Line Coding

In telecommunication, a line code is a pattern of voltage, current, or photons used to represent digital data transmitted down a communication channel or written to a storage medium. This repertoire of signals is usually called a constrained code in data storage systems.
Some signals are more prone to error than others as the physics of the communication channel or storage medium constrains the repertoire of signals that can be used reliably.

Common line encodings are unipolar, polar, bipolar, and Manchester code.

Transmission and storage

After line coding, the signal is put through a physical communication channel, either a transmission medium or data storage medium.Karl Paulsen
"Coding for Magnetic Storage Mediums"
.2007. The most common physical channels are:
* the line-coded signal can directly be put on a transmission line, in the form of variations of the voltage or current (often using differential signaling).
* the line-coded signal (the ''baseband signal'') undergoes further pulse shaping (to reduce its frequency bandwidth) and then is modulated (to shift its frequency) to create an '' RF signal'' that can be sent through free space.
* the line-coded signal can be used to turn on and off a light source in free-space optical communication, most commonly used in an infrared remote control.
* the line-coded signal can be printed on paper to create a bar code.
* the line-coded signal can be converted to magnetized spots on a hard drive or tape drive.
* the line-coded signal can be converted to pits on an optical disc.

Some of the more common binary line codes include:

Each line code has advantages and disadvantages. Line codes are chosen to meet one or more of the following criteria:
* Minimize transmission hardware
* Facilitate synchronization
* Ease error detection and correction
* Achieve a target spectral density
* Eliminate a DC component

Disparity

Most long-distance communication channels cannot reliably transport a DC component. The DC component is also called the ''disparity'', the ''bias'', or the DC coefficient. The disparity of a bit pattern is the difference in the number of one bits vs the number of zero bits. The ''running disparity'' is the running total of the disparity of all previously transmitted bits. The simplest possible line code, unipolar, gives too many errors on such systems, because it has an unbounded DC component.

Most line codes eliminate the DC component such codes are called DC-balanced, zero-DC, or DC-free. There are three ways of eliminating the DC component:

* Use a constant-weight code. Each transmitted code word in a constant-weight code is designed such that every code word that contains some positive or negative levels also contains enough of the opposite levels, such that the average level over each code word is zero. Examples of constant-weight codes include Manchester code and Interleaved 2 of 5.
* Use a paired disparity code. Each code word in a paired disparity code that averages to a negative level is paired with another code word that averages to a positive level. The transmitter keeps track of the running DC buildup, and picks the code word that pushes the DC level back towards zero. The receiver is designed so that either code word of the pair decodes to the same data bits. Examples of paired disparity codes include alternate mark inversion, 8b/10b and 4B3T.
* Use a scrambler. For example, the scrambler specified in for 64b/66b encoding.

Polarity

Bipolar line codes have two polarities, are generally implemented as RZ, and have a radix of three since there are three distinct output levels (negative, positive and zero). One of the principle advantages of this type of code is that it can eliminate any DC component. This is important if the signal must pass through a transformer or a long transmission line.

Unfortunately, several long-distance communication channels have polarity ambiguity. Polarity-insensitive line codes compensate in these channels.
There are three ways of providing unambiguous reception of 0 and 1 bits over such channels:
* Pair each code word with the polarity-inverse of that code word. The receiver is designed so that either code word of the pair decodes to the same data bits. Examples include alternate mark inversion, Differential Manchester encoding, coded mark inversion and Miller encoding.
* differential coding each symbol relative to the previous symbol. Examples include MLT-3 encoding and NRZI.
* Invert the whole stream when inverted syncwords are detected, perhaps using polarity switching

Run-length limited codes

For reliable clock recovery at the receiver, a run-length limitation may be imposed on the generated channel sequence, i.e., the maximum number of consecutive ones or zeros is bounded to a reasonable number. A clock period is recovered by observing transitions in the received sequence, so that a maximum run length guarantees sufficient transitions to assure clock recovery quality.

RLL codes are defined by four main parameters: ''m'', ''n'', ''d'', ''k''. The first two, ''m''/''n'', refer to the rate of the code, while the remaining two specify the minimal ''d'' and maximal ''k'' number of zeroes between consecutive ones. This is used in both telecommunication and storage systems that move a medium past a fixed recording head.

Specifically, RLL bounds the length of stretches (runs) of repeated bits during which the signal does not change. If the runs are too long, clock recovery is difficult; if they are too short, the high frequencies might be attenuated by the communications channel. By modulating the data, RLL reduces the timing uncertainty in decoding the stored data, which would lead to the possible erroneous insertion or removal of bits when reading the data back. This mechanism ensures that the boundaries between bits can always be accurately found (preventing bit slip), while efficiently using the media to reliably store the maximal amount of data in a given space.

Early disk drives used very simple encoding schemes, such as RLL (0,1) FM code, followed by RLL (1,3) MFM code which were widely used in hard disk drives until the mid-1980s and are still used in digital optical discs such as CD, DVD, MD, Hi-MD and