Error-correcting codes are common especially in wireless communication systems, broadband modem standards and modern copper-based high-speed LANs.

In 1993, turbo codes were introduced by Berrou, Glavieux, and Thitimajshima ( from Télécom Bretagne, former ENST Bretagne, France ) in their paper: " Near Shannon Limit Error-correcting Coding and Decoding: Turbo-codes " published in the Proceedings of IEEE International Communications Conference.

Error-correcting codes are used to reliably transmit digital data over unreliable communication channels subject to channel noise.

* Error-correcting code, a type of code

Error-correcting code –

* Error-correcting code

* Benefits of Chipkill-Correct ECC for PC Server Main Memory-A 1997 discussion of SDRAM reliability-some interesting information on " soft errors " from cosmic rays, especially with respect to Error-correcting code schemes

VAX Error-correcting code | ECC memory card with VAXBI interface highlighted.

Many codes occupy the same channel, but only users associated with a particular code can communicate.

Coding theory is concerned with finding explicit methods, called codes, of increasing the efficiency and reducing the net error rate of data communication over a noisy channel to near the limit that Shannon proved is the maximum possible for that channel.

These codes can be roughly subdivided into data compression ( source coding ) and error-correction ( channel coding ) techniques.

Channel coding is concerned with finding such nearly optimal codes that can be used to transmit data over a noisy channel with a small coding error at a rate near the channel capacity.

OFDM can be extended to multi-user channel access method in the orthogonal frequency-division multiple access ( OFDMA ) and multi-carrier code division multiple access ( MC-CDMA ) schemes, allowing several users to share the same physical medium by giving different sub-carriers or spreading codes to different users.

A very rare syndrome with isolated congenital insensitivity to pain has been linked with mutations in the SCN9A gene, which codes for a sodium channel ( Na < sub > v </ sub > 1. 7 ) necessary in conducting pain nerve stimuli.

However, in schemes that include forward error correction codes ( channel coding ), the redundant error code is normally excluded from the throughput.

The BER may be improved by choosing a strong signal strength ( unless this causes cross-talk and more bit errors ), by choosing a slow and robust modulation scheme or line coding scheme, and by applying channel coding schemes such as redundant forward error correction codes.

The Levenshtein distance measurement is more appropriate for measuring raw channel performance before frame synchronization, and when using error correction codes designed to correct bit-insertions and bit-deletions, such as Marker Codes and Watermark Codes.

Coding Theory is the branch of mathematics that covers source codes and channel codes.

Considering all possible multi-level and multi-phase encoding techniques, the Shannon – Hartley theorem states the channel capacity C, meaning the theoretical tightest upper bound on the information rate ( excluding error correcting codes ) of clean ( or arbitrarily low bit error rate ) data that can be sent with a given average signal power S through an analog communication channel subject to additive white Gaussian noise of power N, is:

The physical layer net bitrate, information rate, useful bit rate, payload rate, net data transfer rate, coded transmission rate, effective data rate or wire speed ( informal language ) of a digital communication channel is the capacity excluding the physical layer protocol overhead, for example time division multiplex ( TDM ) framing bits, redundant forward error correction ( FEC ) codes, equalizer training symbols and other channel coding.

Data modems, telephone transmissions, and NASA all employ channel coding techniques to get the bits through, for example the turbo code and LDPC codes.

The aim of channel coding theory is to find codes which transmit quickly, contain many valid code words and can correct or at least detect many errors.

Again there are a class of channel codes that are designed to combat fading.

The properties of this class of codes allow many users ( with different codes ) to use the same radio channel at the same time.

In information theory, turbo codes ( originally in French Turbocodes ) are a class of high-performance forward error correction ( FEC ) codes developed in 1993, which were the first practical codes to closely approach the channel capacity, a theoretical maximum for the code rate at which reliable communication is still possible given a specific noise level.

These sets were expanded in 1963 to 7 bits of coding, called the American Standard Code for Information Interchange ( ASCII ) as the Federal Information Processing Standard which replaced the incompatible teleprinter codes in use by different branches of the U. S. government.

Huffman coding is the most known algorithm for deriving prefix codes, so prefix codes are also widely referred to as " Huffman codes ", even when the code was not produced by a Huffman algorithm.

