Run-length-limited (RLL) coding constrains how long a sequence can continue without a transition. In the common recording-code notation (d,k), it specifies the minimum (d) and maximum (k) number of zeros between consecutive ones. Those limits help make recorded signals easier to read and keep their timing recoverable.
What “run length limited” means
A run is a consecutive series of the same symbol. An RLL code restricts the permitted run lengths in a coded sequence rather than allowing every possible pattern. In recording applications, these constraints are commonly written as (d,k)-constraints, or simply (d,k) codes. The IEEE tutorial on magnetic-storage codes defines d and k as the minimum and maximum numbers of zero symbols between consecutive one symbols: IEEE tutorial on RLL codes for magnetic storage.
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- d: the fewest zeros allowed between successive ones.
- k: the most zeros allowed between successive ones.
This is a constraint on the coded sequence, not a rule that all RLL codes encode data in the same way. The parameters and the code design can differ.
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How to read an RLL (d,k) example
RLL (1,7)
Under the recording convention above, RLL (1,7) requires at least one and no more than seven zeros between consecutive ones. A run of zero symbols between ones therefore cannot be shorter than one zero or longer than seven. Ecma International’s ECMA-353 optical-disk standard lists RLL (1,7) in its acronym list and describes a magneto-optical disk cartridge: ECMA-353, first edition (June 2004).
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Why recording systems use RLL constraints
In a recording channel, the sequence of symbols affects the physical signal that can be read back. The IEEE tutorial describes two related goals. A minimum spacing between ones influences high-frequency content and can help reduce intersymbol interference. A maximum spacing limits low-frequency content and ensures enough transitions to support the clock-synchronization loop, which helps the reader keep track of timing.
These are recording-channel motivations, not a guarantee that every use of RLL has identical goals or results. Code designers choose constraints to suit the channel and its requirements. A 1985 IBM Research publication record describes RLL and spectral-null constraints as part of code-design work comparing magnetic and optical storage; it does not establish which code current consumer devices use: IBM Research publication record.
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RLL is a family of codes, not one universal format
The phrase “RLL” names a class of constrained codes. An (d,k) pair gives two important run-length limits, but it does not by itself specify every detail of an encoding scheme. When comparing actual RLL codes, relevant factors include their d and k limits, code rate (the relationship between input data and coded symbols), and how their signal and timing tradeoffs suit the recording channel. There is no universally best pair established by these sources; the choice depends on the design requirements.
RLL is a documented part of magnetic and optical recording-code design, but that history should not be taken to mean that every present-day storage device uses RLL or any particular variant.
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