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

TL;DR

This paper introduces constant-weight and constant-charge binary RLL sequences with constrained zeros, deriving formulas and generating functions, and demonstrates encoding/decoding methods with applications in digital sequence control.

Contribution

It presents new formulas and generating functions for constant-weight and constant-charge RLL sequences, including implementation of encoding and decoding schemes.

Findings

Derived recurrent and direct formulas for sequence enumeration.

Proved the generating function for constant-charge sequences lacks a closed form.

Demonstrated encoding/decoding procedures using Cover's scheme.

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.