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Topic: Hamming distance


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In the News (Mon 24 Nov 14)

  
  PlanetMath: Hamming distance
This distance is applicable to encoded information, and is a particularly simple metric of comparison, often more useful than the city-block distance or Euclidean distance.
The Hamming distance is a true metric, as it induces a metric space on the set of ordered lists of some fixed length.
This is version 7 of Hamming distance, born on 2002-01-04, modified 2007-07-05.
planetmath.org /encyclopedia/HammingDistance.html   (136 words)

  
  The Dispatch - Serving the Lexington, NC - News   (Site not responding. Last check: )
For a fixed length n, the Hamming distance is a metric on the vector space of the words of that length, as it obviously fulfills the conditions of non-negativity, identity of indiscernibles and symmetry, and it can be shown easily by complete induction that it satisfies the triangle inequality as well.
For binary strings a and b the Hamming distance is equivalent to the number of ones in a xor b.
The metric space of length-n binary strings, with the Hamming distance, is known as the Hamming cube; it is equivalent as a metric space to the set of distances between vertices in a hypercube graph.
www.the-dispatch.com /apps/pbcs.dll/section?category=NEWS&template=wiki&text=Hamming_distance   (506 words)

  
 Hamming distance
In information theory, the Hamming distance is the number of positions in two strings of equal length for which the corresponding elements are different.
The Hamming distance is used in telecommunication to count the number of flipped bits in a fixed-length binary word, an estimate of error, and so is sometimes called the signal distance.
The Hamming distance between 1011101 and 1001001 is 2.
www.xasa.com /wiki/en/wikipedia/h/ha/hamming_distance.html   (173 words)

  
 Hamming distance Information - hamming distance
The Hamming weight of a string is its Hamming distance from the zero string (string consisting of all zeros) of the same length.
The Hamming distance is also equivalent to the Manhattan distance between two vertices in an n-dimensional hypercube, where n is the length of the words.
Hamming weight analysis of bits is used in several hamming distance disciplines including information theory, coding theory, and cryptography.
www.inanot.com /Ina-Electronics_Topics_G_-_H-/Hamming_distance.html   (335 words)

  
 Hamming Distance Tutorial
Hamming distance can also be used for ordinal variables to measure disorder of disorder-vector from a pattern-vector.
Of course, the Hamming distance is equal to the number of unmatched digit.
Since we count four number of interchange, thus the Hamming distance between A and B is 4.
people.revoledu.com /kardi/tutorial/Similarity/HammingDistance.html   (387 words)

  
 Hamming distance - Definition, explanation
In information theory, the Hamming distance, named after Richard Hamming, is the number of positions in two strings of equal length for which the corresponding elements are different.
The Hamming distance is also equivalent to the Manhattan distance between two vertices in an n-dimensional hypercube, where n is the length of the words.
The Hamming distance is used in telecommunication to count the number of flipped bits in a fixed-length binary word, an estimate of error, and so is sometimes called the signal distance.
www.calsky.com /lexikon/en/txt/h/ha/hamming_distance.php   (286 words)

  
 PlanetMath: Hamming distance
This distance is applicable to encoded information, and is a particularly simple metric of comparison, often more useful than the city-block distance or Euclidean distance.
The Hamming distance is a true metric, as it induces a metric space on the set of ordered lists of some fixed length.
This is version 6 of Hamming distance, born on 2002-01-04, modified 2004-03-13.
www.planetmath.org /encyclopedia/HammingDistance.html   (148 words)

  
 Hamming distance
In telecommunication, the Hamming distance or signal distance is the number of digit positions in which the corresponding digits of two binary words of the same length are different.
For instance, the Hamming distance between 1011101 and 1001001 is two.
For example, the Hamming distance between 2143896 and 2233796 is three, and between "toned" and "roses" it is also three.
www.ebroadcast.com.au /lookup/encyclopedia/ha/Hamming_distance.html   (93 words)

  
 Minimum Hamming Distance Probability Distribution Function Analysis
Error correction benefits from selecting a set of codewords such that the minimum hamming distance of the codeword set is a maximum possible for a given n and M. [reference (maybe webpages I've viewed).
Given the number of bits (n) and a target minimum hamming distance (MHD), find directly from experimental data the maximum number of codewords that can be selected from the full codeword set while maintaining the MHD constraint.
Given the number of bits (n) and a target minimum hamming distance (MHD), find from a predictive code derived from analysis of the experimental data, the maximum number of codewords that can be selected from the full codeword set while maintaining the MHD constraint.
firewall.netsup.net /code   (460 words)

