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

Author

Kurmaev, Oleg F.

Author_Institution

Moscow Inst. of Electron. Eng. (MIEE/MIET), Moscow, Russia

Volume

57

Issue

7

fYear

2011

fDate

7/1/2011 12:00:00 AM

Firstpage

4497

Lastpage

4515

Abstract

Constant-weight and constant-charge binary sequences with constrained run length of zeros are introduced. The weight and charge distribution for these sequences are found. Next, recurrent and direct formulas for calculating the number of these sequences are obtained. By considering these numbers of constant-weight and constant-charge run-length limited (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. Subsequently, implementation of encoding and decoding procedures using Cover´s enumerative scheme is shown. Based on the obtained results, some examples, such as enumeration of running-digital sum (RDS) constrained RLL sequences or peak-shifts control capability are also provided.

Keywords

binary codes; binary sequences; decoding; runlength codes; Cover enumerative scheme; binary sequence; charge distribution; constant-charge RLL sequence; constant-charge binary runlength limited code; constant-weight RLL sequence; constant-weight binary runlength limited code; convergent power series coefficient; decoding; encoding; Decoding; Encoding; Equations; Indexes; Materials; Mathematical model; Constrained code; elliptic integral; generating function; mutual recurrence; orthogonal polynomials; running digital sum;

fLanguage

English

Journal_Title

Information Theory, IEEE Transactions on

Publisher

ieee

ISSN

0018-9448

Type

jour

DOI

10.1109/TIT.2011.2145490

Filename

5895073