Title :
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
Abstract :
This paper presents a new class of easily invertible circulant matrices, defined by exploiting the isomorphism from the ring Mn of n times n circulant matrices over GF(p) to the ring Rn = 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;
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
DOI :
10.1109/ISITA.2008.4895413
