A prefix code is a code which meets the "prefix property", which is that no code word is a prefix of any other code word in the set. A code which uses code words {0,10,11} meets the prefix property; a code whose set is {0,1,10,11} does not because "1" is a prefix of both "10" and "11". CODE is a visual programming language and system for parallel programming, letting users compose sequential programs into parallel ones. ... Look up prefix on Wiktionary, the free dictionary. ...

Prefix codes are also known as prefix-free codes, comma-free codes or instantaneous codes; even though Huffman coding is only one algorithm for deriving prefix codes, prefix codes are also widely referred to as "Huffman codes" (even, confusingly, when the codes were not produced by a Huffman algorithm.) In computer science, Huffman coding is an entropy encoding algorithm used for lossless data compression. ...

The prefix property permits code words to be transmitted and properly framed without the need of out-of-band markers (assuming that the receiver can correctly identify the start of the transmission and that there are no uncorrected errors in the symbol stream.) This is not possible with codes that lack the prefix property, such as our example of {0,1,10,11}: a receiver which read 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". In telecommunication, the term framing has the following related meanings: In time-division multiplexing reception, it is a synonym for frame synchronization. ... Out-of-band signaling is telecommunication signaling (exchange of information in order to control a telephone call) that is done on a channel that is dedicated for the purpose and separate from the channels used for the telephone call. ...

Examples of prefix codes are the variable-length Huffman codes, country calling codes, ISBNs and the Secondary Synchronization Codes used in the UMTS W-CDMA 3G Wireless Standard. In computer science, Huffman coding is an entropy encoding algorithm used for lossless data compression. ... This is a list of country calling codes, also known as international direct dialing (IDD) codes, which are needed to access international telephone services. ... The International Standard Book Number, or ISBN (sometimes pronounced is-ben), is a unique identifier for books, intended to be used commercially. ... Universal Mobile Telecommunications System (UMTS) is one of the third-generation (3G) mobile phone technologies. ... W-CDMA (Wideband Code Division Multiple Access) is a type of 3G cellular network. ...

This article is partly derived from Federal Standard 1037C, which uses the term comma-free code. Federal Standard 1037C entitled Telecommunications: Glossary of Telecommunication Terms is a U.S. Federal Standard, issued by the General Services Administration pursuant to the Federal Property and Administrative Services Act of 1949, as amended. ...

prefix codes are a form of entropy encoding used in lossless data compression. An entropy encoding is a coding scheme that assigns codes to symbols so as to match code lengths with the probabilities of the symbols. ... Lossless data compression is a class of data compression algorithms that allows the original data to be reconstructed exactly from the compressed data. ...

When you are reading a newspaper, how do you know where one sentence ends and the next begins? You use a full-stop or a query-mark, symbols different from any other letter, number, or symbol. How do you know where one word ends and the next begins? You use a full-size space, which looks different from any letter, number or symbol. How do you know where one letter ends and the next begins? In block printing, the hairline space between letters separates them. However, this "space" is not necessary -- people are able to read cursive handwriting and shorthand even though one letter runs right into the next. Block printing is a form of printing first developed in China. ... Cursive is a style of handwriting in which all the letters in a word are connected, making a word one single (complicated) stroke. ... Penmanship is the art of writing clearly and quickly. ... Shorthand is a general term referring to any abbreviated or symbolic writing method that improves speed of writing or brevity as compared to a standard method of writing the language. ...

Many communication systems send information as a series of bits. Many storage systems store information as a series of bits. In some systems, the letter 'a' is transmitted as the sequence

 10000110 

while the letter 'd' is transmitted as the sequence

 00100110 

and the full-sized space between words is

 00000100 

. Each letter is formed from a sequence of bits -- how can the computer know where one letter ends and the next one starts ?

the "comma"

Certttttttbainly onvvbe covbuldvc use a spevbcvbvbial bvbbv tvbbvche end of the sentecbvbvnce -- to mbarvbk whevre one letbvvter endvcs and tbbhe bvc. So vbtheb worvcd "dvcbada" coubvcbld be transmittvcbvced

 00101110fg10ffgg000110,00101110,10000110, 

whege tfgdfgdfghe "," represgfdgffgbbents a spegcial sygfmbol, dgifferent from "1" or "0g". Howevfgder, mofgfddern comfgdmufgdgnication sygffdgstgfdgdems senfgfdd everythifdggdng asfdg sefgdgquefgdgnces of "1" or "0" -- addgfgfing a "gffdgdfgsyfdmbol" would be exfdgdgpensive.

