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Forward error correction (FEC) is a method used in digital communication systems to detect and correct errors that may occur during data transmission. It is a type of error control coding that involves adding redundant data to the original data being transmitted. This redundancy allows the receiver to detect and, in many cases, correct errors without the need for retransmission.

Before data is transmitted, it is passed through an encoder that applies an error-correcting code. The encoder adds redundancy to the data by generating parity bits, which are derived from the original data.

The encoded data, including the original data and parity bits, is transmitted over a communication channel. The channel may introduce errors due to noise, interference, or other factors.

Upon receiving the data, the receiver uses a decoder to check for errors. The decoder examines the received data and the parity bits to identify any discrepancies.

If errors are detected, the decoder uses the redundant data to correct them. Depending on the error-correcting code used, the decoder may be able to correct single or multiple-bit errors.

Once errors are corrected (or if no errors are detected), the receiver outputs the original data for further processing or use.

FEC is widely used in various communication systems, including wireless networks, satellite communications, digital broadcasting, and data storage devices, to improve reliability and reduce the need for retransmissions. Common types of FEC codes include Reed-Solomon codes, convolutional codes, and low-density parity-check (LDPC) codes.

FEC is particularly useful in environments where retransmission of data is costly or not feasible, such as in space communications or real-time streaming. By correcting errors at the receiver, FEC helps ensure data integrity and efficient use of bandwidth.

Automatic Repeat reQuest (ARQ) is an error control protocol used in digital communication systems to ensure reliable data transmission. It involves the sender and receiver working together to detect errors in transmitted data and request retransmissions of any corrupted or missing packets. ARQ is commonly used in network communication protocols such as TCP (Transmission Control Protocol) and other data link layer protocols.

The sender transmits data packets to the receiver. Each packet is typically numbered to keep track of the sequence.

After receiving a packet, the receiver checks for errors. If the packet is received without errors, the receiver sends an acknowledgment (ACK) back to the sender to confirm successful receipt. If the packet is corrupted or missing, the receiver sends a negative acknowledgment (NACK) or no acknowledgment at all.

If the sender receives a NACK or no acknowledgment within a specified time frame, it assumes that the packet was not received correctly and retransmits the data.

The sender sets a timeout period during which it waits for an acknowledgment from the receiver. If the timeout expires without receiving an ACK, the sender retransmits the packet.

ARQ protocols often include flow control mechanisms to manage the rate of data transmission and prevent overwhelming the receiver.

Variations of ARQ protocols:

Stop-and-Wait ARQ: The sender transmits one packet at a time and waits for an acknowledgment before sending the next packet.

Go-Back-N ARQ: The sender can transmit multiple packets (up to a specified window size) before waiting for an acknowledgment. If an error occurs, the sender goes back to the last unacknowledged packet and retransmits it and all subsequent packets.

Selective Repeat ARQ: Similar to Go-Back-N ARQ, but the sender retransmits only the specific packets that were not acknowledged, rather than going back to the last unacknowledged packet.

ARQ is a reliable way to handle errors in data transmission, ensuring that the data received is correct and in the proper order. It is widely used in various communication systems, including wireless networks, internet protocols, and data storage systems.