Lower bounds on cross-correlation of codes

Author

Levenshtein, Vladimir

Author_Institution

Inst. of Appl. Math., Acad. of Sci., Moscow, Russia

Volume

2

fYear

1996

fDate

22-25 Sep 1996

Firstpage

657

Abstract

Codes with low cross-correlation are broadly used in code-division multiple-access (CDMA) communication systems. In this paper the best known lower bounds on the cross-correlation of real and complex codes of a given size obtained by the author in 1982 are investigated. For some range of parameters these bounds are strengthened. Their optimality in the framework of the linear programming method for polynomials of restricted degree is proved. New asymptotics, when the size of codes grows as a degree of length, are given. It is shown that the best known lower bounds on cross-correlation of binary and ν-ary codes (ν⩾3) have the same asymptotic behaviour as ones for real and complex codes respectively when the code rate tends to zero

Keywords

code division multiple access; codes; correlation methods; linear programming; polynomials; ν-ary codes; CDMA communication system; asymptotic behaviour; binary codes; code-division multiple-access; complex codes; cross-correlation; linear programming; lower bounds; optimality; polynomials; real codes; Jacobian matrices; Linear programming; Mathematics; Multiaccess communication; Polynomials; Upper bound;

fLanguage

English

Publisher

ieee

Conference_Titel

Spread Spectrum Techniques and Applications Proceedings, 1996., IEEE 4th International Symposium on

Conference_Location

Mainz

Print_ISBN

0-7803-3567-8

Type

conf

DOI

10.1109/ISSSTA.1996.563207

Filename

563207