2 Bit Error Detection
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citations to reliable sources. Unsourced material may be challenged and removed. (August 2008) (Learn how and when to parity error detection and correction remove this template message) In information theory and coding theory
Parity Bit Error Correction
with applications in computer science and telecommunication, error detection and correction or error control are single bit _____ can be used to detect single bit errors techniques that enable reliable delivery of digital data over unreliable communication channels. Many communication channels are subject to channel noise, and thus errors may be introduced
Error Correction Using Parity Bits
during transmission from the source to a receiver. Error detection techniques allow detecting such errors, while error correction enables reconstruction of the original data in many cases. Contents 1 Definitions 2 History 3 Introduction 4 Implementation 5 Error detection schemes 5.1 Repetition codes 5.2 Parity bits 5.3 Checksums 5.4 Cyclic redundancy single bit error detection and correction using hamming code checks (CRCs) 5.5 Cryptographic hash functions 5.6 Error-correcting codes 6 Error correction 6.1 Automatic repeat request (ARQ) 6.2 Error-correcting code 6.3 Hybrid schemes 7 Applications 7.1 Internet 7.2 Deep-space telecommunications 7.3 Satellite broadcasting (DVB) 7.4 Data storage 7.5 Error-correcting memory 8 See also 9 References 10 Further reading 11 External links Definitions[edit] The general definitions of the terms are as follows: Error detection is the detection of errors caused by noise or other impairments during transmission from the transmitter to the receiver. Error correction is the detection of errors and reconstruction of the original, error-free data. History[edit] The modern development of error-correcting codes in 1947 is due to Richard W. Hamming.[1] A description of Hamming's code appeared in Claude Shannon's A Mathematical Theory of Communication[2] and was quickly generalized by Marcel J. E. Golay.[3] Introduction[edit] The general idea for achieving error detection and correction is to add some redundancy (i.e.,
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Parity Bit Error Detection Example
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Error Detection And Correction Techniques
remove this template message) This article may be too technical for most readers to understand. Please help improve error detection and correction codes in digital electronics this article to make it understandable to non-experts, without removing the technical details. The talk page may contain suggestions. (February 2016) (Learn how and when to remove this template message) https://en.wikipedia.org/wiki/Error_detection_and_correction (Learn how and when to remove this template message) Binary Hamming Codes The Hamming(7,4)-code (with r = 3) Named after Richard W. Hamming Classification Type Linear block code Block length 2r − 1 where r ≥ 2 Message length 2r − r − 1 Rate 1 − r/(2r − 1) Distance 3 Alphabet size 2 Notation [2r − 1, 2r https://en.wikipedia.org/wiki/Hamming_code − r − 1, 3]2-code Properties perfect code v t e In telecommunication, Hamming codes are a family of linear error-correcting codes that generalize the Hamming(7,4)-code, and were invented by Richard Hamming in 1950. Hamming codes can detect up to two-bit errors or correct one-bit errors without detection of uncorrected errors. By contrast, the simple parity code cannot correct errors, and can detect only an odd number of bits in error. Hamming codes are perfect codes, that is, they achieve the highest possible rate for codes with their block length and minimum distance of three.[1] In mathematical terms, Hamming codes are a class of binary linear codes. For each integer r ≥ 2 there is a code with block length n = 2r − 1 and message length k = 2r − r − 1. Hence the rate of Hamming codes is R = k / n = 1 − r / (2r − 1), which is the highest possible for codes with minimum distance of three (i.e., the minimal number of bit changes needed to go from an
consecutive bit errors Error rate due to noise: The likelihood of errors due to noise depends on the transmission medium Twisted pairs is pretty "noisy" and has an error http://www.mathcs.emory.edu/~cheung/Courses/455/Syllabus/2-physical/errors.html rate of about 1 bit in every few 1000 bits transmitted. Optical fibers are very "noiseless" and can have 1 bit in several 1,000,000 bits may be in error.... Why detect errors Garbage in, garbage out: processing corrupted intermediate data will always result in incorrect final outcome The sooner we can detect an error, the less computation resources we will waste Transmission errors can be error detection detected at various levels Question we study here: How can we tell if there are errors at the physical (signal) level ? Detecting errors at physical level (signals): error detection and correction codes Principe to detect/correct errors in a "sequence of bits": Embed extra bits into the transmitted message to conforms to a certain (mathematical) property The receiver checks for this property in error detection and the received sequence The mathematical theory that deal with this subject is called coding theory. Commonly used error detection/correction schemes Commonly used schemes: Error detection schemes: Parity checks Cyclic Redundancy Check (CRC) Error Correction Schemes: Hamming's code (can correct 1 bit error) Solomon-Reed's code (can correct 2 bit error)
One-dimensional Parity Scheme Even and Odd Parity: Even parity: Add one extra bit to the message so that the total number of 1's in the message is always even Odd parity: Add one extra bit to the message so that the total number of 1's in the message is always odd Examples: Transmitted data (unprotected): 1111000 1010101 1111111 Even parity: 11110000 10101010 11111111 Odd parity: 11110001 10101011 11111110 Error Checking: When the received message does not have an even (or odd number of 1's in the even (or odd) parity method, the receiver will assume that the message is corrupted Properties: Parity checks can detect all odd number of bit errors Parity checks can not detect even number of bit errors Example: Transmitted data (unprotected): 1111000 Even parity: 111