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Locally repairable codes from combinatorial designs

Science China(Information Sciences) 2020年第2期63卷 174-188页

作者： Yu ZHANG Haibin KAN Shanghai Key Laboratory of Intelligent Information Processing School of Computer ScienceFudan University Fudan-Zhongan Joint Laboratory of Blockchain and Information Security Shanghai Engineering Research Center of Blockchain Shanghai Institute for Advanced Communication and Data Science

Locally repairable codes（LRCs） were proposed to reduce the repair degree in distributed storage systems. In particular, LRCs with availability are highly desirable for distributed storage systems, since this kind of codes provide the mechanism of local repair for code symbols and parallel reading of hot data.In this paper, we propose four types of（n, k, r, t）;LRCs from combinatorial designs. We introduce several constructions of LRCs with strict availability and some constructions of distance-optimal LRCs with information-symbol locality. Most of our constructions in this paper are over F;, i.e., they are suitable for implementation.

关键词： locally repairable codes erasure codes combinatorial designs distributed storage systems codes with availability

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Half Rate Quasi Cyclic Low Density Parity Check Codes Based on combinatorial designs

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Journal of Computer and Communications 2016年第12期4卷 39-49页

作者： Sina Vafi Narges Rezvani Majid School of Engineering and Information Technology Charles Darwin University Darwin Australia

This paper presents new half rate Quasi Cyclic Low Density Parity Check (QC- LDPC) codes formed on the basis of combinatorial designs. In these codes, circulant matrices of the parity check matrix are formed on the basis of subsets in which the difference between any two elements of a subset is unique with all differences obtained from the same or different subsets. This structure of circulant matrices guarantees non-existence of cycle-4 in the Tanner graph of QC-LDPC codes. First, an irregular code with girth 6 constituted by two rows of circulant matrices is proposed. Then, more criteria will be considered on the structure of subsets with the mentioned feature aiming to represent a new scheme of regular QC-LPDC codes with girth at least 8. From simulations, it is confirmed that codes have similar to or better performance than other well-known half rate codes, while require lower complexity in their design.

关键词： Quasi-Cyclic LDPC Codes combinatorial designs Circulant Matrix

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A Novel Least-Entanglement-Assisted Asymmetric Quantum Codes Based on Sliding Grill

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Chinese Journal of Electronics 2014年第3期23卷 569-573页

作者： CAO Dong SONG Yaoliang ZHU Cheng School of Electronic Engineering and Optoelectronic Technology Nanjing University of Science and Technology College of Telecommunications and Information Engineering Nanjing University of Posts and Telecommunications

We propose new methods for constructing novel entanglement-assisted asymmetric quantum codes based on combinatorial designs and sliding grill. Based on a special case of combinatorial designs, our proposed method can construct a type of parity check matrix with greater column weight and better decoding performance. Combined with the characteristic of asymmetric quantum channel, we propose new method of sliding grill. Mother matrix and submatrix can be constructed. The null space of the parity-check matrix gives entanglement-assisted asymmetric quantum code. Tanner graph of the code has a girth of at least 6. Our proposed quantum code has higher code rate with the same error correction capability. These families of entanglement-assisted asymmetric quantum codes consume only one copy of maximally entangled state(ebit),and outperform other quantum codes based on similar construction method according to our numerical computation.

关键词： Quantum error-correcting codes Entanglement-assisted quantum codes combinatorial designs

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