(In general, we call the "pfdgause" between itegfsgfdgms a "comfgma").

fixed-length comma-free codes

Fortunately, the "third symbol" turns out to be unnecessary -- it's possible for a machine to receive the comma-free sequence

 00101110100001100010111010000110 

and correctly decode the word "dada".

The simplest method is to make every letter the same length -- a "fixed-length code". 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. ISO 8859-15 is part 15 of ISO 8859, a standard character encoding defined by ISO. It is also known as Latin-9, and unofficially as Latin-0 but not as Latin-15. ... UTF-32 and UCS-4 are alternate names for a method of encoding Unicode characters, using the fixed amount of exactly 32 bits for each Unicode code point. ... Asynchronous Transfer Mode, or ATM for short, is a cell relay network protocol which encodes data traffic into small fixed sized (53 byte; 48 bytes of data and 5 bytes of header information) cells instead of variable sized packets as in packet-switched networks (such as the Internet Protocol or...

Often we wish a message took less time to send or less space to store. So we use data compression. In computer science, data compression or source coding is the process of encoding information using fewer bits (or other information-bearing units) than a more obvious representation would use, through use of specific encoding schemes. ...

One kind of data compression is to use a different code -- one that uses fewer bits per letter.

If one uses ASCII, for example, one really needs only 7 bits per letter (assuming the standard English alphabet with upper and lower case and no accents). There are 95 printable ASCII characters, numbered 32 to 126. ...

variable-length codes with a comma

One can compress typical text into even fewer bits if one uses a code with a variable number of bits per letter.

If we used a custom code

 0 a 1 d 01 space 

then the phrase "add a dad" could be compressed to

 0,1,1,01,0,01,1,0,1, 

Morse code is an example of a variable-length code with a comma. The long spaces between letters, and even longer spaces between words, help people recognize where one letter/word ends, and the next begins. 1922 Chart of the Morse Code Letters and Numerals Morse code is a method for transmitting information, using standardized sequences of short and long marks or pulses — commonly known as dots and dashes — for the letters, numerals and special characters of a message. ...

Unfortunately, if we remove the commas, the resulting message

 01101001101 

is ambiguous. Does a "0" followed by a "1" represent a space character, or 2 different letters ?

The ambiguity is caused because one complete code (in this case "0" for "a") is just the first part -- the prefix -- of another code (in this case, "01" for space).

variable-length comma-free codes

It is possible to specially design a variable-length code such that there is never any ambiguity. Such a specially designed code is called a "variable-length code" or a "prefix-free code".

There are many variable-length codes.

• VCR Plus+ codes
• country calling codes
• Universal codes such as
  • Elias delta coding
  • Elias gamma coding
  • Elias omega coding
  • Fibonacci coding
  • Golomb coding
  • Unary coding
• Shannon-Fano codes
• Huffman codes

When compressing data, we wonder -- which one is the best code ? (Which code compresses the file into the fewest number of bits ?) Or in other words, which does the best entropy encoding? VCR Plus+ is a scheme to assist in the recording of television programs on VCRs in the United States and Canada. ... This is a list of country calling codes, also known as international direct dialing (IDD) codes, which are needed to access international telephone services. ... In data compression, a universal code maps the integers (representing messages) onto self-delimiting binary codewords. ... Elias delta code is a universal code encoding the positive integers. ... Elias gamma code is a universal code encoding the positive integers. ... Elias omega coding is a universal code encoding the positive integers. ... The Fibonacci code is a universal code which encodes positive integers into binary code words. ... Golomb coding is a form of entropy coding invented by Solomon W. Golomb that is optimal for alphabets following geometric distributions, that is, when small values are vastly more common than large values. ... Unary coding is an entropy encoding that represents a number n with n-1 ones followed by a zero. ... In the field of data compression, Shannon-Fano coding is a technique for constructing a prefix code based on a set of symbols and their probabilities (estimated or measured). ... In computer science, Huffman coding is an entropy encoding algorithm used for lossless data compression. ... An entropy encoding is a coding scheme that assigns codes to symbols so as to match code lengths with the probabilities of the symbols. ...

