Constant-Weight and Constant-Charge Binary Run-Length Limited Codes

Abstract

Constant-weight and constant-charge binary sequences with constrained run length of zeros are introduced. For these sequences, the weight and the charge distribution are found. Then, recurrent and direct formulas for calculating the number of these sequences are obtained. With considering these numbers of constant-weight and constant-charge RLL sequences as coefficients of convergent power series, generating functions are derived. The fact, that generating function for enumerating constant-charge RLL sequences does not have a closed form, is proved. Implementation of encoding and decoding procedures using Cover's enumerative scheme is shown. On the base of obtained results, some examples, such as enumeration of running-digital-sum (RDS) constrained RLL sequences or peak-shifts control capability are also provided.Comment: 29 pages, submitted to IEEE Transactions on Information Theory. This paper is a corrected version of a paper with the same title that appeared on the arXiv in Feb. 2009. The major change is in Section VI, in which Subsection D is now well define