4 Error Correction
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(Discuss) Proposed since January 2015. In telecommunication, information theory, and coding theory, forward error correction (FEC) or channel coding[1] is error correction and detection a technique used for controlling errors in data transmission over unreliable error correction code or noisy communication channels. The central idea is the sender encodes the message in a redundant
Error Detection And Correction Using Hamming Code Example
way by using an error-correcting code (ECC). The American mathematician Richard Hamming pioneered this field in the 1940s and invented the first error-correcting code in 1950: the
Error Correction Techniques
Hamming (7,4) code.[2] The redundancy allows the receiver to detect a limited number of errors that may occur anywhere in the message, and often to correct these errors without retransmission. FEC gives the receiver the ability to correct errors without needing a reverse channel to request retransmission of data, but at the cost error correcting code example of a fixed, higher forward channel bandwidth. FEC is therefore applied in situations where retransmissions are costly or impossible, such as one-way communication links and when transmitting to multiple receivers in multicast. FEC information is usually added to mass storage devices to enable recovery of corrupted data, and is widely used in modems. FEC processing in a receiver may be applied to a digital bit stream or in the demodulation of a digitally modulated carrier. For the latter, FEC is an integral part of the initial analog-to-digital conversion in the receiver. The Viterbi decoder implements a soft-decision algorithm to demodulate digital data from an analog signal corrupted by noise. Many FEC coders can also generate a bit-error rate (BER) signal which can be used as feedback to fine-tune the analog receiving electronics. The noisy-channel coding theorem establishes bounds on the theoretical maximum information transfer rate of a channel with some given noise level. Some advanced FEC systems come very
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Error Correcting Codes Pdf
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Start here for a quick overview of the site Help Center Detailed answers to any questions you might have Meta Discuss the workings and policies of this site About Us Learn more about Stack Overflow the company Business Learn more about hiring developers or posting ads with us Computer Science Questions Tags Users Badges Unanswered Ask Question _ Computer Science Stack Exchange is a question and answer site for students, researchers and practitioners of computer science. Join them; it only takes a minute: Sign up Here's how it works: Anybody can ask a question Anybody can answer The best answers are voted up and rise to the top Hamming distance required for error detection and correction up vote 1 down vote favorite 2 I have already asked a pair of questions on the hamming distance, hamming code, valid and invalid codewords on this website, because I cannot understand those concepts fully, and in a few weeks or less, I am going to have an exam also on those topics, I really do not understand. I have tried to take a look to wikipedia articles, but it is, for me, quite complicated to understand. My question this time is more concrete. I have a figure, representing how many errors can we detect and correct according to the hamming distance. The thing I am not understanding is why, for example, with an hamming distance of 3, we can just detect 2 bit flips and correct 1 bit flip. I know there are 2 formulas (that you can see in the picture), which bring us to that result, but I would like understand why those formulas are correct. Why, with an hamming distance of 3, we can just detect 2 errors and correct 1. This is picture: coding-theory error-correcting-codes share|cite|improve this question edited Oct 17 '14 at 17:30 David Richerby 34.6k755105 asked Oct 17 '14 at 17:15 nbro 2081516 add a comment| 1 Answer 1 active oldest votes up vote 6 down vote The Hamming distance being 3 means that any two code words must differ in at least three bits. Suppose that 10111 and 10000 are codewords and you receive 10110. If you assume that only one bit has been corrupte