Run-length-limited codes with multiple spacing

The general characteristics of run-length-limited codes are briefly summarized. The relationship of three variables-minimum and maximum periods between transitions, and detection window-is demonstrated; and it is shown that the accuracy with which a code may be matched to the characteristics of the recording channel depends upon the flexibility with which these three variables may be manipulated through choice of code parameters. Standard run-length-limited coding, in which the two parameters d and k may be varied, is inflexible in this regard, due to the requirement that the ratio of the minimum period between transitions to the detection window be integral (i.e., d + 1). This limitation vanishes when the run-length constraints are generalized to include an additional degree of freedom: the spacing s of the code. The drawback of such "multiple-spaced" codes is the potentially infinite propagation of detection errors; however, it is shown that for the special case of double-spaced (s = 2) codes, this problem may be eliminated. A detection circuit that implements double-spaced codes is shown, and an example is given of an easily implemented double-spaced code.