A class of invertible circulant matrices for QC-LDPC codes

Author

Baldi, Marco ; Bambozzi, Federico ; Chiaraluce, Franco

Author_Institution

Dipt. di Ing. Biomedica, Univ. Politec. delle Marche, Ancona

fYear

2008

fDate

7-10 Dec. 2008

Firstpage

1

Lastpage

6

Abstract

This paper presents a new class of easily invertible circulant matrices, defined by exploiting the isomorphism from the ring M_n of n times n circulant matrices over GF(p) to the ring R_n = GF(p)[x]/(xⁿ - 1) of the polynomials modulo (xⁿ - 1). Such class contains matrices free of 4-length cycles that, if sparse, can be included in the parity check matrix of QC-LDPC codes. Bounds for the weight of their inverses are also determined, that are useful for designing sparse generator matrices for these error correcting codes.

Keywords

cyclic codes; error correction codes; matrix inversion; parity check codes; polynomial matrices; sparse matrices; QC-LDPC code; error correcting code; inverse matrices; invertible circulant matrices; polynomial modulo; quasi-cyclic low-density parity-check; sparse generator matrices; Encoding; Error correction codes; Galois fields; Information theory; Iterative decoding; Parity check codes; Quantum cascade lasers; Shift registers; Sparse matrices; Telecommunications;

fLanguage

English

Publisher

ieee

Conference_Titel

Information Theory and Its Applications, 2008. ISITA 2008. International Symposium on

Conference_Location

Auckland

Print_ISBN

978-1-4244-2068-1

Electronic_ISBN

978-1-4244-2069-8

Type

conf

DOI

10.1109/ISITA.2008.4895413

Filename

4895413