If one knows ahead of time all the letters that could possibly be used, and has a good estimate of the letter frequencies, the best possible comma-free code is a Huffman code. (Usually the Huffman process generates a variable-length code. But when all the letters have the same frequency, such as previously compressed or encrypted data, and additionally the number of codewords is a power of 2, the Huffman process will generate a fixed-length code.) CAN SOMEONE PLEASE ADD INFORMATION ABOUT HOW TO GENERATE LETTER FREQUENCY TABLES IN FOREIGN LANGUAGES (i. ... In computer science, Huffman coding is an entropy encoding algorithm used for lossless data compression. ...

All other codes (both variable-length and fixed-length) use at least as many bits than a Huffman code. (Usually there are several Huffman codes. All of them compress the file into exactly the same number of bits).

non-codes

Some data compression algorithms can compress files even smaller than Huffman compression. Generally this is because they don't use a code at all. In computer science, Huffman coding is an entropy encoding algorithm used for lossless data compression. ...

• They may represent "a" by one pattern of bits in one place in the compressed file, then use that same pattern of bits to represent a completely different letter later on, as in adaptive Huffman compression.
• They may use a pattern of bits to represent several letters, as in LZW compression -- changing any one of those bits may completely change that block of letters.
• Or they may avoid mapping particular bits to particular letters (the definition of a code) in other creative ways, as in range encoding.

Adaptive Huffman coding is an adaptive coding technique based on Huffman coding, building the code as the symbols are being transmitted, having no initial knowledge of source distribution, that allows one-pass encoding and adaptation to changing conditions in data. ... LZW (Lempel-Ziv-Welch) is a lossless data compression algorithm. ... This article needs cleanup. ...

existence of prefix codes / Krafts inequality

If we have a fixed number of symbols | X | (the alphabet size), then for any given list of codeword lengths (l_i)_{i = 1...n} a prefix code exists if and only if . This is known as Krafts inequality.

error handling

Many communication systems are not completely error-free. There are occasional a single bit errors (toggling a bit, losing a bit, or gaining a bit).

With fixed-length codes, an error toggling a bit causes just that one code to be received in error, but all other codes are received OK. However, losing or gaining a bit (a framing error) turns the rest of the message into gibberish. (This is why most communication protocols periodically re-synchronize. ASCII over RS-232 uses 20% of its bandwidth re-synchronizing after each character). See Synchronization Link protocol Framing error is the following: Generally, a framing error is the result of reading a string of symbols which are grouped in blocks starting at the wrong point. ... Synchronization is coordination with respect to time. ... In communications, the transmission of a unit of data from one node to another (OSI layer 2). ...

With Fibonacci codes and unary codes, all single-bit errors cause one or two erroneous codes, but all other codes are received OK. (These codes are "self-synchronizing"). The Fibonacci code is a universal code which encodes positive integers into binary code words. ... Unary coding is an entropy encoding that represents a number n with n-1 ones followed by a zero. ...

With most other variable-length codes, any kind of single-bit error turns the rest of the message into gibberish.

See also

• binary symmetric channel
• communications protocol
• character encoding

In coding theory, a binary symmetric channel (or BSC) is an idealized model of a communications channel that sends bits. ... This article concerns communication between pairs of electronic devices. ... A character encoding consists of a code that pairs a set of characters (representations of graphemes or grapheme-like units, such as might appear in an alphabet or syllabary for the communication of a natural language) with a set of something else, such as numbers or electrical pulses, in order...

References

• P. Elias, Universal codeword sets and representations of integers, IEEE Trans. Inform. Theory 21 (2) (1975) 194-203.