# Line code

An example of coding a binary signal using rectangular pulse amplitude modulation with polar non-return-to-zero code
An example of Bipolar encoding, or AMI.
Encoding of 11011000100 in Manchester encoding
An example of Biphase mark code
An example of MLT-3 encoding.

Some signals are more prone to error than others when conveyed over a communication channel as the physics of the communication or storage medium constrains the repertoire of signals that can be used reliably.[1] The repertoire of signals is usually called a constrained code in data storage systems. In telecommunication, a line code is a code chosen for use within a communications system for transmitting a digital signal down a transmission line.

Line or constrained coding generates the repertoire of allowed digital signals to be transported, with a waveform or set of allowed waveforms that is appropriate for the specific properties of the physical channel and of the receiving equipment. The pattern of voltage, current or photons used to represent the digital data on a transmission link is called line encoding or constrained encoding. Common line encodings are unipolar, polar, bipolar, and Manchester code.

## Line coding

For reliable clock recovery at the receiver, one usually imposes a maximum run length constraint 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 such clock recovery, while sequences without such a constraint could seriously hamper the detection quality.

After line coding, the signal is put through a physical communication channel, either a transmission medium or data storage medium.[2][3] Sometimes the characteristics of two very different-seeming channels are similar enough that the same line code is used for them. The most common physical channels are:

Some of the more common binary line codes include:

NRZ–L Non return to zero level. This is the standard positive logic signal format used in digital circuits.

1 forces a high level
0 forces a low level

1 forces a transition
0 does nothing (keeps sending the previous level)

1 does nothing (keeps sending the previous level)
0 forces a transition

1 goes high for half the bit period and returns to low
0 stays low for the entire period

Biphase–L Manchester. Two consecutive bits of the same type force a transition at the beginning of a bit period.

1 forces a negative transition in the middle of the bit
0 forces a positive transition in the middle of the bit

Biphase–M Variant of Differential Manchester. There is always a transition halfway between the conditioned transitions.

1 forces a transition
0 keeps level constant

Biphase–S Differential Manchester used in Token Ring. There is always a transition halfway between the conditioned transitions.

1 keeps level constant
0 forces a transition

Differential Manchester
(Alternative)
Need a Clock, always a transition in the middle of the clock period

1 is represented by no transition.
0 is represented by a transition at the beginning of the clock period.

Bipolar The positive and negative pulses alternate.

1 forces a positive or negative pulse for half the bit period
0 keeps a zero level during bit period

An arbitrary bit pattern in various binary line code formats

Each line code has advantages and disadvantages. The particular line code used is chosen to meet one or more of the following criteria:

• Minimize transmission hardware
• Facilitate synchronization
• Ease error detection and correction
• Minimize spectral content
• Eliminate a DC component

## Disparity

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 words.[4]

Unfortunately, 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 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. In other words, each transmitted code word is corrected 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. For example, Manchester code and Interleaved 2 of 5.
• Use a paired disparity code. In other words, the transmitter has to make sure that every code word that averages to a negative level is paired with another code word that averages to a positive level. Therefore, it must keep track of the running DC buildup, and always pick 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. For example, AMI, 8B10B, 4B3T, etc.
• Use a scrambler. For example, the scrambler specified in RFC 2615 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. One of the principle advantages of this type of code is that it can completely 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. To compensate, several people have designed polarity-insensitive transmission systems.[5][6][7][8] There are three ways of providing unambiguous reception of "0" bits or "1" bits over such channels:

## Run-length limited codes

Run-length limited[9] or RLL coding is a line coding technique that is used to send arbitrary data over a communications channel with bandwidth limits. 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 Blu-ray using EFM and EFMPLus[10] codes. Higher density RLL (2,7) and RLL (1,7) codes became the de facto industry standard for hard disks by the early 1990s.

## Synchronization

Line coding should make it possible for the receiver to synchronize itself to the phase of the received signal. If the synchronization is not ideal, then the signal to be decoded will not have optimal differences (in amplitude) between the various digits or symbols used in the line code. This will increase the error probability in the received data.
Biphase line codes require at least one transition per bit time. This makes it easier to synchronize the transceivers and detect errors, however, the baud rate is greater than that of NRZ codes.

## Other considerations

It is also preferred for the line code to have a structure that will enable error detection. Note that the line-coded signal and a signal produced at a terminal may differ, thus requiring translation.

A line code will typically reflect technical requirements of the transmission medium, such as optical fiber or shielded twisted pair. These requirements are unique for each medium, because each one has different behavior related to interference, distortion, capacitance and loss of amplitude.[citation needed]

## Common line codes

Optical line codes: