Coding theory

Codes are studied by various scientific disciplines—such as information theory, electrical engineering, mathematics, linguistics, and computer science—for the purpose of designing efficient and reliable data transmission methods.

This typically involves the removal of redundancy and the correction or detection of errors in the transmitted data.

For example, DEFLATE data compression makes files smaller, for purposes such as to reduce Internet traffic.

A typical music compact disc (CD) uses the Reed–Solomon code to correct for scratches and dust.

Cell phones also use coding techniques to correct for the fading and noise of high frequency radio transmission.

The decisive event which established the discipline of information theory, and brought it to immediate worldwide attention, was the publication of Claude E. Shannon's classic paper "A Mathematical Theory of Communication" in the Bell System Technical Journal in July and October 1948.

In this revolutionary and groundbreaking paper, the work for which Shannon had substantially completed at Bell Labs by the end of 1944, Shannon for the first time introduced the qualitative and quantitative model of communication as a statistical process underlying information theory, opening with the assertion that With it came the ideas of In 1948, Claude Shannon published "A Mathematical Theory of Communication", an article in two parts in the July and October issues of the Bell System Technical Journal.

In 1972, Nasir Ahmed proposed the discrete cosine transform (DCT), which he developed with T. Natarajan and K. R. Rao in 1973.

[2] The DCT is the most widely used lossy compression algorithm, the basis for multimedia formats such as JPEG, MPEG and MP3.

Data compression which explicitly tries to minimize the average length of messages according to a particular assumed probability model is called entropy encoding.

Source coding removes all data superfluous to the need of the transmitter, decreasing the bandwidth required for transmission.

The needed properties of this code mainly depend on the probability of errors happening during transmission.

However, there are more powerful codes known which are very effective at correcting the "burst" error of a scratch or a dust spot when this interleaving technique is used.

Likewise, narrowband modems are limited by the noise, present in the telephone network and also modeled better as a continuous disturbance.

The result is the number of ways for noise to make the receiver choose a neighbor (hence an error) grows as well.

In many cases, they generally offer greater simplicity of implementation over a block code of equal power.

The encoder is usually a simple circuit which has state memory and some feedback logic, normally XOR gates.

Convolutional codes are used in voiceband modems (V.32, V.17, V.34) and in GSM mobile phones, as well as satellite and military communication devices.

Cryptography or cryptographic coding is the practice and study of techniques for secure communication in the presence of third parties (called adversaries).

Modern cryptography exists at the intersection of the disciplines of mathematics, computer science, and electrical engineering.

Applications of cryptography include ATM cards, computer passwords, and electronic commerce.

Cryptography prior to the modern age was effectively synonymous with encryption, the conversion of information from a readable state to apparent nonsense.

Since World War I and the advent of the computer, the methods used to carry out cryptology have become increasingly complex and its application more widespread.

Modern cryptography is heavily based on mathematical theory and computer science practice; cryptographic algorithms are designed around computational hardness assumptions, making such algorithms hard to break in practice by any adversary.

The waveform pattern of voltage or current used to represent the 1s and 0s of a digital data on a transmission link is called line encoding.

A code may be designed so that a phase shift can be easily detected and corrected and that multiple signals can be sent on the same channel.

[citation needed] Another application of codes, used in some mobile phone systems, is code-division multiple access (CDMA).

[citation needed] When transmitting, the code word is used to modulate the data bits representing the voice message.

The origin of the problem has its roots in the Second World War when the United States Army Air Forces needed to test its soldiers for syphilis.

[14] Neural coding is a neuroscience-related field concerned with how sensory and other information is represented in the brain by networks of neurons.