Pascal (unit)

A prefix code is a type of code system (typically a variable-length code) distinguished by its possession of the "prefix property"; which states that there is no valid code word in the system that is a prefix (start) of any other valid code word in the set. For example, a code with code words {9, 55} has the prefix property; a code consisting of {9, 5, 59, 55} does not, because "5" is a prefix of both "59" and "55". A prefix code is an example of a uniquely decodable code: a receiver can identify each word without requiring a special marker between words.

Prefix codes are also known as prefix-free codes, prefix condition codes and instantaneous codes. Although Huffman coding is just one of many algorithms for deriving prefix codes, prefix codes are also widely referred to as "Huffman codes", even when the code was not produced by a Huffman algorithm. The term comma-free code is sometimes also applied as a synonym for prefix-free codes but in most mathematical books and articles (e. g.) it is used to mean self-synchronizing codes, a subclass of prefix codes.

Using prefix codes, a message can be transmitted as a sequence of concatenated code words, without any out-of-band markers to frame the words in the message. The recipient can decode the message unambiguously, by repeatedly finding and removing prefixes that form valid code words. This is not always possible with codes that lack the prefix property, for example {0, 1, 10, 11}: a receiver reading a "1" at the start of a code word would not know whether that was the complete code word "1", or merely the prefix of the code word "10" or "11"; and the string "10" could be interpreted either as a single codeword or as the concatenation of the words "1" then "0".

The variable-length Huffman codes, country calling codes, the country and publisher parts of ISBNs, the Secondary Synchronization Codes used in the UMTS W-CDMA 3G Wireless Standard, and the instruction sets (machine language) of most computer microarchitectures are prefix codes.

Prefix codes are not error-correcting codes. In practice, a message might first be compressed with a prefix code, and then encoded again with channel coding (including error correction) before transmission.

Kraft's inequality characterizes the sets of code word lengths that are possible in a uniquely decodable code.

Techniques

If every word in the code has the same length, the code is called a fixed-length code, or a block code (though the term block code is also used for fixed-size error-correcting codes in channel coding). For example, ISO 8859-15 letters are always 8 bits long. UTF-32/UCS-4 letters are always 32 bits long. ATM packets are always 424 bits long. A block code of fixed length k bits can encode up to $2^k$ source symbols.

Prefixes cannot exist in a fixed-length code without padding fixed codes to the shorter prefixes in order to meet the length of the longest prefixes (however such padding codes may be selected to introduce redundancy that allows autocorrection and/or synchronisation). However, fixed length encodings are inefficient in situations where some words are much more likely to be transmitted than others (in which case some or all of the redundancy may be eliminated for data compression).

Truncated binary encoding is a straightforward generalization of block codes to deal with cases where the number of symbols n is not a power of two. Source symbols are assigned codewords of length k and k+1. where $2^k<n<2^{k+1}$.

Huffman coding is a more sophisticated technique for constructing variable-length prefix codes. The Huffman coding algorithm takes as input the frequencies that the code words should have, and constructs a prefix code that minimizes the weighted average of the code word lengths. This is a form of lossless data compression based on entropy encoding.

Some codes mark the end of a code word with a special "comma" symbol, different from normal data. This is somewhat analogous to the spaces between words in a sentence; they mark where one word ends and another begins. If every code word ends in a comma, and the comma does not appear elsewhere in a code word, the code is prefix-free. However, modern communication systems send everything as sequences of "1" and "0" – adding a third symbol would be expensive, and using it only at the ends of words would be inefficient. Morse code is an everyday example of a variable-length code with a comma. The long pauses between letters, and the even longer pauses between words, help people recognize where one letter (or word) ends, and the next begins. Similarly, Fibonacci coding uses a "11" to mark the end of every code word.

Self-synchronizing codes are prefix codes that allow frame synchronization.

Related concepts

A suffix code is a set of words none of which is a suffix of any other; equivalently, a set of words which are the reverse of a prefix code. As with a prefix code, the representation of a string as a concantenation of such words is unique. A bifix code is a set of words which is both a prefix and a suffix code.