Historically, cryptography was split into a dichotomy of codes and ciphers ; and coding had its own terminology, analogous to that for ciphers: " encoding, codetext, decoding " and so on.

The simplest kind of automated collation is based on the numerical codes of the symbols in a character set, such as ASCII coding ( or any of its supersets such as Unicode ), with the symbols being ordered in increasing numerical order of their codes, and this ordering being extended to strings in accordance with the basic principles of alphabetical ordering ( mathematically speaking, lexicographical ordering ).

The coding system used in the DSM-IV is designed to correspond with the codes used in the ICD, although not all codes may match at all times because the two publications are not revised synchronously.

Despite these differences, all known naturally-occurring codes are very similar to each other, and the coding mechanism is the same for all organisms: three-base codons, tRNA, ribosomes, reading the code in the same direction and translating the code three letters at a time into sequences of amino acids.

If the symbol width is n, the codes of width n + 1 fall naturally into two blocks: the lower block of 2 < sup > n </ sup > codes for coding single symbols, and the upper block of 2 < sup > n </ sup > codes that will be used by the decoder for sequences of length greater than one.

* Cam. ac. uk, On-line textbook: " Information Theory, Inference, and Learning Algorithms " by David MacKay-giving an entertaining and thorough introduction to Shannon theory, including state-of-the-art methods from coding theory, such as arithmetic coding, low-density parity-check codes, and Turbo codes.

As a memory aid in coding, and certainly for readability, there are a large number of constants, such as True and False for logical values, vbOKCancel and vbYesNo for MsgBox codes, vbBlack and vbYellow for color values, vbCR for the carriage return character, and many others.

In coding theory the BCH codes form a class of cyclic error-correcting codes that are constructed using finite fields.

* G. Levasseur, Napoléon et l ’ élaboration des codes répressifs ( Mélanges en homme à Jean Imbert, PUF, 1989 p. 371 ): Legal analysis of the Code of Criminal Procedure.

Foreign ( alphabetically by jurisdiction ): ( i ) codes or statutes in the current codification ( by order in the codification ); ( ii ) statutes currently in force but not in the current codification ( by reverse chronological order of enactment ; ( iii ) repealed statutes ( by reverse chronological order of enactment.

The four zip codes of Collin County that contribute to the county's affluence are ( in descending order of median household income / year ): 75093, 75024, 75025, and 75094.

The roles and responsibilities of personnel in each level are generally as follows ( there are slight differences or variations between different codes and standards ):

Codes registered for 639-2 that are listed as collective codes in ISO 639-5 ( and collective codes by name in ISO 639-2 ):

that are freely-associated states, with which the United States has entered into a Compact of Free Association ( ISO 3166-1 codes in parentheses ):

: Rio Grande ( formerly New Mexico ): This territory includes zip codes in the state of New Mexico and Texas zip code areas 79800-79999, 88500-88599.

* Sterling ( two factories ; codes S109 and M619 ): approx.

There are several kinds of kyphosis ( ICD-10 codes are provided ):

To represent all 128 ASCII values, there are three code sets ( A, B, C ), which can be mixed within a single barcode ( by using codes 98 and 99 in code sets A and B, 100 in code sets A and C and 101 in code sets B and C to switch between them ):

Table codes ( click individual codes to view season tables ):

ASCII source ( ANSI X3. 64 escape codes stripped ):

* < tt > ac </ tt > ( Ascension Island ): This code is a vestige of IANA's decision in 1996 to allow the use of codes reserved in the ISO 3166-1 alpha-2 reserve list for use by the Universal Postal Union.

Specific leukodystrophies include ( ICD-10 codes are provided where available ):

Two of the codes are sequential and structure the text in an irreversible way ( XV ): The hermeneutic code ( HER ) denotes an enigma that moves the narrative forward ; it sets up delays and obstacles that maintain suspense.

Because the hermeneutic code involves a move from a question to an answer it is one of the two codes ( the other being the proairetic or action code ) which Barthes calls “ irreversible ” ( XV ): Once a secret is revealed, it cannot be unrevealed — the moment of cognition is permanent for the reader.

* Les bienséances ( decorum ): Literature should respect moral codes and good taste ; nothing should be presented that flouts these codes, even if they are historical events.

( 6 characters, indicating the functional parts of construction works or structure ): follows a classification system like SfB building codes or Uniclass codes ;