Quantum LDPC codes from balanced incomplete block designs

Ivan B. Djordjevic

doi:10.1109/LCOMM.2008.080083

Quantum LDPC codes from balanced incomplete block designs

Ivan B. Djordjevic

Research output: Contribution to journal › Article › peer-review

57 Scopus citations

Abstract

We present a series of structured LDPC codes suitable for use in quantum error correction. Those codes belong to the class of dual-containing Calderbank-Shor-Steane (CSS) codes. The component CSS code is designed using the combinatorial object known as balanced incomplete block design (BIBD) with an even index. The quantum LDPC codes have the rate around 0.9. Several examples of quantum LDPC codes from BIBDs from unity index, extended by addition of an allones column, are introduced as well. To improve the BER performance, we employed the method of removing the cycles of length four in corresponding bipartite graph.

Original language	English (US)
Pages (from-to)	389-391
Number of pages	3
Journal	IEEE Communications Letters
Volume	12
Issue number	5
DOIs	https://doi.org/10.1109/LCOMM.2008.080083
State	Published - May 2008

Keywords

Calderbank-Shor-Steane codes
Low-density parity-check (LDPC) codes
Quantum error-correction

ASJC Scopus subject areas

Modeling and Simulation
Computer Science Applications
Electrical and Electronic Engineering

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10.1109/LCOMM.2008.080083

Cite this

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title = "Quantum LDPC codes from balanced incomplete block designs",

abstract = "We present a series of structured LDPC codes suitable for use in quantum error correction. Those codes belong to the class of dual-containing Calderbank-Shor-Steane (CSS) codes. The component CSS code is designed using the combinatorial object known as balanced incomplete block design (BIBD) with an even index. The quantum LDPC codes have the rate around 0.9. Several examples of quantum LDPC codes from BIBDs from unity index, extended by addition of an allones column, are introduced as well. To improve the BER performance, we employed the method of removing the cycles of length four in corresponding bipartite graph.",

keywords = "Calderbank-Shor-Steane codes, Low-density parity-check (LDPC) codes, Quantum error-correction",

author = "Djordjevic, {Ivan B.}",

note = "Funding Information: Manuscript received January 18, 2008. The associate editor coordinating the review of this letter and approving it for publication was V. Stankovic. This work is supported by the National Science Foundation under Grant IHCS-0725405.",

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AU - Djordjevic, Ivan B.

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N2 - We present a series of structured LDPC codes suitable for use in quantum error correction. Those codes belong to the class of dual-containing Calderbank-Shor-Steane (CSS) codes. The component CSS code is designed using the combinatorial object known as balanced incomplete block design (BIBD) with an even index. The quantum LDPC codes have the rate around 0.9. Several examples of quantum LDPC codes from BIBDs from unity index, extended by addition of an allones column, are introduced as well. To improve the BER performance, we employed the method of removing the cycles of length four in corresponding bipartite graph.

AB - We present a series of structured LDPC codes suitable for use in quantum error correction. Those codes belong to the class of dual-containing Calderbank-Shor-Steane (CSS) codes. The component CSS code is designed using the combinatorial object known as balanced incomplete block design (BIBD) with an even index. The quantum LDPC codes have the rate around 0.9. Several examples of quantum LDPC codes from BIBDs from unity index, extended by addition of an allones column, are introduced as well. To improve the BER performance, we employed the method of removing the cycles of length four in corresponding bipartite graph.

KW - Calderbank-Shor-Steane codes

KW - Low-density parity-check (LDPC) codes

KW - Quantum error-correction

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Quantum LDPC codes from balanced incomplete block designs

Abstract

Keywords

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