Title :
A Class of Quantum LDPC Codes Constructed From Finite Geometries
Author_Institution :
Dept. of Comput. Sci., Texas A&M Univ., College Station, TX
Abstract :
Low-density parity check (LDPC) codes are a significant class of classical codes with many applications. Several good LDPC codes have been constructed using random, algebraic, and finite geometries approaches, with containing cycles of length at least six in their Tanner graphs. However, it is impossible to design a self-orthogonal parity check matrix of an LDPC code without introducing cycles of length four. In this paper, a new class of quantum LDPC codes based on lines and points of finite geometries is constructed. The parity check matrices of these codes are adapted to be self- orthogonal with containing only one cycle of length four in each pair of two rows. Also, the column and row weights, and bounds on the minimum distance of these codes are given. As a consequence, these codes can be encoded using shift-register encoding algorithms and can be decoded using iterative decoding algorithms over various quantum depolarizing channels.
Keywords :
channel coding; geometric codes; iterative decoding; matrix algebra; parity check codes; quantum communication; finite geometries; iterative decoding algorithm; low-density parity check codes; quantum LDPC code construction; quantum depolarizing channels; self-orthogonal parity check matrix; shift-register encoding algorithms; Application software; Computational geometry; Computer science; Galois fields; Iterative algorithms; Iterative decoding; Parity check codes; Quantum computing; Sparse matrices; Turbo codes;
Conference_Titel :
Global Telecommunications Conference, 2008. IEEE GLOBECOM 2008. IEEE
Conference_Location :
New Orleans, LO
Print_ISBN :
978-1-4244-2324-8
DOI :
10.1109/GLOCOM.2008.ECP.217