See Information theory for more details. See also Communication theory

Data transmission refers to the transfer of information from one entity to another, by means of a Data transmission system .

Data transmission system

See more here: Data transmission system

Properties of data transmission systems

• Code used by the transmitter. See Coding theory.
• Entropy rate of the transmitter (considered as an Information source).
• Channel capacity of the Communication channel. This quantity gives a limit to the rate at which information can be reliably sent through the channel, as established by the Channel coding theorem.

Types of communication channel

• Finite state channel

Types of transmitter/receivers

These are mostly specified by the code they use. In data transmission systems, these are mostly Error-correcting codes.

Data transmission theory

The main desired properties of a data transmission system, and thus the main subjects of study are:

• Reliability. How unlikely is the receiver to interpret message wrongly?
• Speed. What is the maximum rate at which information can be sent over the channel? Measured in (bits decoded)/(channel bits sent)

Thus the main problem of study is: for a particular communication channel, find code so that data transmission rate is as high as possible, while receiver receives the information with negligible probability of error.

This is sometimes called "channel coding" because the most reliable code depends on the properties of the channel. This is done by finding codewords (sequences of input values) such that their images are as disjoint as possible. This is equivalent to sphere packing in high dimensions.

The main result in data transmission theory is the Channel coding theorem, which gives a fundamental limit to the data transmission rate that can be achieved by a code, while keeping error rates negligible. This limit turns out to be the Channel capacity.

Data transmission system engineering

The goals stated above for a data transmission system are achieved in two main ways:

• Design and construction of optimal hardware (see Telecommunication engineering)
• Design and use of optimal codes. This is one of the main goals of Coding theory, and in particular of Error-correcting codes.

See http://pfister.ee.duke.edu/thesis/chap1.pdf, and other chapters.

Entropy in Compression - Computerphile