Extended Single Parity Check Product Codes that Achieve Close-to-Capacity Performance in High Coding Rate

2010 ◽  
Vol E93-A (9) ◽  
pp. 1693-1696
Author(s):  
Akira SHIOZAKI ◽  
Masashi KISHIMOTO ◽  
Genmon MARUOKA
Keyword(s):  
Parity Check ◽  
Product Codes ◽  
Capacity Performance

Close-to-capacity performance of extended single parity check product codes

2011 ◽  
Vol 47 (1) ◽  
pp. 34 ◽  
Author(s):  
A. Shiozaki ◽  
M. Kishimoto ◽  
G. Maruoka
Keyword(s):  
Parity Check ◽  
Product Codes ◽  
Capacity Performance

scholarly journals Degenerate Quantum LDPC Codes With Good Finite Length Performance

Quantum ◽  
2021 ◽  
Vol 5 ◽  
pp. 585
Author(s):  
Pavel Panteleev ◽  
Gleb Kalachev
Keyword(s):  
Minimum Distance ◽  
Belief Propagation ◽  
Fault Tolerant ◽  
Large Family ◽  
Parity Check ◽  
Product Codes ◽  
Medium Length ◽  
Surface Code ◽  
Depolarizing Channel ◽  
Better Than

We study the performance of medium-length quantum LDPC (QLDPC) codes in the depolarizing channel. Only degenerate codes with the maximal stabilizer weight much smaller than their minimum distance are considered. It is shown that with the help of OSD-like post-processing the performance of the standard belief propagation (BP) decoder on many QLDPC codes can be improved by several orders of magnitude. Using this new BP-OSD decoder we study the performance of several known classes of degenerate QLDPC codes including hypergraph product codes, hyperbicycle codes, homological product codes, and Haah's cubic codes. We also construct several interesting examples of short generalized bicycle codes. Some of them have an additional property that their syndromes are protected by small BCH codes, which may be useful for the fault-tolerant syndrome measurement. We also propose a new large family of QLDPC codes that contains the class of hypergraph product codes, where one of the used parity-check matrices is square. It is shown that in some cases such codes have better performance than hypergraph product codes. Finally, we demonstrate that the performance of the proposed BP-OSD decoder for some of the constructed codes is better than for a relatively large surface code decoded by a near-optimal decoder.

scholarly journals Parallel and Serial Concatenated Single Parity Check Product Codes

2005 ◽  
Vol 2005 (6) ◽  
Author(s):  
David M. Rankin ◽  
T. Aaron Gulliver ◽  
Desmond P. Taylor
Keyword(s):  
Parity Check ◽  
Product Codes

Single parity check product codes

2001 ◽  
Vol 49 (8) ◽  
pp. 1354-1362 ◽  
Author(s):  
D.M. Rankin ◽  
T.A. Gulliver
Keyword(s):  
Parity Check ◽  
Product Codes

A Class of Low-Density Parity-Check Product Codes

2009 ◽  
Author(s):  
Marco Baldi ◽  
Giovanni Cancellieri ◽  
Franco Chiaraluce
Keyword(s):  
Low Density ◽  
Parity Check ◽  
Product Codes ◽  
Low Density Parity Check
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