  
 Digital Revolution (III) - Error Correction Codes
Hamming distance is an important concept not only for computing the distance between strings of binary digits, but for strings taken from other "alphabets" as well.
The brilliant insight that Hamming had was that if one has a collection of codewords, each pair of which are at least 2e + 1 apart as measured by the Hamming distance, then one can correct up to e errors (per codeword).
Hamming realized that what he wanted to achieve was to add as few extra symbols as possible to each "information" string so as to get a code word that was relatively short but which still had the right level of error correction power (i.e.
e-math.ams.org /featurecolumn/archive/errors2.html   (1076 words)

  
 Hamming Distance Tutorial
Hamming distance is somewhat related to Simple matching distance.
Hamming distance can also be used for ordinal variables to measure disorder of disorder-vector from a pattern-vector.
Since we count four number of interchange, thus the Hamming distance between A and B is 4.
www.people.revoledu.com /kardi/tutorial/Similarity/HammingDistance.html   (387 words)

  
 PlanetMath: Hamming metric
The Hamming distance holds the properties of a metric (otherwise it would not be truly a distance):
Cross-references: sum, places, inequality, negative, clear, distance, metric, properties, vectors
This is version 4 of Hamming metric, born on 2005-02-01, modified 2005-02-01.
planetmath.org /encyclopedia/HammingDistance2.html   (169 words)

  
 Hamming Distance
We define the Hamming distance for C as
We will use hamming distance to find the codeword closest to the decoded word and to correct an error in our encoded word.
We won't be able to to this for the ``parity bit" codes but the ``Hamming codes" will let us fix one error (and detect up to three) in a received word.
www.ibiblio.org /litlfred/arizona/linearcodes/spring2004/node11.html   (62 words)

  
 Telecom Dictionary H: Phone Service Definitions
Hamming code: An error-detecting and error-correcting binary code, used in data transmission, that can (a) detect all single- and double-bit errors and (b) correct all single-bit errors.
Hamming Distance - The number of digit positions in which the corresponding digits of two binary words of the same length are different.
For example, the Hamming distance between 2143896 and 2233796 is three, and between "toned" and "roses" it is also three.
faxswitch.com /Definitions/telecom_dictionary_h.html   (8310 words)

  
 Hamming distance
The Hamming distance can be interpreted as the number of bits which need to be changed (corrupted) to turn one string into the other.
Hamming distance can be seen as Manhattan distance between bit vectors.
Paul E. Black, "Hamming distance", in Dictionary of Algorithms and Data Structures [online], Paul E. Black, ed., U.S. National Institute of Standards and Technology.
www.nist.gov /dads/HTML/HammingDistance.html   (148 words)

  
 RICHARD HAMMING - Definition
Richard Hamming received his B.S. from the University of Chicago in 1937, his M.A. from the University of Nebraska in 1939, and his Ph.D. in mathematics from the University of Illinois at Urbana-Champaign in 1942.
Although best known for error-correcting codes, Hamming was primarily a numerical analyst, working on integrating differential equations and the Hamming spectral window used for smoothing data before Fourier analysis.
He wrote textbooks, propounded aphorisms ("the purpose of computing is insight, not numbers"), and was a founder of the ACM and a proponent of open-shop computing ("better to solve the right problem the wrong way than the wrong problem the right way.").
www.hyperdictionary.com /computing/richard+hamming   (285 words)

  
 Applying Hamming Code to blocks of data
Hamming code affords a straightforward way to protect a block of data against single bit errors.
This is because the Hamming distance between 2 code points (the data and check bits combined are a “code point”) is enough that single bit errors can be corrected, but double bit errors appear to be a single bit error on a different code point.
The term Hamming distance can be understood to refer to the number of bits that have to change to move from one code point to another.
asics.chuckbenz.com /HammingCode.html   (1338 words)

  
 CommsDesign - Euclid over Hamming by a few dB
Euclidean distance is an important concept, because coding theory has much history in the use of Hamming distance.
Hamming distance measures the number of different digits in a digital word, one that typically has overhead attached for coding-gain purposes.
As an example, for QPSK, adjacent symbol states normalized to a magnitude of unity are separated in Euclidean distance by the square-root of 2, and separated in Hamming distance by 1.
www.commsdesign.com /buildingblocks/showArticle.jhtml?articleID=186100233   (1366 words)

  
 Hamming distance   (Site not responding. Last check: )
In information theory, the Hamming distance between two strings of equal length is the number of positions for which the corresponding symbols are different.
by treating each symbol in the string as a real coordinate; with this embedding, the strings form the vertices of an n-dimensional hypercube, and the Hamming distance of the strings is equivalent to the Manhattan distance between the vertices.
Hamming weight analysis of bits is used in several disciplines including information theory, coding theory, and cryptography.
www.1bx.com /en/Hamming_distance.htm   (546 words)

