Run Length Limited
Run Length Limited ( RLL) is a set of line codes, which are used in the field of telecommunications and storage media such as magnetic disk storage as a writing process. The line code of this group are characterized in that a uniform data sequences from the states of logic-0 or logic-1 guarantees are limited in length. From this property, the name of that line codes is derived.
First RLL codes were patented by IBM in 1972 and used commercially since 1979 in the Direct Access Storage Device IBM 3370 mainframe computer for the Series 4300. Simple RLL codes were used in the 1980s and 1990s in the field of data recording disks. You will find with adaptations even today in the field of magnetic data recording and optical storage media such as compact disc ( CD ) technology.
Classification
RLL codes are classified d and κ in the literature by means of two parameters, and written in the form (d, κ ) RLL. The parameter D specifies the minimum and maximum number of κ the logic 0, which may occur between two logic 1 in the data sequence. κ can be infinite as the limiting case of a degenerate RLL code.
, The RLL code used in conjunction with the differential NRZI line code, as is common in magnetic storage media when using the RLL code for many signal edges for the clock recovery can sufficiently be guaranteed in the read operation of the data sequence. This dynamic clock recovery from the data signal is substantially in mechanical drives, and the flutter in only approximate setting of the revolution speed for the synchronization.
All RLL codes can be described by a finite automaton, which must have κ 1 states. A certain RLL code can then be clearly stated as a state diagram matrix, only the value (d, κ ) - RLL not classified a specific RLL code.
Another important parameter is the minimum length n of the required code words that satisfy a given (d, κ ) condition. The lengths of the specifically selected code words can be uniform, but need not be so. In uniform codeword length of each user data bit or a fixed block of data bits of the length k is uniquely associated with a code word of length n, where the condition holds: n > k An example of the 4B5B code which 4 user bits uniquely associates a 5 -bit code word. The ratio k / n being the code rate R. The number k of information bits which bears a code word sequence of length N (n ) is generally given by:
The capacity C (d, κ ) of RLL codes is
And can be determined using the Shannon - Hartley Act by the largest eigenvalues λ of the state transition matrix. Tables of capacity as a function of (d, κ ) can be found in the relevant literature.
The efficiency of a particular RLL code is the ratio of its code rate R and its capacitance C (d, κ ). In practical applications is usually tried to use RLL codes with the greatest possible efficiency.
Variants
(0,1 ) RLL - FM
The simplest (0,1) RLL code with a fixed codeword length and a rate of ½ is referred to in combination with the differential line NRZI coding as frequency modulation ( FM), and described by the following coding table:
(1,3 ) RLL MFM -
On magnetic storage media such as floppy disks (1,3 ) RLL code is use, also known under the name of Modified Frequency Modulation (MFM). This code also includes a rate of ½:
The condition of x depends on the previous data bit, x is 1 if the previous data bit was 0, and 0 when the previous data bit was 1.
(0,2 ) RLL
A (0,2 ) RLL code with a fixed block length is one among others, originally developed by IBM for magnetic storage (0,2 ) RLL code, which the group of Group - Coded Recording ( GCR ) codes. It is a variant of a 4B5B code, but not with this ident addition, there are various other companies more GCR codes which no (0,2 ) RLL code are, ie not all GCR codes are automatically (0,2 ) RLL.
Another very simple (0,2 ) RLL code, but with a variable data length and a fixed code word length, is as follows:
( 2,7) RLL
Subsequent non-trivial to konstruierender (2,7) RLL code with both variable data length and variable codeword length was used in the 1980s and 1990s by manufacturers of hard drives with " RLL recording " ( it comes from Peter Franaszek ). It fulfills both the Präfixbedingung and has a fixed code rate of ½ on. There are some of them are variants in the table below one possible variant is specified:
(1,7 ) RLL
A ( 1,7) RLL code with a fixed rate of 2 /3, which is characterized by a Boolean education provision and is therefore easy to implement in digital technology without a table, is the following code:
The formation rule is: Meets the input data sequence of the form (x, 0, 0, y) from the code word ( NOT x, x AND y, NOT y, 0, 0, 0 ) is formed. Do the input data is not of this form, (x, y ) ( y NOT NOT x, x AND y ) is determined from the input data, the code word is formed. Since this code does not meet the Präfixbedingung, the order of the lines in the code word education is essential.
Also worth mentioning are the same share free RLL codes. The DC component of freedom is satisfied when each data word sequence having the same average number of ones and zeros. In other words, each data word sequence results in a sequence of code words which in antipodal representation, ie logic 0 has the value -1, logic 1 the value 1, has a DC value of 0. This property is important when the code sequence to be transmitted on channels which can not transmit DC signals, such as radio channels, or pulse transformers for electrical isolation in electrical circuits.
The following is an equal proportion of free ( 1,7) RLL code:
The condition of x depends on the last bit of the immediately preceding code word has: x is 1 if the last code bit was 0, and 0 when the last code bit was 1.