Fast Weighted Bit-Flipping Decoding of Finite-Geometry LDPC Codes

On the Stopping Distance and Stopping Redundancy of Finite Geometry LDPC Codes

IEICE Transactions on Fundamentals of Electronics Communications and Computer Sciences ◽

10.1093/ietfec/e91-a.8.2159 ◽

2008 ◽

Vol E91-A (8) ◽

pp. 2159-2166 ◽

Cited By ~ 3

Author(s):

H.-y. LIU ◽

X.-y. LIN ◽

L.-r. MA ◽

J. CHEN

Keyword(s):

Ldpc Codes ◽

Finite Geometry ◽

Stopping Distance

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A Decoding Algorithm for Finite-Geometry LDPC Codes

IEEE Transactions on Communications ◽

10.1109/tcomm.2004.841964 ◽

2005 ◽

Vol 53 (2) ◽

pp. 380-380

Keyword(s):

Ldpc Codes ◽

Finite Geometry ◽

Decoding Algorithm

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On the stopping distance of finite geometry ldpc codes

IEEE Communications Letters ◽

10.1109/lcomm.2006.1633330 ◽

2006 ◽

Vol 10 (5) ◽

pp. 381-383 ◽

Cited By ~ 20

Author(s):

Shu-Tao Xia ◽

Fang-Wei Fu

Keyword(s):

Ldpc Codes ◽

Finite Geometry ◽

Stopping Distance

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Concatenated finite geometry and finite field LDPC codes

2017 11th International Conference on Signal Processing and Communication Systems (ICSPCS) ◽

10.1109/icspcs.2017.8270513 ◽

2017 ◽

Cited By ~ 1

Author(s):

Mona Nasseri ◽

Xin Xiao ◽

Shaoliang Zhang ◽

Ting Wang ◽

Shu Lin

Keyword(s):

Finite Field ◽

Ldpc Codes ◽

Finite Geometry

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Asymmetric quantum codes: constructions, bounds and performance

Proceedings of The Royal Society A Mathematical Physical and Engineering Sciences ◽

10.1098/rspa.2008.0439 ◽

2009 ◽

Vol 465 (2105) ◽

pp. 1645-1672 ◽

Cited By ~ 57

Author(s):

Pradeep Kiran Sarvepalli ◽

Andreas Klappenecker ◽

Martin Rötteler

Keyword(s):

Ldpc Codes ◽

Finite Geometry ◽

Explicit Construction ◽

Error Correcting Codes ◽

Quantum Codes ◽

Asymmetric Quantum ◽

Asymmetric Quantum Codes ◽

Central Result ◽

And Performance ◽

Css Construction

Recently, quantum error-correcting codes have been proposed that capitalize on the fact that many physical error models lead to a significant asymmetry between the probabilities for bit- and phase-flip errors. An example for a channel that exhibits such asymmetry is the combined amplitude damping and dephasing channel, where the probabilities of bit and phase flips can be related to relaxation and dephasing time, respectively. We study asymmetric quantum codes that are obtained from the Calderbank–Shor–Steane (CSS) construction. For such codes, we derive upper bounds on the code parameters using linear programming. A central result of this paper is the explicit construction of some new families of asymmetric quantum stabilizer codes from pairs of nested classical codes. For instance, we derive asymmetric codes using a combination of Bose–Chaudhuri–Hocquenghem (BCH) and finite geometry low-density parity-check (LDPC) codes. We show that the asymmetric quantum codes offer two advantages, namely to allow a higher rate without sacrificing performance when compared with symmetric codes and vice versa to allow a higher performance when compared with symmetric codes of comparable rates. Our approach is based on a CSS construction that combines BCH and finite geometry LDPC codes.

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