Run-length Limited - Technical Overview

Technical Overview

Generally run-length is the number of bits for which signal remains unchanged. A run-length of 3 for bit 1, represents a sequence of '111'. For instance, the pattern of magnetic polarizations on the disk might be '+−−−−++−−−++++++', with runs of length 1, 4, 2, 3, and 6. However, run length limited coding terminology assumes NRZI encoding, so 1 bits indicate changes and 0 bits indicate the absence of change, the above sequence would be expressed as '11000101001000001', and only runs of zero bits are counted.

Somewhat confusingly, the run length is the number of zeros (0, 3, 1, 2 and 5 in the preceding) between adjacent ones, which is one less than the number of bit times the signal actually remains unchanged. Run length limited sequences are characterized by two parameters, (d) and (k), which stipulate the minimum and maximum zero-bit run length that can occur in the sequence. So RLL's are generally specified as (d,k) RLL. e.g.: (1,3) MFM RLL.

Suppose a magnetic tape can support up to 3,200 flux reversals per inch. A Modified Frequency Modulation or (1,3) RLL encoding stores each data bit as two bits on tape, but since there is guaranteed to be one 0 (non flux reversal) bit between any 1 (flux reversal) bits then it is possible to store 6,400 encoded bits per inch on the tape, or 3,200 data bits per inch. A (1,7) RLL encoding can also store 6,400 encoded bits per inch on the tape, but since it only takes 3 encoded bits to store 2 data bits this is 4,267 data bits per inch. A (2,7) RLL encoding takes 2 encoded bits to store each data bit, but since there is guaranteed to be two 0 bits between any 1 bits then it is possible to store 9,600 encoded bits per inch on the tape, or 4,800 data bits per inch.

The flux reversal densities on hard drives are significantly greater, but the same improvements in storage density are seen by using different encoding systems.