Run Length Limited codes, or RLL codes are widely used in hard disk drives (and notably digital optical discs, such as CD, DVD and BluRay disc) to prevent long stretches of no transitions, and therefore decoding uncertainty, from creeping in.

On a hard disk, a bit is encoded by a polarity transition or the lack thereof. Encoding 000000 would then be easy - just keep the magnetic phase unchanged for a few micrometers. However, when decoding, uncertainty creeps in - how many micrometers did we read? Does this correspond to 6 zeroes or 5? To prevent this problem, data is coded in such a way that these long stretches of no transitions do not occur.

History

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RLL encoding was invented by IBM engineers, who used it in mainframe disk drives. During the late 1980s, PC hard disks began using RLL. RLL codes have found almost universal application in optical disc recording practice since 1980. In consumer electronics, there is the Eight-to-Fourteen Modulation or EFM code (rate = 8/17, d=2, k=10), which is employed in the Compact Disc (CD), and the EFMPlus code (rate = 8/16, d=2, k=10) used in the DVD. See below.

Technical overview

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The length of time (usually expressed in channel bits) between consecutive transitions 0 to 1 or 1 to 0 is known as the runlength. For instance, the runlengths in the word '0111100111000000' are of length 1, 4, 2, 3, and 6. Run length limited sequences are characterized by two parameters, (d+1) and (k+1), which stipulate the minimum (with the exception of the very first and last runlength) and maximum runlength, respectively, that may occur in the sequence. The parameter d controls the smallest pit/land recorded on an optical disc. The maximum runlength parameter k ensures adequate frequency of clocking information for synchronization of the read clock. The grounds on which d and k values are selected, in turn, depend on various factors such as the channel response, the desired data rate (or information density), and the jitter and noise characteristics.

Coding

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1	1 (1000)
	0 (0100)
0	1	1 (001000)
		0 (100100)
	0	1	1 (00001000)
			0 (00100100)
		0 (000100)

Example:
11 000 011
1000 000100 001000

Other encodings

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Other schemes include Group Code Recording, FM and MFM (Modified Frequency Modulation).

See also

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• PRML

External links

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• Chapter 14: Hard Disk Drives - QUE Upgrading & Repairing PCs, Eighth Edition

Audio storage | Rotating disc computer storage media | Video storage | Run Length Limited | Run Length Limited encoding | RLL