Title :
Improved quantum hypergraph-product LDPC codes
Author :
Kovalev, A.A. ; Pryadko, L.P.
Author_Institution :
Dept. of Phys. & Astron., Univ. of California, Riveside, CA, USA
Abstract :
We suggest several techniques to improve the toric codes and the finite-rate generalized toric codes (quantum hypergraph-product codes) recently introduced by Tillich and Zémor. For the usual toric codes, we introduce the rotated lattices specified by two integer-valued periodicity vectors. These codes include the checkerboard codes, and the family of minimal single-qubit-encoding toric codes with block length n = t2 + (t+1)2 and distance d = 2t + 1, t = 1, 2, ... We also suggest several related algebraic constructions which increase the rate of the existing hypergraph-product codes by up to four times.
Keywords :
parity check codes; vectors; LDPC codes; algebraic constructions; checkerboard codes; finite-rate generalized toric codes; integer-valued periodicity vectors; quantum hypergraph-product; rotated lattices; Bismuth; Generators; Lattices; Parity check codes; Polynomials; Symmetric matrices; Vectors;
Conference_Titel :
Information Theory Proceedings (ISIT), 2012 IEEE International Symposium on
Conference_Location :
Cambridge, MA
Print_ISBN :
978-1-4673-2580-6
Electronic_ISBN :
2157-8095
DOI :
10.1109/ISIT.2012.6284206
