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BCH code Reed–Solomon code Block length n Message length k Distance n − k + 1 Alphabet size q = pm ≥ n (p prime) Often n = q − 1. Notation [n, decode error on youtube k, n − k + 1]q-code Algorithms Decoding Berlekamp–Massey Euclidean et al.
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Properties Maximum-distance separable code v t e Reed–Solomon codes are a group of error-correcting codes that were introduced by
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Irving S. Reed and Gustave Solomon in 1960.[1] They have many applications, the most prominent of which include consumer technologies such as CDs, DVDs, Blu-ray Discs, QR Codes, data transmission technologies https://support.microsoft.com/en-us/kb/317455 such as DSL and WiMAX, broadcast systems such as DVB and ATSC, and storage systems such as RAID 6. They are also used in satellite communication. In coding theory, the Reed–Solomon code belongs to the class of non-binary cyclic error-correcting codes. The Reed–Solomon code is based on univariate polynomials over finite fields. It is able to detect and correct multiple symbol errors. By https://en.wikipedia.org/wiki/Reed%E2%80%93Solomon_error_correction adding t check symbols to the data, a Reed–Solomon code can detect any combination of up to t erroneous symbols, or correct up to ⌊t/2⌋ symbols. As an erasure code, it can correct up to t known erasures, or it can detect and correct combinations of errors and erasures. Furthermore, Reed–Solomon codes are suitable as multiple-burst bit-error correcting codes, since a sequence of b+1 consecutive bit errors can affect at most two symbols of size b. The choice of t is up to the designer of the code, and may be selected within wide limits. Contents 1 History 2 Applications 2.1 Data storage 2.2 Bar code 2.3 Data transmission 2.4 Space transmission 3 Constructions 3.1 Reed & Solomon's original view: The codeword as a sequence of values 3.1.1 Simple encoding procedure: The message as a sequence of coefficients 3.1.2 Systematic encoding procedure: The message as an initial sequence of values 3.1.3 Theoretical decoding procedure 3.2 The BCH view: The codeword as a sequence of coefficients 3.2.1 Systematic encoding procedure 3.3 Duality of the two views - discrete Fourier transform 3.4 Remarks 4 Properties 5 Error correction
Search All Support Resources Support Documentation MathWorks Search MathWorks.com MathWorks Documentation Support Documentation Toggle navigation Trial https://www.mathworks.com/help/comm/ug/error-detection-and-correction.html Software Product Updates Documentation Home Communications System Toolbox Examples Functions http://forums.winamp.com/showthread.php?threadid=233499 and Other Reference Release Notes PDF Documentation End-to-End Simulation Error Detection and Correction Cyclic Redundancy Check Coding Communications System Toolbox End-to-End Simulation Error Detection and Correction Convolutional Coding Error Detection and Correction On this page Cyclic Redundancy Check Codes CRC-Code decode error Features CRC Non-Direct Algorithm Example Using CRC Non-Direct Algorithm CRC Direct Algorithm Selected Bibliography for CRC Coding Block Codes Block-Coding Features Terminology Data Formats for Block Coding Using Block Encoders and Decoders Within a Model Examples of Block Coding Notes on Specific Block-Coding Techniques Shortening, Puncturing, and Erasures Reed-Solomon Code in decode error on Integer Format Find a Generator Polynomial Performing Other Block Code Tasks Selected Bibliography for Block Coding Convolutional Codes Convolutional Code Features Polynomial Description of a Convolutional Code Trellis Description of a Convolutional Code Create and Decode Convolutional Codes Design a Rate-2/3 Feedforward Encoder Using MATLAB Design a Rate 2/3 Feedforward Encoder Using Simulink Puncture a Convolutional Code Using MATLAB Implement a Systematic Encoder with Feedback Using Simulink Soft-Decision Decoding Tailbiting Encoding Using Feedback Encoders Selected Bibliography for Convolutional Coding Linear Block Codes Represent Words for Linear Block Codes Configure Parameters for Linear Block Codes Create and Decode Linear Block Codes Hamming Codes Create a Hamming Code in Binary Format Using Simulink Reduce the Error Rate Using a Hamming Code BCH Codes Represent Words for BCH Codes Parameters for BCH Codes Create and Decode BCH Codes Algorithms for BCH and RS Errors-only Decoding Reed-Solomon Codes Represent Words for Reed-Solomon Codes
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