Best Method Of Forward Error Correction
Contents |
(Discuss) Proposed since January 2015. In telecommunication, information theory, and coding theory, forward error correction (FEC) or channel coding[1] is a technique used for controlling errors in data transmission over unreliable or noisy communication channels. The forward error correction tutorial central idea is the sender encodes the message in a redundant way by using forward error correction ppt an error-correcting code (ECC). The American mathematician Richard Hamming pioneered this field in the 1940s and invented the first error-correcting code forward error correction 3/4 in 1950: the 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
Forward Error Correction Algorithm
gives the receiver the ability to correct errors without needing a reverse channel to request retransmission of data, but at the cost 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, forward error correction rate 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 close to the theoretical maximum. The maximum fractions of errors or of missing bits that can be corrected is determined by the design of the FEC code, so different forward error correcting codes are suitable for different conditions. Contents 1 How it works 2 Averaging noise to reduce errors 3 Types of FEC 4 Concatenated FEC codes for improved performance 5 Low-density parity-check (LDPC) 6 Turbo codes 7 Local decoding and testing of codes 8 Interleaving 8.1 Example 8.2 Disadvantages of interleaving 9 List of error-correcting codes 10 See also 11 References 12 F
of Block code is BCH code. As other block code, BCH encodes k data bits into n code bits by adding n-k parity checking bits for the purpose of detecting and checking the errors. Given the length of the codes is for any integer mˇÝ3, we will have forward error correction ethernet t (where t<), is the bound of the error correction. That is, BCH can correct any
Forward Error Correction Library
combination of errors (burst or separate) fewer than t in the n-bit-codes. The number of parity checking bits is n-kˇÜmt. An important concept for BCH
Forward Error Correction Pdf
is Galois Fields (GF), which is a finite set of elements on which two binary addition and multiplication can be defined. For any prime number p there is GF(p) and GF(is called extended field of GF(p). We often use GF(in BCH code. https://en.wikipedia.org/wiki/Forward_error_correction A GF can be constructed over a primitive polynomial such as (The construction and arithmetic of GF are in ˇ°Error Control Codingˇ±, by Shu Lin). Usually, GF table records all the variables, including expressions for the elements, minimal polynomial, and generator polynomial. By referring to the table, we can locate a proper generator polynomial for encoder. For example, when (n, k, t)=(15, 7, 2), a possible generator is . If we have a data stream, the codeword would be and have the style of . http://www.ecs.umass.edu/ece/koren/FaultTolerantSystems/simulator/BCH/FEC.htm The decoder of BCH is complicated because it has to locate and correct the errors. Suppose we have a received codeword, then , where, v(x) is correct codeword and e(x) is the error. First, we must compute a syndrome vector s=, which can be achieved by calculating, where, H is parity-check matrix and can be defined as: . Here,is the element of the GF field and can be located in the GF table. With syndrome, error-location polynomial can be determined. BerkekampˇŻs iterative algorithm is one of solutions to calculate the error-location polynomial. By finding roots of, the location numbers for the errors will be achieved. Usage The program is developed with Java applet. Basically, the implementation involves three steps: Encoder, Error adding, Decoder. ˇ¤ Encoder m and t are available for adjusting. As mentioned above, the codeword length will be. t is the bound of error correction. With m and t being settled, the length of data bits is k=n-mt. Although the program itself has no boundary for m, considering the display limitation, m will be set between 3 and 7. The range checking for m and t are available, if m and t are set to unreasonable values, a red color will be filled input area and program will keep wait for proper inputs. . User will be able to choose either to manually type data stream in binary (user generate) or allow program to randomly generate data stream (randomly generate). If
Boards Communications Components DSPs Dev Tools Digital ICs Displays Electromechanical Embedded FPGAs Interconnects IoT Memory Microcontrollers Microprocessors Passives Power Power Sources Test & Measurement WiFi Windows iOS NewsProducts Trends & http://electronicdesign.com/communications/use-forward-error-correction-improve-data-communications Analysis Image Galleries MarketsAutomotive Defense Energy Lighting Medical Mobile Robotics Learning ResourcesEngineering Essentials http://www.olson-technology.com/mr_fiber/FEC.htm Design Solutions What’s The Difference Between… Ideas for Design Salary Survey Salary Calculator White Papers Basics of Design eBooks Webcasts 2016 Leaders in Electronics Design FAQs Data Sheets Reference Designs 11 Myths About... Electronic Design Library CommunityBlogs Bob Pease Contributing Technical Experts Engineering Hall of Fame Interviews Our Editors STEM Starter Tournament Pop forward error Quizzes Engineering Bracket Challenge CompaniesCompany Directory Part Search Advertisement Home > Technologies > Communications > Use Forward Error Correction To Improve Data Communications Use Forward Error Correction To Improve Data Communications Data-intensive consumer and business applications are driving the need for speed and accuracy in data communication systems. Aug 21, 2000 Contributing Author | Electronic Design EMAIL Tweet Comments 0 As bandwidth demands increase and the tolerance forward error correction for errors and latency decreases, designers of data-communication systems are looking for new ways to expand available bandwidth and improve the quality of transmission. One solution isn't actually new, but has been around for a while. Nevertheless, it could prove quite useful. Called forward error correction (FEC), this design technology has been used for years to enable efficient, high-quality data communication over noisy channels, such as those found in satellite and digital cellular-communications applications. Recently, there have been significant advances in FEC technology that allow today's systems to approach the Shannon limit. Theoretically, this is the maximum level of information content for any given channel. These advances are being used successfully to reduce cost and increase performance in a variety of wireless communications systems including satellites, wireless LANs, and fiber communications. In addition, high-speed silicon ASICs for FEC applications have been developed, promising to further revolutionize communication systems design. The big attraction of FEC technology is how it adds redundant information to a data stream. This enables a receiver to identify and correct errors without the need for retransmission. As the capabilities of FEC increase, the number of errors that can be corrected also increases. The advantage
Forward Error Correction (FEC) Source: David R. Goff. Fiber Optic Video Transmission, 1st ed. Focal Press: Woburn, Massachusetts, 2003 and other private writings. Technology Basics Forward Error Correction (FEC) is a technique that has been used for a number of years in submarine fiber optic systems. It is a technique that allows for near perfect data transmission accuracy even when faced with a noisy transmission channel. A number of FEC algorithms are being used including Hamming code, Reed-Solomon code and Bose-Chandhuri-Hocquenghem code. By way of example, consider the operation of your cell phone when you're about to have your signal fade away. Let's say you wanted to tell the person on the other end of the call a sequence of numbers. There are several techniques that could be used to improve accuracy; For instance, assume the list of numbers that you wish to transmit might be 7, 3, 8, 10, 12, and 21. One method would be to repeat the list of numbers two times and have the person at the receive end write down each list and compare them, If they match, the data transmission is probably OK. The drawback is that, since you have to send all data two times, the throughput of the system is cut in half and if the lists don't match, you will have no idea which one is correct. Using this most basic method, to ensure that you could verify good transmission and correct some errors, you'd have to send the list three times and verify that two out of the three transmissions matched for each number. A second method might be to first announce that you will be sending six numbers, then send the six numbers followed by the total of the six numbers. The transmission sequence would then be 6, 7, 3, 8, 10, 12, 21, and 61. The person at the receive end would look at the first number and then ensure that the correct number of additional numbers is received and then verify that the number at the end of the sequence that is the sum of the transmitted numbers. This method only requires less additional da