  
 EE4253 Hamming Code
For example, given a valid Hamming codeword, a change in bit 3 changes three bits (1,2,3) such that the new codeword is a distance (d=3) from the initial word.
The clever arrangement of the Hamming codewords ensures that this is the case for every valid codeword in the set.
The distances would still be the same if you swapped two columns or complemented the bits in any column, but the codewords would look very different (and the Venn diagrams would not work!).
www.ee.unb.ca /tervo/ee4253/hamming.htm   (1094 words)

  
 Hamming-Grey Codes for Fingerprinting Descriptors
This trade-off may be customized by choosing encodings such the Hamming distance between any pair of related significant descriptors is higher than between any pair related by less significant descriptors.
A Hamming distance greater than zero indicates that the descriptors are in different states.
A set of Hamming codes are a set of code words that have atleast a specified number of bits different between any two non-identical codes.
www.daylight.com /meetings/emug98/Sayle/codes.html   (2337 words)

  
 Hamming (7,4) code
The Hamming distance or distance is the number of digits by which two blocks of the same length differ.
N otably, the minimum distance between blocks in this code is one, because obviously by changing a 0 to a 1 and another 1 to a 0 one word can become another.
Hamming also defined an n-sphere centred at a vertex as all of the vertices within a distance n of the center.
www.cs.mcgill.ca /~smroso/hamming.html   (1879 words)

  
 Character Recognition using Fuzzy Hamming Distance
This project is based on the Fuzzy Hamming Distance concept which was taken from this paper [1].
Although the Hamming distance has several applications, the main concern is the assumption that every bit is independent of its neighbours.
The character which gives the smallest Fuzzy Hamming distance relative to the input character is the one that is chosen as the output of the recognition process.
cgm.cs.mcgill.ca /~athens/cs644/Projects/2004/MarcLanctot-HaniEzzadeen   (1627 words)

  
 Cubes
the Hamming distance from 011 to 100 is 3, from 001 to 111 is two, while from 110 to 111 is 1.
Thus, the distance between the vertices of the 3-cube with these coordinates is 1 in both the Hamming distance and the Euclidean distance!
Since the Hamming distance is a distance function like any other, one can talk about the points which have a particular fixed distance from a vertex of a d-cube in the Hamming metric.
www.ams.org /featurecolumn/archive/cubes4.html   (558 words)

  
 Pipelined "best match" content addressable memory - Patent 4897814
Thus the availability of the distance metric may be of great benefit to the host system, as it is afforded knowledge about the quality of the outcome of the matching process.
The distance measure chosen for the prototype device is the Hamming distance.
The Hamming distance is a count of the number of different symbols in the two vectors being compared and is defined for sequences of equal length only.
www.freepatentsonline.com /4897814.html   (4153 words)

  
 Hamming distance   (Site not responding. Last check: )
* Hamming weight For example: For 'binary strings' a and b can also be seen as the Hamming bits in a fixed-length binary word as an estimate of error, and therefore is References sometimes called the 'signal distance'.
Hamming weight analysis of bits is used History and Applications The Hamming distance between '2
Put another way, it measures the number of positions for which the corresponding symbols are vector space of the words of that length, as it obviously fulfills the can be shown easily by complete induction that it satisfies the triangle words.
fourier.boekebeurs.be /Hammingdistance   (208 words)

  
 'Hamming' it up   (Site not responding. Last check: )
Amateur radio operators are known as "hams." That term dates to the early days of wireless telegraphy, according to an explanation on the relay league's Web site, www.arrl.org.
Hams make use of everything from hand-held units the size of a deck of cards to multistory antennas linked to transmitters the size of footlockers.
Hams from the group helped a half-dozen Scouts meet requirements for a radio merit badge during the field day.
www.post-gazette.com /pg/06190/703912-58.stm   (1264 words)

  
 Hamming code - Wikipedia, the free encyclopedia   (Site not responding. Last check: )
Hamming studied the existing coding schemes, including two-of-five, and generalized their concepts.
The (3,1) repetition has a distance of 3, as three bits need to be flipped in the same triple to obtain another code word.
However, if a parity error is not detected but the Hamming code indicates that there is an error, this is assumed to have been due to a two-bit error, which is detected but cannot be corrected.
www.kean.edu /~asetoode/home/crc2/hamming.htm   (2097 words)

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