Runlengthlimited

Runlengthlimited, often abbreviated as RLL, refers to a class of binary line codes used to constrain the lengths of runs of zeros between ones in a data stream. The primary purpose is to balance timing recovery, error detection, and DC content in a communication or storage channel. By preventing both very long and very short zero runs, RLL codes make it easier for receivers to synchronize with the sender and to operate reliably over imperfect channels.

The most common formal description of an RLL code uses the (d, k) constraint. Here, d denotes the minimum number of consecutive zeros that must appear between two adjacent ones, and k denotes the maximum number of consecutive zeros allowed between ones. A data sequence is encoded so that every pair of successive ones in the output is separated by at least d and at most k zeros. Some systems employ different or additional constraint parameters, but the (d, k) framework remains the standard reference.

Encoding and decoding in RLL systems are typically lossless and invertible. Data is transformed by a finite-state encoder into output sequences that satisfy the chosen constraint, and a corresponding decoder reconstructs the original input from the constrained output.

Applications of RLL coding are widespread in magnetic storage (such as hard disks and tapes) and optical storage, where controlling run lengths aids read-back timing and signal integrity. A well-known example is the (2, 10) constraint used in the eight-to-fourteen modulation scheme for compact discs, which maps 8-bit data into 14-bit channel words while ensuring a minimum and maximum zero run between ones.

Advantages of RLL include improved clock recovery and DC balance. The trade-offs include added redundancy and encoder/decoder complexity, which reduce raw data density relative to unconstrained signaling.