A unified form of exact-MSR codes via product-matrix frameworks

Regenerating codes represent a class of block codes applicable for distributed storage systems. The [n, k, d] regenerating code has data recovery capability while possessing arbitrary k out of n code fragments, and supports the capability for code fragment regeneration through the use of other arbitrary d fragments, for k ≤ d ≤ n - 1. Minimum storage regenerating (MSR) codes are a subset of regenerating codes containing the minimal size of each code fragment. The first explicit construction of MSR codes that can perform exact regeneration (named exact-MSR codes) for d ≥ 2k - 2 has been presented via a product-matrix framework. This paper addresses some of the practical issues on the construction of exact-MSR codes. The major contributions of this paper include as follows. A new product-matrix framework is proposed to directly include all feasible exact-MSR codes for d ≥ 2k - 2. The mechanism for a systematic version of exact-MSR code is proposed to minimize the computational complexities for the process of message-symbol remapping. Two practical forms of encoding matrices are presented to reduce the size of the finite field.

Sian-Jheng Lin, Wei-Ho Chung, Han, Y. S., & Al-Naffouri, T. Y. (2015). A Unified Form of Exact-MSR Codes via Product-Matrix Frameworks. IEEE Transactions on Information Theory, 61(2), 873–886. doi:10.1109/tit.2014.2378255

This work was supported by the Ministry of Science and Technology, Taiwan, under Grants NSC 102-2221-E-001-006-MY2, MOST 103-3113-E-110-002, and NSC 101-2221-E-011-069-MY3. Part of this work was presented at the 2013 IEEE 24th Annual International Symposium on Personal, Indoor, and Mobile Radio Communications (PIMRC 2013).

Institute of Electrical and Electronics Engineers (IEEE)

IEEE Transactions on Information Theory


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