Prefix codes in use today

Examples of prefix codes include:

• variable-length Huffman codes
• country calling codes
• the country and publisher parts of ISBNs
• the Secondary Synchronization Codes used in the UMTS W-CDMA 3G Wireless Standard
• VCR Plus+ codes
• the UTF-8 system for encoding Unicode characters, which is both a prefix-free code and a self-synchronizing code

Techniques

Commonly used techniques for constructing prefix codes include Huffman codes and the earlier Shannon-Fano codes, and universal codes such as:

• Elias delta coding
• Elias gamma coding
• Elias omega coding
• Fibonacci coding
• Levenshtein coding
• Unary coding
• Golomb Rice code
• Straddling checkerboard (simple cryptography technique which produces prefix codes)

Notes

43 year old Petroleum Engineer Harry from Deep River, usually spends time with hobbies and interests like renting movies, property developers in singapore new condominium and vehicle racing. Constantly enjoys going to destinations like Camino Real de Tierra Adentro.

References

• 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.
  
  My blog: http://www.primaboinca.com/view_profile.php?userid=5889534
• One of the biggest reasons investing in a Singapore new launch is an effective things is as a result of it is doable to be lent massive quantities of money at very low interest rates that you should utilize to purchase it. Then, if property values continue to go up, then you'll get a really high return on funding (ROI). Simply make sure you purchase one of the higher properties, reminiscent of the ones at Fernvale the Riverbank or any Singapore landed property Get Earnings by means of Renting
  
  In its statement, the singapore property listing - website link, government claimed that the majority citizens buying their first residence won't be hurt by the new measures. Some concessions can even be prolonged to chose teams of consumers, similar to married couples with a minimum of one Singaporean partner who are purchasing their second property so long as they intend to promote their first residential property. Lower the LTV limit on housing loans granted by monetary establishments regulated by MAS from 70% to 60% for property purchasers who are individuals with a number of outstanding housing loans on the time of the brand new housing purchase. Singapore Property Measures - 30 August 2010 The most popular seek for the number of bedrooms in Singapore is 4, followed by 2 and three. Lush Acres EC @ Sengkang
  
  Discover out more about real estate funding in the area, together with info on international funding incentives and property possession. Many Singaporeans have been investing in property across the causeway in recent years, attracted by comparatively low prices. However, those who need to exit their investments quickly are likely to face significant challenges when trying to sell their property – and could finally be stuck with a property they can't sell. Career improvement programmes, in-house valuation, auctions and administrative help, venture advertising and marketing, skilled talks and traisning are continuously planned for the sales associates to help them obtain better outcomes for his or her shoppers while at Knight Frank Singapore. No change Present Rules
  
  Extending the tax exemption would help. The exemption, which may be as a lot as $2 million per family, covers individuals who negotiate a principal reduction on their existing mortgage, sell their house short (i.e., for lower than the excellent loans), or take part in a foreclosure course of. An extension of theexemption would seem like a common-sense means to assist stabilize the housing market, but the political turmoil around the fiscal-cliff negotiations means widespread sense could not win out. Home Minority Chief Nancy Pelosi (D-Calif.) believes that the mortgage relief provision will be on the table during the grand-cut price talks, in response to communications director Nadeam Elshami. Buying or promoting of blue mild bulbs is unlawful.
  
  A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running
  
  The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more
  
  There are various methods to go about discovering the precise property. Some local newspapers (together with the Straits Instances ) have categorised property sections and many local property brokers have websites. Now there are some specifics to consider when buying a 'new launch' rental. Intended use of the unit Every sale begins with 10 p.c low cost for finish of season sale; changes to 20 % discount storewide; follows by additional reduction of fiftyand ends with last discount of 70 % or extra. Typically there is even a warehouse sale or transferring out sale with huge mark-down of costs for stock clearance. Deborah Regulation from Expat Realtor shares her property market update, plus prime rental residences and houses at the moment available to lease Esparina EC @ Sengkang
• D.A. Huffman, "A method for the construction of minimum-redundancy codes", Proceedings of the I.R.E., Sept. 1952, pp. 1098–1102 (Huffman's original article)
• Profile: David A. Huffman, Scientific American, Sept. 1991, pp. 54–58 (Background story)
• Thomas H. Cormen, Charles E. Leiserson, Ronald L. Rivest, and Clifford Stein. Introduction to Algorithms, Second Edition. MIT Press and McGraw-Hill, 2001. ISBN 0-262-03293-7. Section 16.3, pp. 385–392.
• Template:FS1037C

External links

• Codes, trees and the prefix property by Kona Macphee