming codes are a type of error-correcting code. They add redundant bits to the data in a specific way, allowing the receiver not only to detect errors but also to correct them. The positions of the redundant bits are determined by powers of 2, ensuring that each bit's position corresponds to a specific combination of data bits.
6. BCH Codes (Bose-Chaudhuri-Hocquenghem):BCH codes are a family of error-correcting codes that generalize both Hamming codes and Reed-Solomon codes. They are widely used in various communication systems, including digital storage and satellite communication.

The goal of error detection codes is to provide a mechanism for identifying errors during data transmission. While some codes only detect errors, others, like Hamming codes and Reed-Solomon codes, can correct errors to some extent. The choice of a particular error detection or correction technique depends on factors such as the desired level of reliability, computational complexity, and available resources.